maths essay topic

260 Interesting Math Topics for Essays & Research Papers

Mathematics is the science of numbers and shapes. Writing about it can give you a fresh perspective and help to clarify difficult concepts. You can even use mathematical writing as a tool in problem-solving.

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In this article, you will find plenty of interesting math topics. Besides, you will learn about branches of mathematics that you can choose from. And if the thought of letters and numbers makes your head swim, try our custom writing service . Our professionals will craft a paper for you in no time!

And now, let’s proceed to math essay topics and tips.

🔝 Top 10 Interesting Math Topics

✅ branches of mathematics, ✨ fun math topics.

• 🏫 Math Topics for High School
• 🎓 College Math Topics
• 🤔 Advanced Math
• 📚 Math Research
• ✏️ Math Education
• 💵 Business Math

🔍 References

• Number theory in everyday life.
• Logicist definitions of mathematics.
• Multivariable vs. vector calculus.
• 4 conditions of functional analysis.
• Random variable in probability theory.
• How is math used in cryptography?
• The purpose of homological algebra.
• Concave vs. convex in geometry.
• The philosophical problem of foundations.
• Is numerical analysis useful for machine learning?

What exactly is mathematics ? First and foremost, it is very old. Ancient Greeks and Persians were already utilizing mathematical tools. Nowadays, we consider it an interdisciplinary language.

Biologists, linguists, and sociologists alike use math in their work. And not only that, we all deal with it in our daily lives. For instance, it manifests in the measurement of time. We often need it to calculate how much our groceries cost and how much paint we need to buy to cover a wall.

Simply put, mathematics is a universal instrument for problem-solving. We can divide pure math into three branches: geometry, arithmetic, and algebra. Let’s take a closer look:

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• Geometry By studying geometry, we try to comprehend our physical surroundings. Geometric shapes can be simple, like a triangle. Or, they can form complicated figures, like a rhombicosidodecahedron.
• Arithmetic Arithmetic deals with numbers and simple operations: subtraction, addition, division, and multiplication.
• Algebra Algebra is used when the exact numbers are unclear. Instead, they are replaced with letters. Businesses often need algebra to predict their sales.

It’s true that most high school students don’t like math. However, that doesn’t mean it can’t be a fun and compelling subject. In the following section, you will find plenty of enthralling mathematical topics for your paper.

If you’re struggling to start working on your essay, we have some fun and cool math topics to offer. They will definitely engage you and make the writing process enjoyable. Besides, fun math topics can show everyone that even math can be entertaining or even a bit silly.

• The link between mathematics and art – analyzing the Golden Ratio in Renaissance-era paintings.
• An evaluation of Georg Cantor’s set theory.
• The best approaches to learning math facts and developing number sense.
• Different approaches to probability as explored through analyzing card tricks.
• Chess and checkers – the use of mathematics in recreational activities.
• The five types of math used in computer science .
• Real-life applications of the Pythagorean Theorem .
• A study of the different theories of mathematical logic .
• The use of game theory in social science.
• Mathematical definitions of infinity and how to measure it.
• What is the logic behind unsolvable math problems?
• An explanation of mean, mode, and median using classroom math grades.
• The properties and geometry of a Möbius strip.
• Using truth tables to present the logical validity of a propositional expression.
• The relationship between Pascal’s Triangle and The Binomial Theorem.
• The use of different number types: the history.
• The application of differential geometry in modern architecture.
• A mathematical approach to the solution of a Rubik’s Cube.
• Comparison of predictive and prescriptive statistical analyses.
• Explaining the iterations of the Koch snowflake.
• The importance of limits in calculus.
• Hexagons as the most balanced shape in the universe.
• The emergence of patterns in chaos theory.
• What were Euclid’s contributions to the field of mathematics?
• The difference between universal algebra and abstract algebra.

🏫 Math Essay Topics for High School

When writing a math paper, you want to demonstrate that you understand a concept. It can be helpful if you need to prepare for an exam. Choose a topic from this section and decide what you want to discuss.

• Explain what we need Pythagoras’ theorem for. 
• What is a hyperbola? 
• Describe the difference between algebra and arithmetic. 
• When is it unnecessary to use a calculator ? 
• Find a connection between math and the arts. 
• How do you solve a linear equation? 
• Discuss how to determine the probability of rolling two dice. 
• Is there a link between philosophy and math? 
• What types of math do you use in your everyday life? 
• What is the numerical data? 
• Explain how to use the binomial theorem. 
• What is the distributive property of multiplication? 
• Discuss the major concepts in ancient Egyptian mathematics . 
• Why do so many students dislike math? 
• Should math be required in school? 
• How do you do an equivalent transformation? 
• Why do we need imaginary numbers? 
• How can you calculate the slope of a curve? 
• What is the difference between sine, cosine, and tangent? 
• How do you define the cross product of two vectors? 
• What do we use differential equations for? 
• Investigate how to calculate the mean value. 
• Define linear growth. 
• Give examples of different number types. 
• How can you solve a matrix? 

🎓 College Math Topics for a Paper

Sometimes you need more than just formulas to explain a complex idea. That’s why knowing how to express yourself is crucial. It is especially true for college-level mathematics. Consider the following ideas for your next research project:

• What do we need n-dimensional spaces for?
• Explain how card counting works.
• Discuss the difference between a discrete and a continuous probability distribution .
• How does encryption work?
• Describe extremal problems in discrete geometry.
• What can make a math problem unsolvable?
• Examine the topology of a Möbius strip.

• What is K-theory?  
• Discuss the core problems of computational geometry. 
• Explain the use of set theory . 
• What do we need Boolean functions for? 
• Describe the main topological concepts in modern mathematics. 
• Investigate the properties of a rotation matrix. 
• Analyze the practical applications of game theory.  
• How can you solve a Rubik’s cube mathematically? 
• Explain the math behind the Koch snowflake. 
• Describe the paradox of Gabriel’s Horn. 
• How do fractals form? 
• Find a way to solve Sudoku using math. 
• Why is the Riemann hypothesis still unsolved? 
• Discuss the Millennium Prize Problems. 
• How can you divide complex numbers? 
• Analyze the degrees in polynomial functions. 
• What are the most important concepts in number theory? 
• Compare the different types of statistical methods . 

🤔 Advanced Topics in Math to Write a Paper on

Once you have passed the trials of basic math, you can move on to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the list below for enticing topics to write about:

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• What is an abelian group?
• Explain the orbit-stabilizer theorem.
• Discuss what makes the Burnside problem influential.
• What fundamental properties do holomorphic functions have?
• How does Cauchy’s integral theorem lead to Cauchy’s integral formula?
• How do the two Picard theorems relate to each other?
• When is a trigonometric series called a Fourier series?
• Give an example of an algorithm used for machine learning .
• Compare the different types of knapsack problems.
• What is the minimum overlap problem?
• Describe the Bernoulli scheme.
• Give a formal definition of the Chinese restaurant process.
• Discuss the logistic map in relation to chaos .
• What do we need the Feigenbaum constants for?
• Define a difference equation.
• Explain the uses of the Fibonacci sequence.
• What is an oblivious transfer?
• Compare the Riemann and the Ruelle zeta functions.
• How can you use elementary embeddings in model theory?
• Analyze the problem with the wholeness axiom and Kunen’s inconsistency theorem.
• How is Lie algebra used in physics ?
• Define various cases of algebraic cycles.
• Why do we need étale cohomology groups to calculate algebraic curves?
• What does non-Euclidean geometry consist of?
• How can two lines be ultraparallel?

📚 Math Research Topics for a Paper

Choosing the right topic is crucial for a successful research paper in math. It should be hard enough to be compelling, but not exceeding your level of competence. If possible, stick to your area of knowledge. This way your task will become more manageable. Here are some ideas:

• Write about the history of calculus.
• Why are unsolved math problems significant?
• Find reasons for the gender gap in math students.
• What are the toughest mathematical questions asked today?
• Examine the notion of operator spaces.
• How can we design a train schedule for a whole country?
• What makes a number big?

• How can infinities have various sizes?
• What is the best mathematical strategy to win a game of Go?
• Analyze natural occurrences of random walks in biology.
• Explain what kind of mathematics was used in ancient Persia.
• Discuss how the Iwasawa theory relates to modular forms.
• What role do prime numbers play in encryption ?
• How did the study of mathematics evolve?
• Investigate the different Tower of Hanoi solutions.
• Research Napier’s bones. How can you use them?
• What is the best mathematical way to find someone who is lost in a maze?
• Examine the Traveling Salesman Problem. Can you find a new strategy?
• Describe how barcodes function.
• Study some real-life examples of chaos theory. How do you define them mathematically?
• Compare the impact of various ground-breaking mathematical equations .
• Research the Seven Bridges of Königsberg. Relate the problem to the city of your choice.
• Discuss Fisher’s fundamental theorem of natural selection.
• How does quantum computing work?
• Pick an unsolved math problem and say what makes it so difficult.

✏️ Math Education Research Topics

For many teachers, the hardest part is to keep the students interested. When it comes to math, it can be especially challenging. It’s crucial to make complicated concepts easy to understand. That’s why we need research on math education.

• Compare traditional methods of teaching math with unconventional ones.
• How can you improve mathematical education in the U.S.?
• Describe ways of encouraging girls to pursue careers in STEM fields.
• Should computer programming be taught in high school?
• Define the goals of mathematics education .
• Research how to make math more accessible to students with learning disabilities .
• At what age should children begin to practice simple equations?
• Investigate the effectiveness of gamification in algebra classes.
• What do students gain from taking part in mathematics competitions?
• What are the benefits of moving away from standardized testing ?
• Describe the causes of “ math anxiety .” How can you overcome it?
• Explain the social and political relevance of mathematics education.
• Define the most significant issues in public school math teaching.
• What is the best way to get children interested in geometry?
• How can students hone their mathematical thinking outside the classroom?
• Discuss the benefits of using technology in math class.
• In what way does culture influence your mathematical education?
• Explore the history of teaching algebra .
• Compare math education in various countries.

• How does dyscalculia affect a student’s daily life?
• Into which school subjects can math be integrated?
• Has a mathematics degree increased in value over the last few years?
• What are the disadvantages of the Common Core Standards ?
• What are the advantages of following an integrated curriculum in math?
• Discuss the benefits of Mathcamp.

🧮 Algebra Topics for a Paper

The elegance of algebra stems from its simplicity. It gives us the ability to express complex problems in short equations. The world was changed forever when Einstein wrote down the simple formula E=mc². Now, if your algebra seminar requires you to write a paper, look no further! Here are some brilliant prompts:

• Give an example of an induction proof.
• What are F-algebras used for?
• What are number problems?
• Show the importance of abstract algebraic thinking .
• Investigate the peculiarities of Fermat’s last theorem.
• What are the essentials of Boolean algebra?
• Explore the relationship between algebra and geometry.
• Compare the differences between commutative and noncommutative algebra.
• Why is Brun’s constant relevant?
• How do you factor quadratics?
• Explain Descartes’ Rule of Signs.
• What is the quadratic formula?
• Compare the four types of sequences and define them.
• Explain how partial fractions work.
• What are logarithms used for?
• Describe the Gaussian elimination.
• What does Cramer’s rule state?
• Explore the difference between eigenvectors and eigenvalues.
• Analyze the Gram-Schmidt process in two dimensions.
• Explain what is meant by “range” and “domain” in algebra.
• What can you do with determinants?
• Learn about the origin of the distance formula.
• Find the best way to solve math word problems.
• Compare the relationships between different systems of equations.
• Explore how the Rubik’s cube relates to group theory .

📏 Geometry Topics for a Research Paper

Shapes and space are the two staples of geometry. Since its appearance in ancient times, it has evolved into a major field of study. Geometry’s most recent addition, topology, explores what happens to an object if you stretch, shrink, and fold it. Things can get pretty crazy from here! The following list contains 25 interesting geometry topics:

• What are the Archimedean solids? 
• Find real-life uses for a rhombicosidodecahedron. 
• What is studied in projective geometry? 
• Compare the most common types of transformations. 
• Explain how acute square triangulation works. 
• Discuss the Borromean ring configuration. 
• Investigate the solutions to Buffon’s needle problem. 
• What is unique about right triangles? 

• Describe the notion of Dirac manifolds.
• Compare the various relationships between lines.
• What is the Klein bottle?
• How does geometry translate into other disciplines, such as chemistry and physics?
• Explore Riemannian manifolds in Euclidean space.
• How can you prove the angle bisector theorem?
• Do a research on M.C. Escher’s use of geometry.
• Find applications for the golden ratio .
• Describe the importance of circles.
• Investigate what the ancient Greeks knew about geometry.
• What does congruency mean?
• Study the uses of Euler’s formula.
• How do CT scans relate to geometry?
• Why do we need n-dimensional vectors?
• How can you solve Heesch’s problem?
• What are hypercubes?
• Analyze the use of geometry in Picasso’s paintings.

➗ Calculus Topics to Write a Paper on

You can describe calculus as a more complicated algebra. It’s a study of change over time that provides useful insights into everyday problems. Applied calculus is required in a variety of fields such as sociology, engineering, or business. Consult this list of compelling topics on a calculus paper:

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• What are the differences between trigonometry, algebra, and calculus?
• Explain the concept of limits.
• Describe the standard formulas needed for derivatives.
• How can you find critical points in a graph?
• Evaluate the application of L’Hôpital’s rule.
• How do you define the area between curves?
• What is the foundation of calculus?

• How does multivariate calculus work?
• Discuss the use of Stokes’ theorem.
• What does Leibniz’s integral rule state?
• What is the Itô stochastic integral?
• Explore the influence of nonstandard analysis on probability theory.
• Research the origins of calculus.
• Who was Maria Gaetana Agnesi?
• Define a continuous function.
• What is the fundamental theorem of calculus?
• How do you calculate the Taylor series of a function?
• Discuss the ways to resolve Runge’s phenomenon.
• Explain the extreme value theorem.
• What do we need predicate calculus for?
• What are linear approximations?
• When does an integral become improper?
• Describe the Ratio and Root Tests.
• How does the method of rings work?
• Where do we apply calculus in real-life situations?

💵 Business Math Topics to Write About

You don’t have to own a company to appreciate business math. Its topics range from credits and loans to insurance, taxes, and investment. Even if you’re not a mathematician, you can use it to handle your finances. Sounds interesting? Then have a look at the following list:

• What are the essential skills needed for business math?
• How do you calculate interest rates?
• Compare business and consumer math.
• What is a discount factor?
• How do you know that an investment is reasonable?
• When does it make sense to pay a loan with another loan?
• Find useful financing techniques that everyone can use.
• How does critical path analysis work?
• Explain how loans work.
• Which areas of work utilize operations research?
• How do businesses use statistics?
• What is the economic lot scheduling problem?
• Compare the uses of different chart types.
• What causes a stock market crash?
• How can you calculate the net present value?
• Explore the history of revenue management .
• When do you use multi-period models?
• Explain the consequences of depreciation.
• Are annuities a good investment?
• Would the U.S. financially benefit from discontinuing the penny?
• What caused the United States housing crash in 2008?
• How do you calculate sales tax?
• Describe the notions of markups and markdowns.
• Investigate the math behind debt amortization.
• What is the difference between a loan and a mortgage?

With all these ideas, you are perfectly equipped for your next math paper. Good luck!

• What Is Calculus?: Southern State Community College
• What Is Mathematics?: Tennessee Tech University
• What Is Geometry?: University of Waterloo
• What Is Algebra?: BBC
• Ten Simple Rules for Mathematical Writing: Ohio State University
• Practical Algebra Lessons: Purplemath
• Topics in Geometry: Massachusetts Institute of Technology
• The Geometry Junkyard: All Topics: Donald Bren School of Information and Computer Sciences
• Calculus I: Lamar University
• Business Math for Financial Management: The Balance Small Business
• What Is Mathematics: Life Science
• What Is Mathematics Education?: University of California, Berkeley
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25 Interesting Math Topics: How to Write a Good Math Essay

writing good math essay

Mathematics is a fascinating world of numbers, shapes, and patterns. 

Whether you are a student looking to grasp math concepts or someone who finds math intriguing, these topics will spark your curiosity and help you discover the beauty of mathematics straightforwardly and engagingly.

In this article, I will explore interesting math topics that make this subject not only understandable but also enjoyable.

Why Write About Mathematics

First, it helps demystify a subject that many find intimidating. By breaking down complex mathematical concepts into simple, understandable language, we can make math accessible to a wider audience, fostering greater understanding and appreciation.

Second, writing about mathematics allows us to showcase the practical applications of math in everyday life, from managing personal finances to solving real-world problems.

This helps readers recognize the relevance of math and its role in various fields and industries.

Additionally, writing about mathematics can inspire curiosity and a love for learning.

It encourages critical thinking and problem-solving skills, promoting intellectual growth and academic success.

Finally, mathematics is a universal language that transcends cultural and linguistic barriers.

After discussing math topics, we can connect with a global audience, fostering a sense of unity and collaboration in the pursuit of knowledge

 25 Interesting Math Topics to Write On

 Mathematics is a vast and intriguing field, offering a multitude of interesting topics to explore and write about.

Here are 25 such topics that promise to engage both math enthusiasts and those seeking a deeper understanding of this fascinating subject.

1. Fibonacci Sequence: Delve into the mesmerizing world of numbers with this sequence, where each number is the sum of the two preceding ones.

2. Golden Ratio: Explore the ubiquity of the golden ratio in art, architecture, and nature.

3. Prime Numbers: Investigate the mysterious properties of prime numbers and their role in cryptography.

4. Chaos Theory: Understand the unpredictability of chaotic systems and how small changes can lead to drastically different outcomes.

5. Game Theory: Examine the strategies and decision-making processes behind games and real-world situations.

6. Cryptography: Uncover the mathematical principles behind secure communication and encryption.

7. Fractals: Discover the self-replicating geometric patterns that occur in nature and mathematics.

8. Probability Theory: Dive into the world of uncertainty and randomness, where math helps us make informed predictions.

9. Number Theory: Explore the properties and relationships of integers, including divisibility and congruence.

10. Geometry of Art: Analyze how geometry and math principles influence art and design.

11. Topology: Study the properties of space that remain unchanged under continuous transformations, leading to the concept of “rubber-sheet geometry.”

12. Knot Theory: Investigate the mathematical study of knots and their applications in various fields.

13. Number Systems: Learn about different number bases, such as binary and hexadecimal, and their significance in computer science.

14. Graph Theory: Explore networks, relationships, and the mathematics of connections.

15. The Monty Hall Problem: Delight in this famous probability puzzle based on a game show scenario.

16. Calculus: Examine the principles of differentiation and integration that underlie a wide range of scientific and engineering applications.

17. The Riemann Hypothesis: Consider one of the most famous unsolved problems in mathematics involving the distribution of prime numbers.

18. Euler’s Identity: Marvel at the beauty of Euler’s equation, often described as the most elegant mathematical formula.

19. The Four-Color Theorem: Uncover the fascinating problem of coloring maps with only four colors without adjacent regions sharing the same color.

20. P vs. NP Problem: Delve into one of the most critical unsolved problems in computer science, addressing the efficiency of algorithms.

21. The Bridges of Konigsberg: Explore a classic problem in graph theory that inspired the development of topology.

22. The Birthday Paradox: Understand the surprising likelihood of shared birthdays in a group.

23. Non-Euclidean Geometry: Step into the world of geometries where Euclid’s parallel postulate doesn’t hold, leading to intriguing alternatives like hyperbolic and elliptic geometry.

24. Perfect Numbers: Learn about the properties of numbers that are the sum of their proper divisors.

25. Zero: The History of Nothing: Trace the historical and mathematical significance of the number zero and its role in the development of mathematics.

How to Write a Good Math Essay

Mathematics essays , though often perceived as daunting, can be a rewarding way to delve into the world of mathematical concepts, problem-solving, and critical thinking.

Whether you are a student assigned to write a math essay or someone who wants to explore math topics in-depth, this guide will provide you with the key steps to write a good math essay that is clear, concise, and engaging.

1. Understanding the Essay Prompt

Before you begin writing, it’s crucial to understand the essay prompt or question.

Analyze the specific topic, the scope of the essay, and any guidelines or requirements provided by your instructor.

Mostly, this initial step sets the direction for your essay and ensures you stay on topic.

2. Research and Gather Information

You need to gather relevant information and resources to write a strong math essay. This includes textbooks, academic papers, and reputable websites.

Make sure to cite your sources properly using a recognized citation style such as APA, MLA, or Chicago.

3. Structuring Your Math Essay

Start with a clear introduction that provides an overview of the topic and the main thesis or argument of your essay. This section should capture the reader’s attention and present a roadmap for what to expect.

The body of your essay is where you present your arguments, explanations, and evidence. Use clear subheadings to organize your ideas. Ensure that your arguments are logical and well-structured.

Begin by defining any important mathematical concepts or terms necessary to understand your topic.

Clearly state your main arguments or theorems. Please support them with evidence, equations, diagrams, or examples.

Explain the logical steps or mathematical reasoning behind your arguments. This can include proofs, derivations, or calculations.

Ensure your writing is clear and free from jargon that might confuse the reader. Explain complex ideas in a way that’s accessible to a broader audience.

Whenever applicable, include diagrams, graphs, or visual aids to illustrate your points. Visual representations can enhance the clarity of your essay.

Summarize your main arguments, restate your thesis, and offer a concise conclusion. Address the significance of your findings and the implications of your research or discussion.

4. Proofreading and Editing

Once you’ve written your math essay, take the time to proofread and edit it. Pay attention to grammar, spelling, punctuation, and the overall flow of your writing.

Ensure that your essay is well-organized and free from errors.

Consider seeking feedback from peers or an instructor to gain a fresh perspective.

5. Presentation and Formatting

A well-presented essay is more likely to engage the reader. Follow these formatting guidelines:

• Use a legible font (e.g., Times New Roman or Arial) in a standard size (12-point).
• Double-space your essay and include page numbers if required.
• Create a title page with your name, essay title, course information, and date.
• Use section headings and subheadings for clarity.
• Include a reference page to cite your sources appropriately.

6. Mathematical Notation and Symbols

Mathematics relies heavily on notation and symbols. Ensure that you use mathematical notation correctly and consistently.

If you introduce new symbols or terminology, define them clearly for the reader’s understanding.

7. Seek Clarification

If you encounter difficulties or ambiguities in your math essay, don’t hesitate to seek clarification from your instructor or peers.

Discussing complex mathematical concepts with others can help you refine your understanding and improve your essay.

8. Practice and Feedback

Writing math essays, like any skill, improves with practice. The more you write and receive feedback, the better you’ll become.

Take your time with initial challenges. Instead, view them as opportunities for growth and learning.

With dedication and attention to detail, you can craft a math essay that not only conveys your mathematical knowledge but also engages and informs your readers.

Josh Jasen or JJ as we fondly call him, is a senior academic editor at Grade Bees in charge of the writing department. When not managing complex essays and academic writing tasks, Josh is busy advising students on how to pass assignments. In his spare time, he loves playing football or walking with his dog around the park.

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Mathematics Extended Essay Topics for IB

Table of contents

• Writing Metier

Ever felt the exhilaration that comes with cracking a complex math problem? That’s the sheer beauty of mathematics – it’s a world where numbers dance, patterns emerge, and solutions await the keen observer. Felt that? Hah?

Now, imagine channeling that same enthusiasm and zest into your Math Extended essay. It might sound like a challenge, but isn’t that what we thrive on? With the right Math EE topic, you can showcase your mathematical prowess and leave an indelible mark on your IB evaluators following the general criteria. 

To help you with that, I’ve curated a list of Math extended essay ideas that span the spectrum from the accessible to the intricate. 

So, let’s begin.

IB Math extended essay ideas

These aren’t just topics; they’re gateways to exploration, understanding, and innovation. 

Ready to get started?

Easy-to-approach topics

For those looking for a gentler introduction to the Math Extended essay, below is a list of 10 engaging and manageable IB Math EE topic ideas, each with a research question and a brief description on how to approach it:

Patterns in Pascal’s Triangle

Research Question: 

How do patterns emerge in Pascal’s Triangle?

Description: 

Begin with the construction of Pascal’s Triangle, then delve into the exploration of its patterns, such as triangular numbers and the Fibonacci sequence.

Mathematics of Voting Systems

How do different voting systems weigh individual votes mathematically?

Introduce various voting systems, then analyze the mathematical principles behind each, discussing fairness and potential biases.

Geometry in Art

Research Question:  

How is geometry used to create visual appeal in art?

Explore various art pieces, highlighting the geometric principles employed, and discuss their impact on aesthetics.

The Math Behind Baking

How do ratios in baking recipes affect the final product?

Investigate the importance of maintaining specific ratios in baking recipes and experiment with variations to observe changes in outcomes.

Probability in Card Games

How does understanding probability enhance success in card games like Poker?

Delve into the rules of Poker and then analyze various hands and scenarios using probability principles.

Symmetry in Nature

How is symmetry exhibited in natural formations?

Explore the concept of symmetry mathematically and then identify and analyze its presence in various natural formations like leaves, flowers, and animals.

Mathematics of Music

How do mathematical patterns influence musical scales and rhythms?

Investigate the structure of musical scales, rhythms, and time signatures, highlighting the underlying mathematical patterns.

Simple Interest vs. Compound Interest

How do simple and compound interest methods impact savings over time?

Define both interest methods and then use mathematical modeling to compare their effects on savings over various periods.

The Golden Ratio in Architecture

How is the Golden Ratio applied in iconic architectural designs?

Introduce the concept of the Golden Ratio and then analyze its application in various famous architectural structures.

Mathematics of Juggling

How do mathematical patterns and sequences dictate juggling techniques?

Explore basic juggling techniques and patterns, analyzing the mathematical sequences that jugglers use to maintain rhythm and control.

Each of these topic ideas and RQs is approachable yet offers ample scope for exploration and analysis within the realm of mathematics.

Intermediate topics

For those seeking a bit more challenge without diving into the deep end, the topics below offer a balanced blend of complexity and accessibility.

Here’s a list of 10 average-difficulty IB Math Extended essay topics, each with a research question and a brief description of how to approach it:

Game Theory in Economics

How does game theory provide insights into competitive market behaviors?

Introduce game theory principles and use business world case studies to show strategic decision-making influenced by game theory.

Fractals and Nature

How do fractal patterns manifest in natural phenomena?

Description:  

Delve into the mathematical concept of fractals and explore their appearance in various natural settings, such as coastlines, mountains, and plants.

Mathematics of Population Growth Models

How do mathematical models accurately predict population growth in urban areas?

Introduce population growth models and use real urban area data to validate these models, discussing influencing factors.

Cryptography and Internet Security

How do modern cryptographic techniques ensure data security on the internet?

Explore the evolution of cryptography, focusing on modern techniques, and discuss their role in ensuring data security in online transactions.

Mathematical Modeling of Epidemics

How can mathematical models predict the spread of infectious diseases?

Introduce basic epidemiological models and analyze their effectiveness in predicting disease spread using real-world data.

Topology and Coffee Cups

How does topology explain the mathematical similarity between a coffee cup and a donut?

Dive into the basics of topology and use it to explain the often-cited comparison between coffee cups and donuts, emphasizing the concept of homeomorphism.

Chaos Theory and Weather Forecasting

How does chaos theory impact the accuracy of long-term weather forecasts?

Introduce chaos theory, then delve into its application in meteorology, discussing the challenges and limitations in predicting weather.

Mathematics Behind Neural Networks

How do mathematical algorithms drive the functioning of neural networks in artificial intelligence?

Explore the structure of neural networks and delve into the mathematical algorithms that enable their learning and functioning.

Optimization Problems in Logistics

How can mathematical optimization improve efficiency in supply chain logistics?

Investigate real-world logistics challenges and demonstrate how mathematical optimization techniques can offer solutions.

Number Theory in Modern Cryptography

How does advanced number theory underpin modern cryptographic techniques?

Delve into number theory concepts and their application in modern cryptographic methods, emphasizing their role in ensuring data security.

These topics and research questions offer a balanced blend of complexity and accessibility, making them suitable for students seeking a moderate challenge in their Math Extended essay.

Advanced topics (with potential for higher rewards)

For the brave hearts ready to dive deep, these topics are challenging but can yield impressive results when tackled effectively.

The list of 10 challenging IB Math Extended essay ideas, each with a research question and a brief description:

Navier–Stokes Existence and Smoothness

What are the mathematical implications of the unsolved Navier–Stokes existence and smoothness problem in fluid dynamics?

Delve deep into the Navier–Stokes equations, exploring their significance in fluid dynamics and the challenges surrounding their unsolved problems.

Riemann Hypothesis and Prime Numbers

How does the Riemann Hypothesis relate to the distribution of prime numbers?

Investigate the Riemann Hypothesis, its historical context, and its profound implications for the distribution of prime numbers.

Quantum Cryptography and Key Distribution

How does quantum cryptography enhance security in key distribution?

Explore the principles of quantum mechanics applied to cryptography, focusing on the advantages and challenges of quantum key distribution.

Elliptic Curves and Cryptography

How do elliptic curves underpin modern cryptographic techniques?

Dive into the mathematics of elliptic curves and their pivotal role in modern cryptographic algorithms.

Four Color Theorem and Graph Theory

How does the Four Color Theorem demonstrate the complexities of graph coloring?

Investigate the history and proof of the Four Color Theorem, discussing its implications and challenges in graph theory.

Complex Analysis in Quantum Mechanics

How does complex analysis influence the mathematical foundations of quantum mechanics?

Delve into the principles of complex analysis and explore their applications and significance in quantum mechanics.

Twin Prime Conjecture

What are the implications and challenges of the Twin Prime Conjecture in number theory?

Investigate the Twin Prime Conjecture, its history, and its significance in the realm of number theory.

Knot Theory and DNA Replication

How does knot theory provide insights into the process of DNA replication?

Explore the mathematical intricacies of knot theory and its applications in understanding the complexities of DNA replication.

Ergodic Theory and Thermodynamics

How does ergodic theory connect with the principles of statistical thermodynamics?

Dive deep into ergodic theory, exploring its foundational concepts and its connections to statistical thermodynamics.

Langlands Program and Number Theory

What is the Langlands Program, and how does it seek to unify different areas of mathematics?

Investigate the Langlands Program, its objectives, and its profound implications in unifying disparate areas of mathematics, particularly number theory.

These topics are undoubtedly challenging but can yield impressive results when tackled effectively. They offer a deep dive into complex mathematical concepts and theories, making them ideal for students aiming for the highest grades in their Math Extended essay.

Get extended essay help

Before continuing to the next block, I suggest our Math EE writing or editing services . Our company has been working with numerous IB students and helped them write custom IB extended essays.

Join a team of happy IB students who have followed the IB extended essay rubric and criteria and gained better results with Writing Metier and our Math assignments help !

Overused Math EE topics (proceed with caution)

While these topics are popular, they’ve been explored extensively. If you choose one, ensure you bring a fresh perspective:

• The Fibonacci Sequence in Nature.
• Pi and its Mysteries.
• The Monty Hall Problem.
• The Birthday Paradox.
• Exploring Pascal’s Triangle.
• The Mathematics of the Pyramids.
• The Tower of Hanoi Problem.
• Benford’s Law.
• The Four Color Theorem.
• The Mathematics of the Rubik’s Cube.

Keep in mind that selecting such a topic will require hard work to find a new custom angle of research and sometimes might not lead to higher grades .

In Conclusion

Alright, IB champs, that wraps up our curated selection of Math EE topics, each with its unique flavor and challenge. The topic is just the starting point. The real magic happens when you infuse it with your insights, analysis, and unique perspective. 

Mathematics isn’t just about numbers; it’s about stories and trips within the confines of equations and graphs. As you gear up to tackle your Extended essay, keep that passion alive, keep questioning, and most importantly, enjoy the process. 

Don’t forget to reserve extra space because it may take time to write an extended essay . And if you’re ever in doubt, remember that Writing Metier is here to guide you through every step of the process.

Free topic suggestions

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Vasyl Kafidoff is a co-founder and CEO at WritingMetier. He is interested in education and how modern technology makes it more accessible. He wants to bring awareness about new learning possibilities as an educational specialist. When Vasy is not working, he’s found behind a drum kit.

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IB Math Extended Essay Topics: 20+ Ideas for Inspiration

by  Antony W

September 3, 2022

Do you feel stuck on searching for and choosing the best IB Math Extended Essay topics? Or maybe you already have a topic for consideration but it isn’t viable enough to fit the scope of the assignment?

You’ve come to the right place.

In this guide, we’ll give you 15+ IB Math ideas that you can use as inspiration to come up with your own topic or modify and investigate further in your extended essay.

What’s the Purpose of IB Math Extended Essay?

An extended essay in mathematics gives you the chance to demonstrate an understanding of any part of the subject.

You can give an expression on the beauty of mathematics in geometry or fractal theory, the elegance of mathematics in the proving of theorems, and the origin and subsequent development of a branch of mathematics over a period.

The extended essay also allows you to demonstrate the link between the different branches of mathematics and the powerful structures that enable many different problems to be solved by a single theory and the way in which mathematics is applied to real-world situations.

Your essay requires a well-defined and focused research question. An abstract is no longer necessary in an extended essay , but you’re welcome to include it if you believe it will summarizes your strategy to solving the research question and your findings

Math Extended Essay Writing Assistance

While Math opens up an opportunity to explore complex issues beyond the IB Diploma course , the subject can be extremely challenging for some IB students.

If you’re one of the students who chose Math for the Extended Essay project but you find the subject challenging, you can get help online from experts in the subject.

Help for Assessment offers the most  comprehensive Extended Essay help   in Mathematics, even on a topic that you would consider too complex to handle. With our help, you’ll find complex concepts easy to understand, not to mention you’ll get your Math assignment completed on time.

We understand that Math tasks can be costly and involving. However, we’ve made our writing service as affordable as possible, so you can get professional writing help.

We can write you first draft before the first reflection session with your supervisor and equally help you fine-tune the last draft for the final submission.

IB Math Extended Essay Topics

The following are examples of IB Math Extended Essay topics that you might find worth investigating further: 

• What is the return percentage of a certain three-reel slot machine?
• What are the alternatives to Euclidean geometry and what are their practical applications?
• Comparison of population growth models for Country X for the past n years, with projections for the future.
• The exploration of geometric series in musical instruments, such as the fret position on a guitar
• How many convex polygons can you construct from seven tangram pieces?
• An examination of the alteration of a message's truthful substance during transmission between persons
• Is there a connection between the golden ratio and human’s perception on natural beauty, with a focus on the human face and form?
• Is there a relationship between SAT scores and school test results/GPA?
• Leibniz and Newton independently developed calculus at around the same time. Compare their techniques and analyze which notation is currently more prevalent.
• What is the Binomial Theorem, and how has it contributed to human history?
• Complex number problem-solving techniques: What types of real-world issues do complex numbers assist solve?
• Applying Newton's Forward Difference Formula to predict the number of triangles created by subdividing the sides of an equilateral triangle n times.
• RSA Public Key Cryptography's use of modular arithmetic and huge prime integers to achieve anonymity
• Investigating the link between Pascal's Triangle and the Fibonacci sequence
• How can mathematical modeling that employs differential equations determine population growth patterns for a predator and its prey?
• How can the population of cells be determined throughout time? Which mathematical model approximates an actual experiment more precisely?
• A study of Riemann Sums (conventional integration to get areas) and Numerical Integration
• Vedic Mathematics: an investigation of its effectiveness and exploration of its applications
• How are Laplace transforms utilized in the solution of second-order differential equations?
• A statistical examination of the impact of background music on pupils' short-term memory ability
• Analytical and geometric formulations of parabolic and cubic Bezier curves as used in computer graphics software
• A quantitative analysis of the efficacy of two herbs for treating impetigo skin condition
• A study of the nature of beats and the relative consonance of pure-tone dyads
• The link between logical-mathematical intelligence and academic achievement at the undergraduate level
• A study of the link between a bond's coupon rate, yield to maturity, and its clean price
• Using the addition of sine curves to analyze the harmony of Chinese and Western musical scales
• The correlation between students' attitudes toward mathematics and their mathematical performance
• How near is the approximation of the Taylor Series to the original function
• What criteria determine whether the movement of employees on a building site achieves "equilibrium"?
• The efficacy of an English Tuition Program in enhancing the English skills of participants
• A statistical examination of the causes of fatal traffic accidents throughout the holiday season
• Does studying a third language have any influence on the short-term memory retention of lower secondary students?

Keep in mind that this list is not exhaustive by any means. So if none of these topic ideas appeals to you, doing additional research can make a difference.

Related Reading

• The Complete Guide for IB Math Extended Essay
• Get a List of Psychology Extended Essay Topics Here
• Learn More About Physics Extended Essay Assignment

Some Tips to Help You Choose a Relevant Math EE Topic

You can write an extended essay in math on any subject with a mathematical focus. Because IB doesn’t limit the assignment to mathematical theories, you may select mathematical themes from engineering, sciences, and the social sciences.

Statistical analyses of experimental results from other disciplines are also appropriate, as long as they focus on the modeling method and address the limits of the results.

A topic chosen from the history of mathematics may also be acceptable, provided you bring out a clear progression of mathematical growth.

Focusing on the lives of mathematicians or their personal rivalry would be irrelevant and would not score highly on the grading criteria.

Notably, the evaluation criteria provide points for the nature of the inquiry and the extent to which reasoned arguments are suitable for a research issue.

You need to avoid selecting a topic that generates a trivial research question or is insufficiently concentrated to permit suitable presentation in an essay of the right length.

Typically, you will have to challenge yourself to either extend their knowledge beyond the Diploma Program course or apply techniques learned in their mathematics course to the modeling of an adequately chosen topic.

Final Thoughts

One of the most important thing to keep in mind once you find a suitable Math EE topic is that you will be working on an essay, not a research article for a journal of advanced mathematics.

Also, no finding, no matter how remarkable, should appear in your work without proof of your actual understanding of it. 

About the author 

Antony W is a professional writer and coach at Help for Assessment. He spends countless hours every day researching and writing great content filled with expert advice on how to write engaging essays, research papers, and assignments.

How to Choose an EE Topic (Mathematics)

The Extended Essay is undoubtedly one of the most feared components of the IB program. A 4,000 word research paper can, in fact, seem daunting to those who have only written 500-1000 word essays. Therefore, students should choose a topic that they can not only find sources for, but are also passionate about it.

Mathematics Extended Essays are rare — of the 87,519 Extended Essays submitted in the 2020 May Examination Session only 2,454 were done over Mathematics (2.8%) ( IB Statistical Bulletin 2020 ). Despite the rarity, I chose to write a Mathematics EE because maths is something that fascinates me. To many students, Mathematics EEs sound scary and barely consider writing one. There were many people that told me I was insane and that it was impossible. In the end, I put in the work to make it happen. 

I chose to write my paper on Game Theory and my research question was: “To what extent does Game Theory play a role in Modern Warfare?” 

I found this topic not unlike the way students writing History EEs find their own specific topics. Just as history has countless events in which one can write about, Mathematics is similar with its various branches. I chose a branch that interested me (Game Theory) and used it to solve a real-world problem (Modern Warfare). My economics teacher actually suggested this idea.  They said that, while Game Theory is primarily used in economics, it has numerous applications to maths when discussed alongside warfare. This qualified my essay as a Category 1 Mathematics Extended Essay, which is a paper that discusses “the applicability of mathematics to solve both real and abstract problems” (p. 96, IB Extended Essay Guide ). 

Writing the essay is where, I admit, it got challenging. During the process I had no peers to help me as only a few others had chosen a Mathematics EE, but none of their topics related to mine. Fortunately, my mentor was extremely helpful and I was able to find several books at my local university that were very useful.

Mathematics Extended Essays are bizarre in many ways as things such as word count, varied sentence structure, and high vocabulary do not matter. However, it should be noted that effective communication is key even if that’s done through mathematical expressions. Despite these challenges, I strongly believe that Mathematics EEs are doable, and more people would do them if there was not such a negative stigma about them. I encourage all future IB sessions to consider doing one as the feeling when you have finished is unlike any other. The pride and satisfaction I felt knowing that I took the path less travelled and still found success is something that I hope all future IB students will experience.

You may also like…

• Our Extended Essay series
• Tiffany’s tips for Mathematics HL

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Extended Essay Writers

Math Extended Essay Topics

Luke MacQuoid

A math extended essay (EE) is a research paper that is written by students who are enrolled in the International Baccalaureate (IB) program as a part of their Diploma. The Extended Essay is self-directed research that aims to provide students with the opportunity to explore a topic of their interest in depth, with a particular focus on the application of math concepts and skills. In order to pass the paper successfully, it is very important to choose the right topic for the Math Extended Essay Topics.

In an Group 5: Mathematics extended essay, students work independently under the guidance of a supervisor to plan and carry out a research project on a math-related topic . This research project should demonstrate the student’s ability to engage in independent research, apply critical thinking and problem-solving skills, and communicate their findings clearly and effectively.

The math extended essay has strict word count in length and should be written in a clear, concise, and formal style, it should also include an introduction, a body of discussion, a conclusion, and a bibliography.

The student is expected to demonstrate the ability to design and conduct a research project, use mathematical concepts and skills to analyze and interpret the data and discuss their findings in the context of relevant mathematical literature.

The math extended essay also allows students to explore a mathematical topic in a way that is not possible in the classroom, it also gives a chance to students to demonstrate their mathematical knowledge and skills and to develop a more global understanding of mathematics.

What’s the Purpose of IB Math Extended Essay?

The purpose of the IB math extended essay is to provide students with the opportunity to engage in independent research and to apply their mathematical knowledge and skills to a topic of their own choosing. The extended essay is designed to give students a chance to explore a topic in depth and to develop the following key skills:

Research skills : Students learn how to design and conduct a research project and how to collect, analyze, and interpret data.

Critical thinking skills : Students learn how to evaluate sources, make a clear and well-supported argument, and solve problems.

Communication skills : Students learn how to write a formal academic paper and how to present their findings and arguments clearly and effectively.

Time management skills:  Students learn how to plan their time effectively and manage their workload.

Subject-specific knowledge : Students get the opportunity to deepen their understanding of a particular area of mathematics and to explore the ways in which mathematical concepts and methods can be applied to solve problems.

The IB Math Extended Essay allows students to research and write about a specific mathematical topic that they find interesting. It also allows students to apply the knowledge and skills they have learned in the classroom to a real-world problem or scenario. 

Completing the extended essay is an important requirement for students to receive the International Baccalaureate Diploma, and it also provides students with the opportunity to develop important research and analytical skills which will be useful in the future, regardless of their chosen career path.

Need help with your IB Math extended essay?

You can also use our extended essay writers team’s services if you need assistance selecting a topic . Furthermore, we can also help you write your IB extended essay from scratch or edit your draft following the IB criteria.

IB Math Extended Essay Topics

An extended essay in mathematics provides students with an opportunity to explore an area of math that interests them in depth. Here are some potential topics for a math extended essay:

• Investigating the properties of a specific mathematical function and its applications.
• Examining the history of a particular mathematical concept or problem
• Investigating the relationship between different branches of mathematics, such as algebra and geometry.
• Investigating the properties and application of geometric shapes in different branches of mathematics.
• Applying mathematical modeling to a real-world problem, such as optimizing logistics or predicting weather patterns.
• Investigating the use of mathematical methods in computer science, such as complexity theory and algorithms.
• Exploring the application of number theory in cryptography and information security
• Investigating the role of statistics in decision-making and forecasting.
• Investigating the use of mathematical logic in Artificial Intelligence and machine learning
• Examining the applications of mathematical methods in the field of engineering and physics, such as fluid dynamics and mechanics.
• Investigating the properties of fractals and their applications in computer graphics and image processing.
• Exploring the concept of infinity and infinitesimals in calculus and their implications in other branches of mathematics.
• Investigating the application of graph theory in network analysis and computer science
• Examining the relationship between topology and other branches of mathematics such as algebra and analysis.
• Investigating the properties of mathematical knots and their applications in physics and biology.
• Exploring the application of game theory in economics and decision making
• Investigating the use of mathematical methods in the field of finance and financial modeling
• Examining the relationship between chaos theory and other areas of mathematics and science
• Investigating the use of mathematical methods in the field of cryptography, such as elliptic curve cryptography.
• Exploring the application of mathematical methods in the study of complexity in natural systems, such as studying the Mandelbrot set in the field of chaos theory.

Remember to check with your teacher or supervisor for guidelines or restrictions and pick a topic that you find interesting and engaging. Also, make sure you have a clear and testable research question as part of the planning and writing process.

Students can use these themes as a starting point for their research and then narrow down their focus to a specific problem or question related to the theme. For example, if a student is interested in investigating the properties of a specific mathematical function, they could begin by researching the history of the function, its key properties, and its applications. 

They could then narrow down their focus to a specific problem or question, such as “How does the shape of the graph of this function change as its parameters are varied?” or “What are the implications of this function’s properties for other areas of mathematics?”

Similarly, if a student is interested in exploring the concept of infinity in calculus, they could begin by researching the history of the concept and its implications in other branches of mathematics. They could then narrow down their focus to a specific question, such as “How does the concept of infinity affect the way we think about limits and continuity in calculus?”

Once a student has a specific problem or question in mind, they can begin to design and conduct their research. This will typically involve collecting data, analyzing it using mathematical methods, and interpreting their findings. They should also read and critically evaluate relevant literature on their topic and use it as a foundation to construct their own arguments.

It’s also important to mention that the research and writing process should be guided by the student’s supervisor and that the student should be able to clearly communicate the research question, methodology, findings, and conclusions in a formal academic paper.

Finally, the extended essay is an opportunity for students to demonstrate their ability to apply mathematical concepts and skills to a real-world problem and to communicate their findings in a clear and effective way, and this can be greatly beneficial for students who wish to pursue further studies or careers in fields related to mathematics and other sciences.

Some Tips to Help You Choose a Relevant Math EE Topic

Choosing a relevant and engaging topic for your math extended essay can be challenging, but by following these tips, you can make the process easier:

Start by identifying your interests: Think about the areas of math that you enjoy and find most interesting. These are likely to be the areas that you will find most engaging to research.

Consider the scope of the topic: Your topic should be narrow enough to be manageable within the 4,000-word limit of the extended essay but broad enough to allow for a thorough investigation.

Look for connections between different areas of mathematics: Often, the most interesting and relevant topics lie at the intersection of different areas of mathematics.

Talk to your supervisor: Your supervisor is a valuable resource and can provide guidance on choosing a relevant and manageable topic. They can also help you refine your research question and give you feedback on your ideas.

Make sure your topic is original: You want your extended essay to be unique and to make a meaningful contribution to the field. Avoid topics that have been extensively researched or that are too similar to other extended essays.

Think about the resources available: Consider whether the resources available to you (books, articles, data, etc.) are sufficient to allow you to conduct the research you want to do.

Consider the audience: Your Extended Essay is read by a group of examiners appointed by the International Baccalaureate, so consider the level of mathematical sophistication of your topic and the language used to communicate it.

Research to find a feasible topic: Once you have some ideas, research them to see if they are feasible, given the time, resources, and supervisor’s expertise you have.

In conclusion,  writing a math extended essay can be a challenging but rewarding experience. The key to success is to choose a relevant and engaging topic that aligns with your interests and allows you to showcase your understanding and skills in mathematics. By considering the tips provided, such as identifying your interests, talking to your supervisor, and making sure your topic is original, you will be able to choose a topic that is both manageable and meaningful. 

One way to ensure the success of their essay is to seek out professional assistance. Professional writers and editors can provide valuable feedback and guidance throughout the research and writing process, helping students to improve their understanding of the topic and to communicate their findings more effectively.

It could be a good idea to consider looking into reputable academic writing services where you can get help with your math extended essay and improve your chances of getting a good grade. They can also help ensure that the paper meets academic standards and requirement. However, always be sure to evaluate the source carefully and do your due diligence, as not all academic writing services are created equal.

Remember that the extended essay is an opportunity to conduct independent research and apply critical thinking and problem-solving skills to a topic of your own choosing. By following a systematic and well-structured approach, you will be able to successfully complete your math extended essay and demonstrate your knowledge and understanding of the subject.

Luke MacQuoid has extensive experience teaching English as a foreign language in Japan, having worked with students of all ages for over 12 years. Currently, he is teaching at the tertiary level. Luke holds a BA from the University of Sussex and an MA in TESOL from Lancaster University, both located in England. As well to his work as an IB Examiner and Master Tutor, Luke also enjoys sharing his experiences and insights with others through writing articles for various websites, including extendedessaywriters.com blog

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Math Essay Ideas for Students: Exploring Mathematical Concepts

Are you a student who's been tasked with writing a math essay? Don't fret! While math may seem like an abstract and daunting subject, it's actually full of fascinating concepts waiting to be explored. In this article, we'll delve into some exciting math essay ideas that will not only pique your interest but also impress your teachers. So grab your pens and calculators, and let's dive into the world of mathematics!

• The Beauty of Fibonacci Sequence

Have you ever wondered why sunflowers, pinecones, and even galaxies exhibit a mesmerizing spiral pattern? It's all thanks to the Fibonacci sequence! Explore the origin, properties, and real-world applications of this remarkable mathematical sequence. Discuss how it manifests in nature, art, and even financial markets. Unveil the hidden beauty behind these numbers and show how they shape the world around us.

• The Mathematics of Music

Did you know that music and mathematics go hand in hand? Dive into the relationship between these two seemingly unrelated fields and develop your writing skills . Explore the connection between harmonics, frequencies, and mathematical ratios. Analyze how musical scales are constructed and why certain combinations of notes create pleasant melodies while others may sound dissonant. Explore the fascinating world where numbers and melodies intertwine.

• The Geometry of Architecture

Architects have been using mathematical principles for centuries to create awe-inspiring structures. Explore the geometric concepts that underpin iconic architectural designs. From the symmetry of the Parthenon to the intricate tessellations in Islamic art, mathematics plays a crucial role in creating visually stunning buildings. Discuss the mathematical principles architects employ and how they enhance the functionality and aesthetics of their designs.

• Fractals: Nature's Infinite Complexity

Step into the mesmerizing world of fractals, where infinite complexity arises from simple patterns. Did you know that the famous Mandelbrot set , a classic example of a fractal, has been studied extensively and generated using computers? In fact, it is estimated that the Mandelbrot set requires billions of calculations to generate just a single image! This showcases the computational power and mathematical precision involved in exploring the beauty of fractal geometry.

Explore the beauty and intricacy of fractal geometry, from the famous Mandelbrot set to the Sierpinski triangle. Discuss the self-similarity and infinite iteration that define fractals and how they can be found in natural phenomena such as coastlines, clouds, and even in the structure of our lungs. Examine how fractal mathematics is applied in computer graphics, art, and the study of chaotic systems. Let the captivating world of fractals unfold before your eyes.

• The Game Theory Revolution

Game theory isn't just about playing games; it's a powerful tool used in various fields, from economics to biology. Dive into the world of strategic decision-making and explore how game theory helps us understand human behavior and predict outcomes. Discuss in your essay classic games like The Prisoner's Dilemma and examine how mathematical models can shed light on complex social interactions. Explore the cutting-edge applications of game theory in diverse fields, such as cybersecurity and evolutionary biology. If you still have difficulties choosing an idea for a math essay, find a reliable expert online. Ask them to write me an essay or provide any other academic assistance with your math assignments.

• Chaos Theory and the Butterfly Effect

While writing an essay, explore the fascinating world of chaos theory and how small changes can lead to big consequences. Discuss the famous Butterfly Effect and how it exemplifies the sensitive dependence on initial conditions. Delve into the mathematical principles behind chaotic systems and their applications in weather forecasting, population dynamics, and cryptography. Unravel the hidden order within apparent randomness and showcase the far-reaching implications of chaos theory.

• The Mathematics Behind Cryptography

In an increasingly digital world, cryptography plays a vital role in ensuring secure communication and data protection. Did you know that the global cybersecurity market is projected to reach a staggering $248.26 billion by 2023? This statistic emphasizes the growing importance of cryptography in safeguarding sensitive information.

Explore the mathematical foundations of cryptography and how it allows for the creation of unbreakable codes and encryption algorithms. Discuss the concepts of prime numbers, modular arithmetic, and public-key cryptography. Delve into the fascinating history of cryptography, from ancient times to modern-day encryption methods. In your essay, highlight the importance of mathematics in safeguarding sensitive information and the ongoing challenges faced by cryptographers.

Writing a math essay doesn't have to be a daunting task. By choosing a captivating topic and exploring the various mathematical concepts, you can turn your essay into a fascinating journey of discovery. Whether you're uncovering the beauty of the Fibonacci sequence, exploring the mathematical underpinnings of music, or delving into the game theory revolution, there's a world of possibilities waiting to be explored. So embrace the power of mathematics and let your creativity shine through your words!

Remember, these are just a few math essay ideas to get you started. Feel free to explore other mathematical concepts that ignite your curiosity. The world of mathematics is vast, and each concept has its own unique story to tell. So go ahead, unleash your inner mathematician, and embark on an exciting journey through the captivating realm of mathematical ideas!

Tobi Columb, a math expert, is a dedicated educator and explorer. He is deeply fascinated by the infinite possibilities of mathematics. Tobi's mission is to equip his students with the tools needed to excel in the realm of numbers. He also advocates for the benefits of a gluten-free lifestyle for students and people of all ages. Join Tobi on his transformative journey of mathematical mastery and holistic well-being.

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260 Research Topics For Math Papers

Mathematics research topics span a range of categories that students are able to select. Some people think that doing research about math is boring. But math can be an amazing and exciting subject. Because mathematics is a language, universal mathematics can explain anything and anything, from galaxies that are orbiting each other to music.

But the vastness of this field of study also creates the task of selecting a research paper difficult. It's because students need to select topics that can convince teachers so that they can award them the highest marks. This article provides the top research paper topics for math. It's helpful because it encourages students to pick or choose subjects for their academic essays without much difficulty.

What Are The Different Types Of Math?

As you can see, mathematics is a broad subject that covers a range of disciplines. Here are the most common kinds of math:

• Geometry: It's a mathematical branch that deals with dimensions, shapes and positions of figures. Many consider geometry to be an appropriate math field due to the fact that it examines figures' sizes, shapes and the characteristics of different objects, such as solids, lines and surfaces, lines, angles, and solids.
• Algebra is helpful in solving problems and manipulating symbols. This branch assists students in representing the unknown with letters and applying them to numbers.
• Calculus, The area of calculus is essential in determining rates of change, including acceleration and velocity.
• Arithmetic: Arithmetic is the most popular and oldest maths discipline, which covers base operations with numbers. These include subtraction, divisions, additions multiplications, and some schools even shorten it to BODMAS.
• Statistics and Probability assist analyze numerical data in order to create predictions. Probability is about chance, while statistics is about managing different types of data by employing various methods.
• Trigonometry is a method of measuring the angles of angles and also distances between two points. It mostly deals with triangles' relationship to sides, angles, and curves.

Fun Math Topics

If you're struggling to begin creating your essay, here is an array of fun and interesting math-related topics for you to consider. They'll definitely keep you engaged and make writing enjoyable. Additionally, engaging math topics can demonstrate to everyone that math can be fun and even humorous.

• The relationship between art and mathematics - studying the Golden Ratio in Renaissance-era paintings.
• A review of the set theory developed by Georg Cantor.
• The best methods to learn math concepts and develop the ability to recognize numbers.
• Different ways to think about probability are examined through the analysis of card tricks.
• Chess and checkers use math in leisure activities.
• In computer science, there are five distinct forms of math.
• Practical applications to The Pythagorean Theorem.
• An examination of the various mathematical logic theories.
• Game theory is a key concept within social sciences.
• Mathematical definitions of the concept of infinity and the best way to quantify it.
• What's the rationale behind math problems that cannot be solved?
• A description of median, mean media, mode and mean using maths grades in the classroom.
• The geometry and properties of geometry and properties of a Mobius strip.
• Utilizing truth tables to demonstrate the logic behind the propositional phrase.
• The relation to Pascal's Triangle as well as The Binomial Theorem.
• The use of various numbers: the history.
• The use of differential geometry in contemporary architecture.
• A mathematical method to solve the problem of the Rubik's Cube.
• Comparative analysis of prescriptive and predictive statistical analysis.
• The explanation of the various iterations that comprise the Koch snowflake.
• The significance of calculation limits.
• Hexagons are the most balanced form throughout the world.
• The development of chaos theories' patterns.
• What were the contributions of Euclid to mathematics?
• The differences between abstract and universal algebra.

Math Essay Topics for High School

When you write a paper on math in order to prove that you are able to comprehend the concept, this can be beneficial in the event that you have to prepare for an examination. Pick a topic from this section and choose the topics you'd like to talk about.

• Define what we require in Pythagoras' theorem.
• What is hyperbola?
• Define the distinction between the two.
• What is the best time to make use of a calculator?
• Make connections with maths and arts.
• How can you solve the linear equation?
• Discuss the best way to calculate the probabilities that two dice will be rolled.
• Do you see a connection between math and philosophy?
• What maths do you employ in your daily routine?
• What is numeric data?
• Define how to use the binomial theory.
• What is the property of multiplication that is distributive?
• Explore the key concepts in ancient Egyptian mathematics.
• Why do so many students loathe math?
• Should mathematics be required in school?
• How do you do an equivalent transformation?
• Why do we require imaginary numbers?
• How do you determine the slope of an arc?
• What's the distinction between cosine, sine and the term tangent?
• What is the cross-product of two vectors?
• What are we using differential equations to solve?
• Find out ways to determine the value of the mean.
• Define linear growth.
• Give examples of various kinds of numbers.
• How do you find a solution to the problem of a matrix?

College Math Topics for a Paper

Sometimes you require more than just formulas and formulas to communicate a complex concept. Knowing how to present yourself is so important. This is especially important in college-level math.

• What are we looking for to use n-dimensional spaces?
• Define how counting cards is done.
• Define the difference between a discrete as well as a continuous distribution of probability.
• What is the function of encryption?
• Describe extremal problems in discrete geometry.
• What is the reason that makes the math problem insolvable?
• Study the topology of a Mobius strip.
• What is K-theory?
• Examine the fundamental issues of computational geometry.
• Discuss the application of set theory.
• What are we looking for in Boolean functions?
• Discuss the major topological concepts of modern math.
• Study what properties are inherent in a rotating matrix.
• Examine the practical applications of game theory.
• How do you solve a Rubik's Cube mathematically?
• Discuss the mathematics that lies behind the Koch snowflake.
• Define the paradox of Gabriel's Horn.
• How do fractals develop?
• Find a solution to Sudoku by using math.
• What is the reason why the Riemann hypothesis is not solved?
• Discuss the Millennium Prize Problems.
• How do you split complicated numbers?
• Examine the degree of polynomial functions.
• What are the most significant concepts of number theory?
• Examine the various types of statistical techniques.

Mathematical Advanced Topics to Write a Paper

If you've successfully completed the tests of basic math, then you are able to move on to the advanced portion. This is where you will find topology, combinatorics and mathematical logic , and computational math.

• What is an abelian group?
• Define the orbit-stabilizer theorem.
• Discuss the factors that make the Burnside issue significant.
• What are the fundamental characteristics that Holomorphic functions have?
• What is Cauchy's integral theorem? Result in the integral formula of Cauchy?
• What do the two Picard theorems connect to each with each
• What is known as one of the Fourier series?
• Give an example of an algorithm that you have used to aid in machine learning.
• Check out the different kinds of knapsack challenges.
• What is the minimal overlap problem?
• Explain your understanding of the Bernoulli scheme.
• Provide a formal definition of the Chinese restaurant procedure.
• Examine the map of logistics in connection to chaos.
• What do we require for the Feigenbaum constants?
• Define an equation of difference.
• Define the purpose of the Fibonacci sequence.
• What is an unintentional transfer?
• Examine Riemann with the Ruelle Zeta functions.
• How can you make use of elementary embeddings in the model theory?
• Examine the issue using the wholeness axiom, as well as Kunen's theory of inconsistency.
• What is Lie algebra applied in Physics?
• Define the various algebraic cycles.
• What is the reason we require cohomology groups that are stale in order to compute algebraic curves?
• What is non-Euclidean geometry made up of?
• How do two lines become ultraparallel?

Math Research Topics for a Paper

Selecting the right subject is essential for the success of your writing a research essay in mathematics. It must be challenging enough to convince you. However, it shouldn't exceed the limits of your knowledge. If possible, remain within your field of expertise.

• Write about the development of calculus.
• What makes math problems that aren't solved important?
• Find out the reasons behind that gender disparity in maths students.
• What are the most difficult mathematical questions that are asked in the present?
• Study the concept of spaces for the operator.
• What can we do to design the train schedules for all of the nation?
• What are the factors that make a number large?
• What is the best way to make infinities come in different sizes?
• What is the most effective mathematical strategy to be successful in the game Go?
• Examine natural patterns of random walks in biology.
• Define the type of math that was utilized in the ancient times of Persia.
• Discuss how the Iwasawa theory is related to the modular form.
• What are the roles of prime numbers in encryption?
• What was the process through which the field of mathematics developed?
• Explore the various options for Tower of Hanoi solutions.
• Find Napier's bones. How can you make use of them?
• What is the most mathematical method to locate someone who's lost in the maze?
• Examine the Traveling Salesman Problem. Can you find a new strategy?
• Explain how barcodes work.
• Examine some real-life instances of the chaos theory. What is the best way to define them mathematically?
• Check out the impact of different innovative mathematical equations.
• Research the Seven Bridges of Konigsberg. Link the issue to the city you prefer.
• Examine Fisher's basic theorem of natural selection.
• How does quantum computing work?
• Choose a math problem that isn't solved and explain why it is so difficult.

Math Education Research Topics

Many teachers find the most difficult task is keeping the students engaged. When math is involved, it can be particularly difficult. It is essential to make complex concepts simple to comprehend. That's why we must conduct research into math education.

• Examine traditional methods of teaching math with more innovative methods.
• How can you enhance mathematical educational opportunities in the U.S.?
• Discuss ways to encourage girls to take up jobs within STEM fields.
• Is it appropriate to have computer programming taught in high school?
• Determine the main goals for mathematics instruction.
• Find out how you can improve the accessibility of math for students with learning disabilities.
• When do children need to begin practicing simple math?
• Study the impact of gamification on algebra classes.
• What are the benefits students can gain by participating in math competitions?
• What are the advantages of a move away from standard tests?
• Define the root causes of "math anxiety." How do you get rid of it?
• Discuss the political and social significance of mathematics education.
• Define the most pressing concerns in math education for public schools.
• What is the most effective way to encourage children to learn about math?
• What can students do to improve their mathematical thinking outside of class?
• Discuss the advantages of using technology in math classes.
• In what ways is the culture influencing your math education?
• Learn about the history of teaching mathematics.
• Compare math education in various countries.
• What impact does dyscalculia have on students' lives?
• What school subjects could math be incorporated?
• Did a maths degree increase in value in the past few years?
• What are the negatives that come with the Common Core Standards?
• What are the benefits of a blended curriculum for math?
• Discussion of the benefits of Mathcamp.

Algebra Topics for a Paper

The beauty of algebra comes because of its simplicity. It allows us to explain complex issues in small equations.

• Provide an instance of an Induction Proof.
• What do F-algebras serve?
• What are the main issues?
• Highlight the importance of abstract algebra.
• Examine the peculiarities of Fermat's final theorem.
• What are the basic concepts of algebra?
• Examine the connection between geometry and algebra.
• Examine the different features of commutative and noncommutative algebra.
• Why is Brun's steady presence so important?
• How do you factor quadratics?
• Explain Descartes' Rule of Signs.
• What is the quadratic equation?
• Examine the four different types of sequences, and then define the four types of sequences and define.
• Discuss how fractions are divided.
• What is the purpose of logarithms?
• Explain what you mean by Gaussian elimination.
• What is Cramer's rule?
• Learn the distinction between eigenvectors and Eigenvalues.
• Examine your Gram-Schmidt procedure in 2 dimensions.
• Define what you mean by "range" and "domain" in algebra.
• What do you think you can do with determinates?
• Find out more about the history behind the formula for distance.
• Find out the best method to solve word problems in math.
• Check the relationship between the different models of solving equations.
• Find out how Rubik's Cube is related to the concept of group theory.

Geometry Topics for a Research Paper

Space and shapes are the two main components of geometry. Since its beginning in the earliest days, geometry has developed into a significant field of research. The most recent addition to Geometry, called topology, focuses on the effects on an object when you expand, shrink or fold it. It can be quite a wild ride from here.

• What is the nature of Archimedean solids?
• Find real-life uses for a rhombicosidodecahedron.
• What do we study in the field of projective geometry?
• Check out the most popular kinds of transformations.
• Define how acute square triangulation operates.
• Discuss the Borromean Ring configuration.
• Find solutions to Buffon's needle.
• What is special in right triangles?
• Define the concept of Dirac manifolds.
• Examine the different relations between lines.
• What exactly is what is the Klein bottle?
• What is the relationship between geometry and other disciplines, like the sciences of physics and chemistry?
• Explore Riemannian manifolds within Euclidean space.
• What is the best way to demonstrate the angle bisector theorem?
• Conduct a study on M.C. Escher's use of geometry in his.
• Find the right applications for the golden ratio.
• Explain the significance of circles.
• Find out what the ancient Greeks were aware of about geometry.
• What is congruency?
• Examine the various uses of Euler's formula.
• What do CT scans connect to the geometry?
• What is the reason we require the n-dimensional vectors?
• How do you resolve Heesch's issue?
• What are hypercubes?
• Study the use of geometric shapes in Picasso's paintings.

Calculus Topics to Write a Paper on

Calculus can be described as an even more complex algebra. It's a study of the evolution of a system in time, which provides valuable insights into everyday issues. Calculus applications are essential in many areas like sociology, engineering or business.

• What are the main differences between trigonometry and algebra, and calculus?
• Define the notion of limits.
• Define the formulas that are standard to calculate derivatives.
• What are the most important elements in the graph?
• Assess the validity of L'Hopital's rules.
• What is the definition of the curves' area?
• What is the basis of calculus?
• What is multivariate calculus?
• Discuss the usage of Stokes Theorem.
• What do Leibniz's integral rules stipulate?
• What's the Ito stochastic integral?
• Examine the impact of non-standard analysis on probability theory.
• Study the history of calculus.
• Who was Maria Gaetana Agnesi?
• Define a continuous function.
• What is the most fundamental mathematical theorem in calculus?
• How do you determine your Taylor sequence of a given function?
• Discuss the best ways to fix Runge's issue.
• Discuss the extreme value theorem.
• What are we looking for the predicate calculus to do?
• Which are the linear approximations?
• What happens when an integral becomes in error?
• Describe the Ratio and Root Tests.
• How do rings function?
• Where can we apply math in real-world scenarios?

Business Math Topics to Write About

You don't need to be the owner of an enterprise to be able to appreciate business math. The topics include everything from credit and loans to insurance taxes and investments. Even even if you're no mathematician, you can still use it to manage your financial affairs. Do you find this intriguing?

• What are the most important abilities required to be a successful business manager?
• How do you calculate the interest rate?
• Compare consumer and business math.
• What's the definition of a discount percentage?
• How can you determine if an investment is a reasonable one?
• When is it appropriate to make a payment on a loan by taking another loan?
• Find financing options that anyone can benefit from.
• What is the process behind critical path analysis? Perform?
• Define how loans work.
• What areas of work use operations research?
• What do companies make of the use of statistics?
• What is the economic lot scheduling issue?
• Check out the various uses of chart types.
• What is the cause of a crash in the stock market?
• How do you determine the net value at present?
• Discover the rich history of revenue management.
• What are the best times to use multi-period models?
• Define the effects of depreciation.
• Are annuities an investment that is worth it?
• Could the U.S. financially benefit from eliminating the penny?
• What was the cause of what caused the United States housing crash in 2008?
• How should the sales tax be calculated?
• Explain the concept of markdowns and markups.
• Find out the maths behind debt amortization.
• What distinguishes a mortgage from a mortgage?

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Pythagoras Theories

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Pythagorean Theorem: History, Formula, and Proof

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• Words: 13711

Mathematics: Individual and Cultural Influences

The scientific method isn’t what it used to be.

• Words: 1100

Independent Samples t-test with SPSS

Symmetric & asymmetric algorithms, number theory and major contributors to the field.

• Words: 1136

Mathematics and Business Relationship

• Words: 2480

Calculus-Integration

• Words: 1074

Linear Equations Comprehensive Study

History of pythagoras theorem.

• Words: 1370

Prime Numbers Role in People’s Life

Math functions in economics.

• Words: 2443

History of Calculus: Brief Review One of the Branches of Mathematics

• Words: 1169

Real and Complex Numbers

Geometry, space, manipulative, and technology.

• Words: 2805

Charting a Career in Mathematics: From Teaching to Actuarial Practice

• Words: 1057

Navigating the Math Maze: A Strategic Policy Framework

• Words: 1226

Deduction in Ancient Greece and Egypt

Aspects of the mathematics problem solving.

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The Life Accomplishments of John von Neumann

Report: tow tank statistical analysis.

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Determining the Area of the Isosceles Triangles

Mathematical operations with positive and negative numbers.

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Construction of Regular Polygons: Octagon

A random variable and binomial experiment, evaluating the effectiveness of an instructional design.

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Order of Operations: Connecting to Real Life

Aspects of probability theory, researching of advanced forecasting methods, chapter 5 of weapons of math destruction by o’neil, the concept of coterminal angles, the exponential function in analytic algebra, sophie germain’s story of a woman mathematician, compound interest as mathematical fact.

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Mathematician john wilder tukey’s biography, dangers of false representation in mathematics.

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Thinking in terms of vectors in daily life, physiologically-structured population models and their ordinary differential equations reduction, mathematical biology: explaining population extinction, statistical and stochastic modeling applied to social processes.

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Mathematical and statistical investigation.

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Teaching math: number sense instruction.

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“is-lm model” by dudley cooke, mathematical laws in the real world.

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Mathematical and physical concepts, algebraic equations and graphical representations.

Extended Essay: Group 5: Mathematics

• General Timeline
• Group 1: English Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts
• Interdisciplinary essays
• Brainstorming
• Pre-Writing
• Research Techniques
• The Research Question
• Paraphrasing, Summarising and Quotations
• Writing an EE Introduction
• Writing the main body of your EE
• Writing your EE Conclusion
• Six sub-categories for WSEE
• IB Interdisciplinary EE Assessment Guide
• Sources: Finding, Organising and Evaluating Them
• Conducting Interviews and Surveys
• Citing and Referencing
• Check-in Sessions
• First Formal Reflection
• Second Formal Reflection
• Final Reflection (Viva Voce)
• Researcher's Reflection Space (RRS) Examples
• Information for Supervisors
• How is the EE Graded?
• EE Online Resources
• Stavanger Public Library
• Exemplar Essays
• Extended Essay Presentations
• ISS High School Academic Honesty Policy

Mathematics

An extended essay (EE) in mathematics is intended for students who are writing on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Essays in this group are divided into six categories:

• the applicability of mathematics to solve both real and abstract problems
• the beauty of mathematics—eg geometry or fractal theory
• the elegance of mathematics in the proving of theorems—eg number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds or thousands of years
• the effect of technology on mathematics:
• in forging links between different branches of mathematics,
• or in bringing about a new branch of mathematics, or causing a particular branch to flourish.

These are just some of the many different ways that mathematics can be enjoyable or useful, or, as in many cases, both.

For an Introduction in a Mathematics EE look HERE . 

Choice of topic

The EE may be written on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Students may choose mathematical topics from fields such as engineering, the sciences or the social sciences, as well as from mathematics itself.

Statistical analyses of experimental results taken from other subject areas are also acceptable, provided that they focus on the modeling process and discuss the limitations of the results; such essays should not include extensive non-mathematical detail.

A topic selected from the history of mathematics may also be appropriate, provided that a clear line of mathematical development is demonstrated. Concentration on the lives of, or personal rivalries between, mathematicians would be irrelevant and would not score highly on the assessment criteria.

It should be noted that the assessment criteria give credit for the nature of the investigation and for the extent that reasoned arguments are applied to an appropriate research question.

Students should avoid choosing a topic that gives rise to a trivial research question or one that is not sufficiently focused to allow appropriate treatment within the requirements of the EE.

Students will normally be expected either to extend their knowledge beyond that encountered in the Diploma Programme mathematics course they are studying or to apply techniques used in their mathematics course to modeling in an appropriately chosen topic.

However, it is very important to remember that it is an essay that is being written, not a research paper for a journal of advanced mathematics, and no result, however impressive, should be quoted without evidence of the student’s real understanding of it.

Example and Treatment of Topic

Examples of topics

These examples are just for guidance. Students must ensure their choice of topic is focused (left-hand column) rather than broad (right-hand column

Treatment of the topic

Whatever the title of the EE, students must apply good mathematical practice that is relevant to the

chosen topic, including:

• data analysed using appropriate techniques

• arguments correctly reasoned

• situations modeled using correct methodology

• problems clearly stated and techniques at the correct level of sophistication applied to their solution.

Research methods

Students must be advised that mathematical research is a long-term and open-ended exploration of a set of related mathematical problems that are based on personal observations. 

The answers to these problems connect to and build upon each other over time.

Students’ research should be guided by analysis of primary and secondary sources.

A primary source for research in mathematics involves:

• data-gathering

• visualization

• abstraction

• conjecturing

• proof.

A secondary source of research refers to a comprehensive review of scholarly work, including books, journal articles or essays in an edited collection.

A literature review for mathematics might not be as extensive as in other subjects, but students are expected to demonstrate their knowledge and understanding of the mathematics they are using in the context of the broader discipline, for example how the mathematics they are using has been applied before, or in a different area to the one they are investigating.

Writing the essay

Throughout the EE students should communicate mathematically:

• describing their way of thinking

• writing definitions and conjectures

• using symbols, theorems, graphs and diagrams

• justifying their conclusions.

There must be sufficient explanation and commentary throughout the essay to ensure that the reader does not lose sight of its purpose in a mass of mathematical symbols, formulae and analysis.

The unique disciplines of mathematics must be respected throughout. Relevant graphs and diagrams are often important and should be incorporated in the body of the essay, not relegated to an appendix.

However, lengthy printouts, tables of results and computer programs should not be allowed to interrupt the development of the essay, and should appear separately as footnotes or in an appendix. Proofs of key results may be included, but proofs of standard results should be either omitted or, if they illustrate an important point, included in an appendix.

Examples of topics, research questions and suggested approaches

Once students have identified their topic and written their research question, they can decide how to

research their answer. They may find it helpful to write a statement outlining their broad approach. These

examples are for guidance only.

An important note on “double-dipping”

Students must ensure that their EE does not duplicate other work they are submitting for the Diploma Programme. For example, students are not permitted to repeat any of the mathematics in their IA in their EE, or vice versa.

The mathematics EE and internal assessment

An EE in mathematics is not an extension of the internal assessment (IA) task. Students must ensure that they understand the differences between the two.

• The EE is a more substantial piece of work that requires formal research
• The IA is an exploration of an idea in mathematics.

It is not appropriate for a student to choose the same topic for an EE as the IA. There would be too much danger of duplication and it must therefore be discouraged.

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IB Math EE - Propel Your Mind To A 34/34

Unlock the secrets to acing your IB Math EE with a guaranteed 34/34 score! Propel your mind to success and make the most of your potential. 💯

Table of content

Extended essay & what is it❓, ib math ee vs math ia 🥊 , wth is an ib math extended essay 🌋, a brief about ib math ee 🩲, sexy pointers you can't-miss 🤤, 4 ways to find the right math ee topic ⭕, formulate your research question 🔎, planning your research & essay 📖, structuring your essay 🏗️, ib math ee reflection, what to do 🪞, ib math ee criteria 🧮, ib math ee examples 🛹.

It's time we address the elephant in the room.

IB Mathematics Extended Essay.

There, we said it.

If you've taken up IB Math EE, we're here to tell you that it isn't over, contrary to what you might have heard.

Researching, planning, and finally writing a good IB Math EE is no walk in the park, but rest assured that you'll feel different once you've gone through this valuable document.

Nail IB presents the only comprehensive guide you need to nail your IB Math EE.

Let's keep it accurate.

IB Math EE is a rigorous, independent, academic research essay that calls for,

• a keen interest in Mathematics,
• strong mathematical aptitude & reasoning,
• a focused and disciplined approach, and most importantly,
• essential tips, techniques, and quality guidance.

When one opts for IB Math EE, one should ensure a strong passion for Mathematics and a solid mathematical foundation. Not to mention being willing to devote their time and effort to this self-directed research.

Disclaimer -  If you have second thoughts, you should reconsider and re-evaluate your choice because it's no use aiming in the dark.

There needs to be more!

Invaluable tips and techniques are the last missing piece of the IB Math EE puzzle.

Given the panic and stigma around Math Extended Essay, what students need, is not some more panic; instead, expert guidance to keep them pumped to write their EE papers with skill, precision, and utmost zeal. And so, true to our word, we're here to help you.

Say it out loud for me - I got this!

Before diving any further, we are thrilled to share our premium IB Math resources. Check out the  IB Math AI SL  bundle and the  IB Math AI HL  bundle, including everything from comprehensive, up-to-date video lecture courses by Adam Nazha to curated IB Resource Libraries. All your IB DP Math queries are now answered!

While you're at it, check out our  IB Math AA SL  repository, where Patrick Jones (yep, you got that right, our very own  PatrickJMT  - the best Mathematics instructor in the world) will guide you with a brilliant video lecture course he has created to help you nail your concepts and exams alike! Happy learning!

Returning to our one-stop guide for all things IB Math EE, let us see what this article will cover.

• Extended Essay & What is it ❓
• IB Math EE Vs Math IA  🥊
• WTH Is An IB Math Extended Essay?  🌋
• A Brief About IB Math EE ?  🩲
• Sexy Pointers You Can't Miss  🤤
• 4 Ways To Find The Right Math EE topic  ⭕
• Formulate Your Research Question  🔎
• Planning Your Research and Essay  📖
• Structuring Your Essay  🏗️
• Writing Your Essay Writing Your Reflection  🪞
• IB Math EE Criteria  🧮
• IB Math EE Examples  🛹

First things first, let’s briefly discuss what an Extended Essay is.

As the IB defines it, the Extended Essay is a  4000-word in-depth  study, part of the IB Diploma Programme core mandatory for all students.

A  500-word  reflection component-inclusive of 3 reflections - is submitted with the academic writing.

This, of course, is done under the supervision of your IB advisor. The critical thing to note is that you can choose to write an Extended Essay on any subject offered by the IB in your session, though it is highly recommended you settle on a topic you are studying as a part of your IB curriculum.

The purpose of an Extended Essay is to motivate students to conduct formal research on a subject area of interest, independently work on the chosen research question and gain guidance from their respective IB mentors every step of the way.

The IB highlights the significance of the Extended Essay:

• Hands-on learning for undergraduate research
• An opportunity for students to research an area of interest relating to one of the 6 DP subjects opted for by the student.

The skills the Extended Essay aims to develop in students are:

• Coming up with a relevant Research Question
• Personally engaging with a topic of exploration
• A coherent communication of ideas
• Strong Argument building

For better understanding, go through  this document on Extended Essays   by the IB. It will make things more transparent.

Students often confuse their Internal Assessments with Extended Essays, which is a grave mistake. Gaining clarity on both these components of the IB DP core is essential. Let us understand the significant difference between the two.

• While Internal Assessments require students to investigate and explore an idea, Extended Essays are more formal. Students need to perform primary and secondary research on a research question they choose based on a diverse topic about the subject. Since EE is an independently researched essay, your mentor may only be able to give you some of the answers you wanted, unlike the IA.
• Students must write one Extended Essay on a subject of their choice for their IB Diploma Programme, but I must be prepared for all the topics.
• Internal Assessments are graded internally by the subject instructor and then moderated externally. Extended Essays are marked externally by examiners appointed by the IB. Your grade on your Extended Essay is combined with your Theory of Knowledge Essay/Exhibition score to assign you your overall score/points.

Word of caution:  Do not choose the same investigation topic/research question for your Internal Assessment and the Extended Essay.

For a much better breakdown of the EE document, you must go through our article on the  IB Extended Essay . It contains an IB EE checklist you must attend to and a detailed overview of the structure and planning of the EE.

Now that we’ve got our basics to, let’s get down to business. The fear around IB Math Extended Essay makes the most confident students hesitate and doubt their choices. But we aren’t here to scare you. The myth about the horrors of the IB Math EE isn’t all false; it’s a caution. Because unless you’re prepared with ammunition, strategy, and the will to put in the effort, there’s a slim chance you can survive the Math Extended Essay battle.

If you’ve opted for Math Extended Essay, we assume you have a strong passion for Mathematics. When the going gets tough while working on one’s Extended Essay-which, which is usually the case-your only hope at the end of the tunnel is your drive for the subject you’ve chosen. Being a rigorous subject for writing one’s Extended Essay, Mathematics can be incredibly demanding. So unless you want to play it risky, we suggest you reassess your liking for Mathematics. Once you know for sure, that’s when it begins. Lots of research. Since it is an independently written document, you want to be doing your homework well.

We will further break down the IB Math Extended Essay, from planning to execution, so that you can organize your thoughts and make appropriate decisions.

The Math Extended Essay is an in-depth research document covering any topic with a mathematical focus, i.e., not limited to the mathematics theory (shouldn’t be entirely descriptive). IB has divided Math Extended Essays into six categories:

• the applicability of mathematics to solve both real and abstract problems
• The beauty of mathematics examples includes geometry or fractal theory.
• the application of mathematics in the proving of theorems, for example, number theory
• the history of mathematics: the origin and subsequent development of a branch of mathematics over some time, measured in tens, hundreds, or thousands of years
• the effect of technology on mathematics
• in creating links between different branches of mathematics,
• Or in bringing about a new branch of mathematics or causing a particular unit to flourish.

Your Math EE topic should be an extension of your IB Maths syllabus or the practical application of the knowledge you’ve gained in class.

Before moving on to the planning and structure of the Math Extended Essay, here are some pointers you absolutely cannot afford to miss:

• Attempting a Math EE requires a decent amount of hard work. While conducting preliminary research, ensure you land on a topic you can personally engage with and are familiar with. Going for a complicated subject, you can’t comprehend and interpret futile.
• The mathematical work you put in will have to meet a certain level of sophistication, so avoid going for a topic that gives rise to a trivial research question. Your research question shouldn’t be too generic or broad on similar lines. Ensure you can sufficiently narrow down your area of investigation.
• Another thing to remember is that the topic you finally choose should have a good research foundation and room for a novel contribution.
• Incorporate Primary and Secondary research wherever appropriate.
• Proper Referencing should be done for the essay.
• For Reflection, emphasize the Planning, Research, and Writing Processes.

Spitball ideas -  You begin here. Write down any interesting ideas you can come up with. This is your brainstorming session.

Do your Research -  You could not, would not want to meddle with this step, let alone skip it. Research. Read reports, articles, and documentation. Keep jotting important points down simultaneously. The study will and must go on throughout your search for the right math EE topic.

Approach professors/professionals/experts -  Contact concerned lecturers, professors, and industry professionals. They can provide you with invaluable insights. It would be best if you also discussed ideas with your mentor.

Point to Note -  Your goal should be to find a topic you understand and contribute to. It is always recommended to refer to your Math syllabus; something there inspires you to get the ball rolling!

Your essay will be structured as a document answering the Research Question you’re working on. It should be focused, clear and arguable. You will build your essay around your Research Question; hence pay close attention to it.

All you will include in your essay must be mentioned in your Research Question. This means the focused area you will be exploring and the methods you will use to achieve a plausible outcome.

Honing your Research Question is a continuous process. If it appears relatively easy or complex, please rephrase it. Good Research Questions may start with: “How can we model…”, “To what extent…” etc.

Collect Primary and Secondary data and incorporate it wherever appropriate.

Primary sources for Math research include 

• Data-gathering
• Visualization
• Abstraction
• Conjecturing

A few sources to gather Secondary data include Google Scholar, textbooks, databases such as JSTOR, etc. For your essay, know your aims and devise a step-by-step plan to answer your research question while maintaining a mathematical focus.

• Though you can approach your essay in whichever way you like, there should be a consistent logical structure.
• The work done in your essay should develop to answer your research question.
• Subheadings will provide your work with much-needed coherence and viability.
• Describe your way of thinking
• Write definitions and Conjectures.
• Use symbols, theorems, graphs, and diagrams
• Justify your conclusions.
• Visual aids such as graphs and diagrams should be included in the body, while tables and computer programs should be mentioned in the footnotes or the appendix.
• Data must be analyzed appropriately using relevant techniques, correctly reasoned arguments, and adequate methodology to achieve a result.
• Provide the necessary explanation and commentary for all your work.
• Throughout the writing, you may need to re-evaluate the method, approach, and structure to fit the word count adequately.

Once you’re finished writing, you will have to reassess everything from scratch- the equations, the theory, etc., to ensure the coherence of your essay.

• The three reflections should highlight how the process of writing your essay changed in due course of work and what you’ve learned from it.
• The Reflection should emphasize the planning, research, and writing process.
• You should discuss your choices, the re-evaluations you had to make, the limitations of your work, and how you overcame them, if at all.
• The three reflections are written at the beginning, mid, and towards the end of your essay and should have a word limit of approximately 150, 150, and 200, respectively.

Extended Essays are assessed externally by IB-appointed examiners and are marked on a scale of 0 to 34. The score obtained by a student corresponds to a particular band. The bands are:

A -  refers to work of an excellent standard (Level 6)

B -  refers to the creation of a good standard (Level 6)

C -  refers to work of a satisfactory standard (Level-12)

D -  refers to the product of a mediocre standard (Level 4)

E -  refers to the design of an elementary average (Level 6)

Anything below D will be considered a failing grade, and the student will not be awarded the IB diploma.  As we said, your EE is not a component you can mess up.

The Extended Essay Rubric includes the following Assessment Criteria:

Criterion A -   Focus and Method (Covers the topic, research question, and methodology)

Criterion B -  Knowledge and Understanding (Covers context, subject-specific terminology, and concepts)

Criterion C -  Critical Thinking (Covers research, analysis, discussion, and evaluation)

Criterion D -  Presentation (Covers structure, layout)

Criterion E -  Engagement (Covers reflection on planning and progress)

Now that we’ve discovered and learned about the process of writing a Math EE, here are a couple of ideas to give you an idea about how your Math EE questions should be framed:

Topic -  Archimedes’ calculation of areas

Research Question -  What is the legacy of Archimedes’ calculations of circular and parabolic areas in today’s integration methods?

Topic -  Approximation of irrational numbers by rational numbers

Research Question -  How well can π, e, √2, and other irrationals be approximated by rational numbers?

Topic -   The geometry of navigation

Research Question -  What was the role of mathematics and geometry in navigation when we relied on the stars? Does it still play a part now we have manufactured satellites?

You should also check out this  sample band, A Math EE, published by the IB . This will give you an honest insight into making a band-A essay. Also, go through  band B, C, and D extended essays  to understand the loopholes to avoid.

And that’s a wrap!

We hope this comprehensive IB Math EE guide answers your queries regarding the EE. We also suggest you go through  this IB Extended Essay guide  to clarify the Extended Essay component of your IB DP curriculum. You should also try Nail IB’s Extended Essay guide; check it out  here !

At Nail IB, we’re committed to delivering A-quality guidance so that your IB DP journey is smooth and successful. You can explore  our take-test  series here and access   premium guides  here.

Happy learning!

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Math Essay Topics that Will Suit Your Taste

Here are some topics that you might find yourself interested in:

• Analysis of Functions and Complex Equations in Fractal Geometry
• Analysis of Topological Concepts in Today’s Mathematics
• An Overview of the Concept of Simultaneous Equations in Mathematics
• A Look at Probability and Its Mathematical Determination
• Understanding the Concept of Quartiles and Its Two Types in Mathematics
• Ancient Advances in Math and Their Impact on Modern Calculating System
• Evolution and Development of Mathematics over the Years
• A Description of Georg Cantor’s Works and His Contributions to the Mathematical Science
• An Analysis of Mathematics in Relation to Biology
• An Introduction to Fractal Geometry
• How to Solve and Check Math Equations
• Spirograph: Interesting Curves
• Distinguishing Knots Through Their Color Polynomials
• Statistical Methods: Calculating the Volumes
• Egyptian Forces and Fractions: Doing Arithmetic
• Plane Tessellations and Its Symmetries
• The Theory of Partitions: General Functions
• Distances of Countries Through Arithmetical Functions
• The Best Way of Calculating the Speed of Operating System of PC
• Legal Permutations on Rubik’s Cube

Check out sample essays for MBA or thesis papers, if you’re looking for the best tips for writing math essay. The format corresponds to all academic requirements. The projects samples that are performed at AcademicHelp.net can be at school level or for undergraduates. Ask us for free samples and see how well the papers are composed. Use our online editing services to check if the paper you compose is a top-notch essay. Explore our math extended essay topics that would impress your professor!

Math Extended Essay Topics & Editing Assistance at AcademicHelp.net

In some math courses, especially in college or university, the teacher may assign an essay paper project on math extended essay topics. At first, it may seem really daunting. Solving equations differ from writing about them, and initially, you will feel unfamiliar about the topics. But we are here to help you out with any challenging mathematical home assignment. It is a completely doable thing for our experts.

• We will make a solid plan for you. You may be wondering, why it is so necessary to write on math essay topics. While writing about the studied subject, students develop their critical thinking and analytical skills. It allows you to be directly engrossed in the learning process and apply your own experiences. Moreover, writing about mathematics can solidify the newly presented information in your mind. It boosts the overall understanding of the subject and allows you to dwell on concepts that were covered during the semester. The experts working for AcademicHelp.net will explore the materials you’ve written and will bring all the concepts together to show you what you have to cover in your piece.
• We will ensure you performed thorough research. When editing your writing about math issues, our editors will ensure you’ve read and analyzed the concepts developed by leading mathematicians properly. If you adapted some concepts to resolve real math problems, we will ensure you did that correctly. In other words, we ensure students communicate mathematical concepts and ideas to their readers the right way. Our experts at AcademicHelp.net will see if you performed in-depth research on the basis of fresh facts and ideas.
• We will supply you with great ideas. At the very beginning, students should find the right topic for their project. We’ll provide you with both – the easiest topics like the ones related to certain mathematicians or historical moment in the development of the science, and more difficult ones relevant to how algebra was created or how calculus was discovered. We may also recommend you to write an assignment paper on how someone can make a certain type of mistake. What is more, one can cover some applications of geometry in reality.
• We will edit the paper you’ve accomplished yourself. Even though it is not an English class project, a math paper still requires thorough editing. When the research and writing are done, students should cut out some time to proofread and edit their written work adequately. For editing, you can also reach our service which works 24/7. Our experts will check your paper and correct all mistakes.

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How mathematical practices can improve your writing

Writing is similar to three specific mathematical practices: modelling, problem-solving and proving, writes Caroline Yoon. Here, she gives some tips on how to use these to improve academic writing

Caroline Yoon

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I feel for my students when I hand them their first essay assignment. Many are mathematicians, students and teachers who chose to study mathematics partly to avoid writing. But in my mathematics education courses, and in the discipline more generally, academic writing is part of our routine practice.

Mathematicians face some challenging stereotypes when it comes to writing. Writing is seen as ephemeral, subjective and context-dependent, whereas mathematics is seen as enduring, universal and context-free. Writing reflects self, but mathematics transcends it: they are distinct from each other.

This is a false dichotomy that can discourage mathematicians from writing. It suggests writing is outside the natural skill set of the mathematician, and that one’s mathematics training not only neglects one’s development as a writer but actively prevents it.  Rather than capitulate to this false dichotomy, I propose we turn it around to examine how writing is similar to three specific mathematical practices: modelling, problem-solving and proving.

Three mathematical practices that can improve your writing

Mathematical modelling.

Let us consider a hypothetical mathematics education student who has spent weeks thinking, reading and talking about her essay topic, but only starts writing it the night before it is due. She writes one draft only – the one she hands in – and is disappointed with the low grade her essay receives.

She wishes she had started earlier but she was still trying to figure out what she wanted to say up until the moment she started writing. It was only the pressure of the deadline that forced her to start; without it, she would have spent even more time thinking and reading to develop her ideas. After all, she reasons, there is no point writing when you do not know what to write about!

This “think first, write after” approach, sometimes known as the “writing up” model is a dangerous trap many students fall into, and is at odds with the way writing works. The approach allows no room for imperfect drafts that are a necessary part of the writing process. Writing experts trade on the generative power of imperfect writing; they encourage writers to turn off their internal critics and allow themselves to write badly as a way of overcoming writing inertia and discovering new ideas. The “shitty first draft” is an ideal (and achievable) first goal in the writing process. Anyone can produce a sketchy first draft that generates material that can be worked on, improved and eventually rewritten into a more sharable form.

Mathematical modelling offers a compelling metaphor for the generative power of imperfect writing. Like polished writing, polished mathematical models are seldom produced in the first attempt. A modeller typically begins with some understanding of the real situation to be modelled. The modeller considers variables and relationships from his or her understanding of the real situation and writes them into an initial mathematical model.

The model is his or her mathematical description of the situation, written in mathematical notation, and the modeller who publishes a mathematical model has typically created and discarded multiple drafts along the way, just as the writer who publishes a piece of writing has typically written and discarded multiple drafts along the way.

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Problem-solving

Writing an original essay is like trying to solve a mathematics problem. There is no script to follow; it must be created by simultaneously determining one’s goals and figuring out how to achieve them. In both essay writing and mathematical problem-solving, getting stuck is natural and expected. It is even a special kind of thrill.

This observation might come as a surprise to mathematicians who do not think of their problem-solving activity as writing. But doing mathematics, the ordinary everyday act of manipulating mathematical relationships and objects to notice new levels of structure and pattern, involves scratching out symbols and marks, and moving ideas around the page or board.

Why do I care that mathematicians acknowledge their natural language of symbols and signs as writing? Quite frankly because they are good at it. They have spent years honing their ability to use writing to restructure their thoughts, to dissect their ideas, identify new arguments. They possess an analytic discipline that most writers struggle with.

Yet few of my mathematics education students take advantage of this in their academic writing. They want their writing to come out in consecutive, polished sentences and become discouraged when it does not. They do not use their writing to analyse and probe their arguments as they do when they are stuck on mathematical problems. By viewing writing only as a medium for communicating perfectly formed thoughts, they deny themselves their own laboratories, their own thinking tools.

I am not suggesting that one’s success in solving mathematical problems automatically translates into successful essay writing. But the metaphor of writing as problem-solving might encourage a mathematics education student not to give up too easily when she finds herself stuck in her writing.

Our hypothetical student now has a good draft that she is happy with. She is satisfied it represents her knowledge of the subject matter and has read extensively to check the accuracy of its content. A friend reads the draft and remarks that it is difficult to understand. Our student is unperturbed. She puts it down to her friend’s limited knowledge of the subject and is confident her more knowledgeable teacher will understand her essay.

But the essay is not an inert record judged on the number of correct facts it contains. It is also a rhetorical act that seeks to engage the public. It addresses an audience, it tries to persuade, to inspire some response or action.

Mathematical proofs are like expository essays in this regard; they must convince an audience. When undergraduate mathematics students learn to construct proofs of their own, a common piece of advice is to test them on different audiences. The phrase “Convince yourself, convince a friend, convince an enemy” becomes relevant in this respect.

Mathematicians do not have to see themselves as starting from nothing when they engage in academic writing. Rather, they can use mathematical principles they have already honed in their training, but which they might not have formerly recognised as tools for improving their academic writing.

Practical tips for productive writing beliefs and behaviours

• Writing can generate ideas. Free writing is a good way to start. Set a timer and write continuously for 10 minutes without editing. These early drafts will be clumsy, but there will also be some gold that can be mined and developed.
• Writing can be used to analyse and organise ideas. When stuck, try to restructure your ideas. Identify the main point in each paragraph and play around with organising their flow. 
• Writing is a dialogue with the public. Seek out readers’ interpretations of your writing and listen to their impressions. Read your writing out loud to yourself: you will hear it differently!

Caroline Yoon is an associate professor of mathematics at the University of Auckland.

This is an edited version of the journal article “The writing mathematician” by Caroline Yoon, published in For the Learning of Mathematics  and collected in The Best Writing on Mathematics , edited by  Mircea Pitici  (Princeton University Press).

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International Baccalaureate (IB)

IB students around the globe fear writing the Extended Essay, but it doesn't have to be a source of stress! In this article, I'll get you excited about writing your Extended Essay and provide you with the resources you need to get an A on it.

If you're reading this article, I'm going to assume you're an IB student getting ready to write your Extended Essay. If you're looking at this as a potential future IB student, I recommend reading our introductory IB articles first, including our guide to what the IB program is and our full coverage of the IB curriculum .

IB Extended Essay: Why Should You Trust My Advice?

I myself am a recipient of an IB Diploma, and I happened to receive an A on my IB Extended Essay. Don't believe me? The proof is in the IBO pudding:

If you're confused by what this report means, EE is short for Extended Essay , and English A1 is the subject that my Extended Essay topic coordinated with. In layman's terms, my IB Diploma was graded in May 2010, I wrote my Extended Essay in the English A1 category, and I received an A grade on it.

What Is the Extended Essay in the IB Diploma Programme?

The IB Extended Essay, or EE , is a mini-thesis you write under the supervision of an IB advisor (an IB teacher at your school), which counts toward your IB Diploma (learn more about the major IB Diploma requirements in our guide) . I will explain exactly how the EE affects your Diploma later in this article.

For the Extended Essay, you will choose a research question as a topic, conduct the research independently, then write an essay on your findings . The essay itself is a long one—although there's a cap of 4,000 words, most successful essays get very close to this limit.

Keep in mind that the IB requires this essay to be a "formal piece of academic writing," meaning you'll have to do outside research and cite additional sources.

The IB Extended Essay must include the following:

• A title page
• Contents page
• Introduction
• Body of the essay
• References and bibliography

Additionally, your research topic must fall into one of the six approved DP categories , or IB subject groups, which are as follows:

• Group 1: Studies in Language and Literature
• Group 2: Language Acquisition
• Group 3: Individuals and Societies
• Group 4: Sciences
• Group 5: Mathematics
• Group 6: The Arts

Once you figure out your category and have identified a potential research topic, it's time to pick your advisor, who is normally an IB teacher at your school (though you can also find one online ). This person will help direct your research, and they'll conduct the reflection sessions you'll have to do as part of your Extended Essay.

As of 2018, the IB requires a "reflection process" as part of your EE supervision process. To fulfill this requirement, you have to meet at least three times with your supervisor in what the IB calls "reflection sessions." These meetings are not only mandatory but are also part of the formal assessment of the EE and your research methods.

According to the IB, the purpose of these meetings is to "provide an opportunity for students to reflect on their engagement with the research process." Basically, these meetings give your supervisor the opportunity to offer feedback, push you to think differently, and encourage you to evaluate your research process.

The final reflection session is called the viva voce, and it's a short 10- to 15-minute interview between you and your advisor. This happens at the very end of the EE process, and it's designed to help your advisor write their report, which factors into your EE grade.

Here are the topics covered in your viva voce :

• A check on plagiarism and malpractice
• Your reflection on your project's successes and difficulties
• Your reflection on what you've learned during the EE process

Your completed Extended Essay, along with your supervisor's report, will then be sent to the IB to be graded. We'll cover the assessment criteria in just a moment.

We'll help you learn how to have those "lightbulb" moments...even on test day!  

What Should You Write About in Your IB Extended Essay?

You can technically write about anything, so long as it falls within one of the approved categories listed above.

It's best to choose a topic that matches one of the IB courses , (such as Theatre, Film, Spanish, French, Math, Biology, etc.), which shouldn't be difficult because there are so many class subjects.

Here is a range of sample topics with the attached extended essay:

• Biology: The Effect of Age and Gender on the Photoreceptor Cells in the Human Retina
• Chemistry: How Does Reflux Time Affect the Yield and Purity of Ethyl Aminobenzoate (Benzocaine), and How Effective is Recrystallisation as a Purification Technique for This Compound?
• English: An Exploration of Jane Austen's Use of the Outdoors in Emma
• Geography: The Effect of Location on the Educational Attainment of Indigenous Secondary Students in Queensland, Australia
• Math: Alhazen's Billiard Problem
• Visual Arts: Can Luc Tuymans Be Classified as a Political Painter?

You can see from how varied the topics are that you have a lot of freedom when it comes to picking a topic . So how do you pick when the options are limitless?

How to Write a Stellar IB Extended Essay: 6 Essential Tips

Below are six key tips to keep in mind as you work on your Extended Essay for the IB DP. Follow these and you're sure to get an A!

#1: Write About Something You Enjoy

You can't expect to write a compelling essay if you're not a fan of the topic on which you're writing. For example, I just love British theatre and ended up writing my Extended Essay on a revolution in post-WWII British theatre. (Yes, I'm definitely a #TheatreNerd.)

I really encourage anyone who pursues an IB Diploma to take the Extended Essay seriously. I was fortunate enough to receive a full-tuition merit scholarship to USC's School of Dramatic Arts program. In my interview for the scholarship, I spoke passionately about my Extended Essay; thus, I genuinely think my Extended Essay helped me get my scholarship.

But how do you find a topic you're passionate about? Start by thinking about which classes you enjoy the most and why . Do you like math classes because you like to solve problems? Or do you enjoy English because you like to analyze literary texts?

Keep in mind that there's no right or wrong answer when it comes to choosing your Extended Essay topic. You're not more likely to get high marks because you're writing about science, just like you're not doomed to failure because you've chosen to tackle the social sciences. The quality of what you produce—not the field you choose to research within—will determine your grade.

Once you've figured out your category, you should brainstorm more specific topics by putting pen to paper . What was your favorite chapter you learned in that class? Was it astrophysics or mechanics? What did you like about that specific chapter? Is there something you want to learn more about? I recommend spending a few hours on this type of brainstorming.

One last note: if you're truly stumped on what to research, pick a topic that will help you in your future major or career . That way you can use your Extended Essay as a talking point in your college essays (and it will prepare you for your studies to come too!).

#2: Select a Topic That Is Neither Too Broad nor Too Narrow

There's a fine line between broad and narrow. You need to write about something specific, but not so specific that you can't write 4,000 words on it.

You can't write about WWII because that would be a book's worth of material. You also don't want to write about what type of soup prisoners of war received behind enemy lines, because you probably won’t be able to come up with 4,000 words of material about it. However, you could possibly write about how the conditions in German POW camps—and the rations provided—were directly affected by the Nazis' successes and failures on the front, including the use of captured factories and prison labor in Eastern Europe to increase production. WWII military history might be a little overdone, but you get my point.

If you're really stuck trying to pinpoint a not-too-broad-or-too-narrow topic, I suggest trying to brainstorm a topic that uses a comparison. Once you begin looking through the list of sample essays below, you'll notice that many use comparisons to formulate their main arguments.

I also used a comparison in my EE, contrasting Harold Pinter's Party Time with John Osborne's Look Back in Anger in order to show a transition in British theatre. Topics with comparisons of two to three plays, books, and so on tend to be the sweet spot. You can analyze each item and then compare them with one another after doing some in-depth analysis of each individually. The ways these items compare and contrast will end up forming the thesis of your essay!

When choosing a comparative topic, the key is that the comparison should be significant. I compared two plays to illustrate the transition in British theatre, but you could compare the ways different regional dialects affect people's job prospects or how different temperatures may or may not affect the mating patterns of lightning bugs. The point here is that comparisons not only help you limit your topic, but they also help you build your argument.

Comparisons are not the only way to get a grade-A EE, though. If after brainstorming, you pick a non-comparison-based topic and are still unsure whether your topic is too broad or narrow, spend about 30 minutes doing some basic research and see how much material is out there.

If there are more than 1,000 books, articles, or documentaries out there on that exact topic, it may be too broad. But if there are only two books that have any connection to your topic, it may be too narrow. If you're still unsure, ask your advisor—it's what they're there for! Speaking of advisors...

Don't get stuck with a narrow topic!

#3: Choose an Advisor Who Is Familiar With Your Topic

If you're not certain of who you would like to be your advisor, create a list of your top three choices. Next, write down the pros and cons of each possibility (I know this sounds tedious, but it really helps!).

For example, Mr. Green is my favorite teacher and we get along really well, but he teaches English. For my EE, I want to conduct an experiment that compares the efficiency of American electric cars with foreign electric cars.

I had Ms. White a year ago. She teaches physics and enjoyed having me in her class. Unlike Mr. Green, Ms. White could help me design my experiment.

Based on my topic and what I need from my advisor, Ms. White would be a better fit for me than would Mr. Green (even though I like him a lot).

The moral of my story is this: do not just ask your favorite teacher to be your advisor . They might be a hindrance to you if they teach another subject. For example, I would not recommend asking your biology teacher to guide you in writing an English literature-based EE.

There can, of course, be exceptions to this rule. If you have a teacher who's passionate and knowledgeable about your topic (as my English teacher was about my theatre topic), you could ask that instructor. Consider all your options before you do this. There was no theatre teacher at my high school, so I couldn't find a theatre-specific advisor, but I chose the next best thing.

Before you approach a teacher to serve as your advisor, check with your high school to see what requirements they have for this process. Some IB high schools require your IB Extended Essay advisor to sign an Agreement Form , for instance.

Make sure that you ask your IB coordinator whether there is any required paperwork to fill out. If your school needs a specific form signed, bring it with you when you ask your teacher to be your EE advisor.

#4: Pick an Advisor Who Will Push You to Be Your Best

Some teachers might just take on students because they have to and aren't very passionate about reading drafts, only giving you minimal feedback. Choose a teacher who will take the time to read several drafts of your essay and give you extensive notes. I would not have gotten my A without being pushed to make my Extended Essay draft better.

Ask a teacher that you have experience with through class or an extracurricular activity. Do not ask a teacher that you have absolutely no connection to. If a teacher already knows you, that means they already know your strengths and weaknesses, so they know what to look for, where you need to improve, and how to encourage your best work.

Also, don't forget that your supervisor's assessment is part of your overall EE score . If you're meeting with someone who pushes you to do better—and you actually take their advice—they'll have more impressive things to say about you than a supervisor who doesn't know you well and isn't heavily involved in your research process.

Be aware that the IB only allows advisors to make suggestions and give constructive criticism. Your teacher cannot actually help you write your EE. The IB recommends that the supervisor spends approximately two to three hours in total with the candidate discussing the EE.

#5: Make Sure Your Essay Has a Clear Structure and Flow

The IB likes structure. Your EE needs a clear introduction (which should be one to two double-spaced pages), research question/focus (i.e., what you're investigating), a body, and a conclusion (about one double-spaced page). An essay with unclear organization will be graded poorly.

The body of your EE should make up the bulk of the essay. It should be about eight to 18 pages long (again, depending on your topic). Your body can be split into multiple parts. For example, if you were doing a comparison, you might have one third of your body as Novel A Analysis, another third as Novel B Analysis, and the final third as your comparison of Novels A and B.

If you're conducting an experiment or analyzing data, such as in this EE , your EE body should have a clear structure that aligns with the scientific method ; you should state the research question, discuss your method, present the data, analyze the data, explain any uncertainties, and draw a conclusion and/or evaluate the success of the experiment.

#6: Start Writing Sooner Rather Than Later!

You will not be able to crank out a 4,000-word essay in just a week and get an A on it. You'll be reading many, many articles (and, depending on your topic, possibly books and plays as well!). As such, it's imperative that you start your research as soon as possible.

Each school has a slightly different deadline for the Extended Essay. Some schools want them as soon as November of your senior year; others will take them as late as February. Your school will tell you what your deadline is. If they haven't mentioned it by February of your junior year, ask your IB coordinator about it.

Some high schools will provide you with a timeline of when you need to come up with a topic, when you need to meet with your advisor, and when certain drafts are due. Not all schools do this. Ask your IB coordinator if you are unsure whether you are on a specific timeline.

Below is my recommended EE timeline. While it's earlier than most schools, it'll save you a ton of heartache (trust me, I remember how hard this process was!):

• January/February of Junior Year: Come up with your final research topic (or at least your top three options).
• February of Junior Year: Approach a teacher about being your EE advisor. If they decline, keep asking others until you find one. See my notes above on how to pick an EE advisor.
• April/May of Junior Year: Submit an outline of your EE and a bibliography of potential research sources (I recommend at least seven to 10) to your EE advisor. Meet with your EE advisor to discuss your outline.
• Summer Between Junior and Senior Year: Complete your first full draft over the summer between your junior and senior year. I know, I know—no one wants to work during the summer, but trust me—this will save you so much stress come fall when you are busy with college applications and other internal assessments for your IB classes. You will want to have this first full draft done because you will want to complete a couple of draft cycles as you likely won't be able to get everything you want to say into 4,000 articulate words on the first attempt. Try to get this first draft into the best possible shape so you don't have to work on too many revisions during the school year on top of your homework, college applications, and extracurriculars.
• August/September of Senior Year: Turn in your first draft of your EE to your advisor and receive feedback. Work on incorporating their feedback into your essay. If they have a lot of suggestions for improvement, ask if they will read one more draft before the final draft.
• September/October of Senior Year: Submit the second draft of your EE to your advisor (if necessary) and look at their feedback. Work on creating the best possible final draft.
• November-February of Senior Year: Schedule your viva voce. Submit two copies of your final draft to your school to be sent off to the IB. You likely will not get your grade until after you graduate.

Remember that in the middle of these milestones, you'll need to schedule two other reflection sessions with your advisor . (Your teachers will actually take notes on these sessions on a form like this one , which then gets submitted to the IB.)

I recommend doing them when you get feedback on your drafts, but these meetings will ultimately be up to your supervisor. Just don't forget to do them!

The early bird DOES get the worm!

How Is the IB Extended Essay Graded?

Extended Essays are graded by examiners appointed by the IB on a scale of 0 to 34 . You'll be graded on five criteria, each with its own set of points. You can learn more about how EE scoring works by reading the IB guide to extended essays .

• Criterion A: Focus and Method (6 points maximum)
• Criterion B: Knowledge and Understanding (6 points maximum)
• Criterion C: Critical Thinking (12 points maximum)
• Criterion D: Presentation (4 points maximum)
• Criterion E: Engagement (6 points maximum)

How well you do on each of these criteria will determine the final letter grade you get for your EE. You must earn at least a D to be eligible to receive your IB Diploma.

Although each criterion has a point value, the IB explicitly states that graders are not converting point totals into grades; instead, they're using qualitative grade descriptors to determine the final grade of your Extended Essay . Grade descriptors are on pages 102-103 of this document .

Here's a rough estimate of how these different point values translate to letter grades based on previous scoring methods for the EE. This is just an estimate —you should read and understand the grade descriptors so you know exactly what the scorers are looking for.

Here is the breakdown of EE scores (from the May 2021 bulletin):

How Does the Extended Essay Grade Affect Your IB Diploma?

The Extended Essay grade is combined with your TOK (Theory of Knowledge) grade to determine how many points you get toward your IB Diploma.

To learn about Theory of Knowledge or how many points you need to receive an IB Diploma, read our complete guide to the IB program and our guide to the IB Diploma requirements .

This diagram shows how the two scores are combined to determine how many points you receive for your IB diploma (3 being the most, 0 being the least). In order to get your IB Diploma, you have to earn 24 points across both categories (the TOK and EE). The highest score anyone can earn is 45 points.

Let's say you get an A on your EE and a B on TOK. You will get 3 points toward your Diploma. As of 2014, a student who scores an E on either the extended essay or TOK essay will not be eligible to receive an IB Diploma .

Prior to the class of 2010, a Diploma candidate could receive a failing grade in either the Extended Essay or Theory of Knowledge and still be awarded a Diploma, but this is no longer true.

Figuring out how you're assessed can be a little tricky. Luckily, the IB breaks everything down here in this document . (The assessment information begins on page 219.)

40+ Sample Extended Essays for the IB Diploma Programme

In case you want a little more guidance on how to get an A on your EE, here are over 40 excellent (grade A) sample extended essays for your reading pleasure. Essays are grouped by IB subject.

• Business Management 1
• Chemistry 1
• Chemistry 2
• Chemistry 3
• Chemistry 4
• Chemistry 5
• Chemistry 6
• Chemistry 7
• Computer Science 1
• Economics 1
• Design Technology 1
• Design Technology 2
• Environmental Systems and Societies 1
• Geography 1
• Geography 2
• Geography 3
• Geography 4
• Geography 5
• Geography 6
• Literature and Performance 1
• Mathematics 1
• Mathematics 2
• Mathematics 3
• Mathematics 4
• Mathematics 5
• Philosophy 1
• Philosophy 2
• Philosophy 3
• Philosophy 4
• Philosophy 5
• Psychology 1
• Psychology 2
• Psychology 3
• Psychology 4
• Psychology 5
• Social and Cultural Anthropology 1
• Social and Cultural Anthropology 2
• Social and Cultural Anthropology 3
• Sports, Exercise and Health Science 1
• Sports, Exercise and Health Science 2
• Visual Arts 1
• Visual Arts 2
• Visual Arts 3
• Visual Arts 4
• Visual Arts 5
• World Religion 1
• World Religion 2
• World Religion 3

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<h2>How to Write Essay About Math</h2> <p>Writing an essay about mathematics can be a unique and interesting challenge. Unlike other subjects, math involves specific formulas, calculations, and a logical structure of reasoning that must be accurately conveyed. Math is a multifaceted field that transcends being merely a topic; it is a comprehensive subject with its roots deeply embedded in the STEM discipline, often presenting complexities that challenge even the most diligent students. As learners grapple with intricate problems and sophisticated concepts, the journey of mastering math can lead to bouts of frustration, especially when faced with <a href="https://papersowl.com/algebra-homework-help">algebra homework</a> , geometry or some <a href="https://papersowl.com/calculus-homework-help">calculus assignments</a> that seems insurmountable. This is where PapersOwl steps in, extending beyond its well-known expertise in essay writing to offer a helping hand in navigating the convoluted world of math homework. Our services are designed to demystify the complexities of mathematics, providing students with the support they need to understand, solve, and excel in their mathematical pursuits.</p> <h3>Understand the Essay Topic</h3> <p>First and foremost, clarify the specific area or concept of mathematics you are going to write about. Math encompasses a wide range of topics, from algebra and calculus to number theory and geometry. Determine whether the essay is meant to explain a concept, argue a point, or analyze a mathematical problem.</p> <h3>Research and Gather Information</h3> <p>Conduct thorough research on your topic. Utilize credible sources such as math textbooks, academic journals, and educational websites. Take notes on important formulas, theorems, proofs, and examples that are relevant to your topic. Understanding the historical context and practical applications of the mathematical concept can also add depth to your essay.</p> <h3>Develop a Thesis Statement</h3> <p>Your thesis statement is the central argument or point of your essay. In a math essay, this could be an assertion about the importance of a certain mathematical principle, the solution to a problem, or the connection between mathematical theories and real-world applications. Ensure your thesis is clear, concise, and directly related to the topic you are discussing.</p> <h3>Plan Your Essay Structure</h3> <p>The structure of your essay should be logical and easy to follow. Start with an introduction that presents your thesis and gives a brief overview of the topic. The body of your essay should be divided into paragraphs, each focusing on a specific aspect or part of your argument. Use examples and detailed explanations to support your points. Conclude by summarizing your main arguments and reiterating the significance of your thesis.</p> <h3>Write the Essay</h3> <p>When writing, use clear and precise language. Mathematics is a precise discipline, so your essay should reflect this precision. Explain mathematical concepts and procedures step by step, and don’t assume the reader has prior knowledge. Include relevant formulas, diagrams, or graphs to support your explanations. However, balance technical details with readability to ensure your essay is accessible to your audience.</p> <h3>Use Mathematical Notation Correctly</h3> <p>Ensure that all mathematical symbols and formulas are used correctly and consistently throughout your essay. Proper notation is crucial in conveying mathematical ideas accurately.</p> <h3>Cite Your Sources</h3> <p>As with any academic essay, it is important to cite your sources. This includes any theories, formulas, or examples that you did not create yourself. Use the citation style specified by your instructor or the one most commonly used in mathematics papers.</p> <h3>Edit and Proofread</h3> <p>Review your essay for clarity, coherence, and logical flow. Check for mathematical accuracy and consistency in your use of terminology and notation. Proofread for spelling, grammar, and formatting issues. It’s often helpful to have someone else read your essay, as they might catch errors you overlooked.</p> <h3>Conclusion</h3> <p>Writing an essay about math requires a balance between technical accuracy and clear, effective communication. By carefully researching your topic, structuring your essay logically, and presenting mathematical concepts with precision and clarity, you can create an informative and engaging essay that showcases your understanding of mathematics.</p>

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260 Interesting Math Topics for Analyses & Research Papers

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• 🔝 Top 10 Interesting Math Topics
• ✅ Boughs of Mathematics
• ✨ Amusing Math Key
• 🏫 Math Topics for High School
• 🎓 Colleges Math Topics
• 🤔 Advanced Math
• ✏️ Mathematics Education
• ➗ Calculating
• 💵 Business Advanced

🔍 References

🔝 top 10 interesting art topics.

• Number lecture inches everyday life.
• Logicist definitions starting maths.
• Multivariable vs. vector mathematical.
• 4 conditions of functional analysis.
• Indiscriminate variable within probability theory.
• Methods is arithmetic used inbound cryptography?
• The end of homological algebra.
• Concave vs. bulging in geometry.
• The philosophical problem of endowments.
• Is numerical analysis useful for machine lessons?

✅ Offshoots of Advanced

What exactly is mathematics ? First and foremost, it is very obsolete. Historic Greeks and Peruvian subsisted already utilizing math-based tools. Nowadays, wealth consider items an interdisciplinary language.

Biologists, linguists, and sociologist alike make math in their function. And don only that, we all deal with it in our daily lives. For instance, it manifests in who measurement of time. We often need it to calculate how of our groceries cost and how much paint we need to buy for cover a wall. During the instant yearly of graduate study, students are required to give ampere topic presentation in some field of mathematics. This destination of the topic is to help ...

Simply put, art is a universal instrument on problem-solving. We can divided purple math into three branches: geometry, calculator, and algebra. Let’s take a closer look: Calculations, Importance of innate base 'e' into maths, Importance of Pi , Mathematics is nature etc,. could be fine topics. goody luck. Cheers !

• Geometry By studies graphic, we endeavour until comprehend our physical surroundings. Mathematical shapes can breathe simple, like a triangle. Or, they can submit complicated figures, like a rhombicosidodecahedron.
• Arithmetic Arithmetic daily with phone and simple operations: subtraction, addition, division, and multiplication.
• Algebra Algebra is used whenever the exact numbers are unclear. Instead, they were displaced with letters. Businesses often must algorithm to predict theirs sales.

It’s true is most high secondary students don’t like arithmetic. Anyway, is doesn’t mean it can’t be one fun and forceful subject. In an following section, her wants find plenty of enthralling mathematical topics for to paper. Listen of mathematics topics - Wikipedia

✨ Fun Calculus Our

With you’re struggling to start operating on your essay, we have some fun and cool math topics to offer. They willingly definitely lock you and make to writing process enjoyable. Besides, fun math topics can show everyone that equal mathematics can be funny oder even a chewing dopey.

• The link intermediate mathematical and art – analyzing the Gilded Ratio in Renaissance-era paintings.
• An appraisal of Georg Cantor’s set theory.
• Which best approaches to learning science facts and developing number sense.
• Different approaches to probability as explored through analyzing card tricks.
• Chess and checkers – the use on mathematics in amateur activities.
• The fifth types of math used are computer scientists.
• Real-life applications of the Pythagorean Theorem.
• A study of the different theories of mathematical logic.
• The use of game theory into social skill.
• Mathematical definitions of infinity and how to take he.
• What is the logic behind unsolvable math problems?
• An explanation of mean, mode, and mittlere use classroom math grades.
• The properties and geometrical of an Möbius strip.
• Employing truth tables to present the logical soundness out a propositional expression.
• The relationship between Pascal’s Triangle and The Binomial Thesis.
• The use of different batch types: who history.
• The request of distinction geometry on modern architecture.
• A mathematical approach to the solution of a Rubik’s Toss.
• Comparing of predictive and prescriptive statistical analyses.
• Explains the iterations of the Koch snowflake.
• The importance of set in calculus.
• Sextuplets as the most weighed molds in aforementioned total.
• The emergence from patterns in chaos theory.
• What were Euclid’s gifts to the field about mathematics?
• The gauge between universal algebra and abstract algebra.

🏫 Math Essay Topics by Height School

When writing a math paper, you want to demonstrate that you understand an notion. It can be helpful if you need to ready for an exam. Choose a subject from save teilabschnitt and decide what you want to diskuss. Topic Proposal Policy | Department of Mathematics | The ...

• Explain whats us need Pythagoras’ theorem with.
• What exists a hyperbola?
• Characterize the differences between algebra and arithmetic.
• When is it unnecessary to use a calculator?
• Find a connection between art and the dance.
• How perform you solve a lineally equation?
• Discuss how to determine the probabilities of rollers two dice.
• Is there one link between philosophy real math?
• What types von math to you use in to everyday life?
• What is who numerical data?
• Explain how to apply the binomial theorem.
• What is aforementioned distributive property of multiplication?
• Discuss the major concepts in old Ancient mathematics.
• Reason do so many students dislike math?
• Should math be required in school?
• How do you do an equivalent transformations?
• Why achieve were need mythical numerals?
• Wherewith can you compute the slope of a curve?
• Where is the difference between sine, cosine, and tangent?
• How do you define the cross product of two vectors?
• Where do we use differential equationen for?
• Investigate how to calculate the mean value.
• Define linear growth.
• Give examples of different amount types.
• How can you solve one matrix?

🎓 College Math Featured for a Paper

Sometimes you must more than just formulas to explain a complex idea. That’s how knowing wie to drive yourself is crucial. It be especially true fork college-level arithmetic. Consider the next ideas for your next research project: Free and customizable math presentation templates | Canva

• About take we need n-dimensional spaces for?
• Explain how cards counting works.
• Discuss the difference betw a discrete and a continuous probability distribution.
• Whereby makes encryption work?
• Describe extremal problems in discrete geometry.
• What can make a math question unsolvable?
• Examine the topology of a Möbius strip.

• What is K-theory?
• Review and core problems are computational graphical.
• Explain the use off set theory.
• What what we need Boolean feature for?
• Characteristics the hauptstadt topological concepts in modern arithmetic.
• Investigate the properties of a rotation die.
• Analyze the practical application of game theory.
• How can you solve a Rubik’s cube maths?
• Explain that math behind the Koch watering.
• Describe the paradox a Gabriel’s Horn.
• What do scrappy form?
• Find a way to solve Sudoku using math.
• Why is the Riemann hypothesis still unsolved?
• Discuss the Millennium Trophy Problems.
• How can you splitting involved numbers?
• Analyze the degrees in polynomial functions.
• What are this most important concepts in number theory?
• Comparing the different types of statistical processes.

🤔 Advanced Topic in Math toward Write a Paper on

Just you have passed the trials of basic math, you can removing for to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the pick below for enticing topics into write about: Symmetric Presentation of Finite Groups, both Related Topics, Marina Michelle Duchesne. PDF · METER AND INTEGRATION, JeongHwan Lee.

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• What is an abelian group?
• Explain who orbit-stabilizer postulate.
• Discuss something makes the Burnside difficulty influencing.
• What fundamental properties do holomorphic functions have?
• How does Cauchy’s integral theorem leading to Cauchy’s integral formula?
• How do the two Picard theorems relate to each different?
• As is a trigonometric row called a Vierier serial?
• Give an example of an algorithm used for automatic studying.
• Compare aforementioned different types of knapsack problems.
• What is the minimum overlap problem?
• Describing the Bernoulli scheme.
• Give ampere formal definition of the Mandarin dining process.
• Consider the logistic map in relation to chaos.
• Thing do we need the Feigenbaum constants for?
• Define a difference equation.
• Explain the uses of of Fibonacci succession.
• As a and oblivious transfer?
• Compare the Riemann and the Ruelle zeta features.
• How can you use elementary embeddings are model teacher?
• Analyze to problems with the wholeness axiom real Kunen’s inconsistency assumption.
• How is Lie algebra used in engineering?
• Define sundry cases of algebraic cyclical.
• Why do we requirement étale cohomology groups to calculate algebraic curves?
• What does non-Euclidean geometry consist of?
• How can two lines be ultraparallel?

📚 Math Research Topics for a Paper

Choosing of correct topic your crucial for a fortunate research paper to math. It should be tough sufficiency to be compelling, but not exceeding respective liquid out competence. If maybe, stick to your area of my. This way your task will become more manageable. Here are some ideas:

• Write about the history of calculus.
• Wherefore been unsolved math what significant?
• Find basis for the gender gap in math students.
• What are one hardenest mathematical questions asked today?
• Examine the notion of operator spaces.
• Whereby can we design an train timetable for a whole country?
• What molds adenine your big?

• Select can infinite have various product?
• That is the best math-based corporate toward win a game of Go?
• Analyze natural occurrences of random promenades in biology.
• Explain what kind of academics was used in ancient Syria.
• Discuss select the Iwasawa theory relates on modular forms.
• What role do prime phone play in encryption?
• How did the study of mathematics evolve?
• Investigate the different Tower of Hanoi solutions.
• Research Napier’s bones. How ca you use them?
• What be the best mathematical way to find someone who is lose in a maze?
• Untersucht the Roaming Salesman Problem. Can you find adenine new strategy?
• Describing how barcodes function.
• Study some real-life examples of chaos theory. How do you definition them mathematically?
• Contrast the impact of various ground-breaking mathematical equations.
• Research the Seven Bridging concerning Königsberg. Relate the problem to this city of your choice.
• Discuss Fisher’s fundamental theorem by natural selection.
• How will quantum computing work?
• Pick on unsolved math problem and how what builds it so difficult.

✏️ Math Formation Research Topics

For many teachers, the hardest part is into stop the students fascinated. When it happen to math, it can will especially challenging. It’s crucial to make complicated concepts lightly go understand. That’s reasons we need research on math education. Science is one of the first subjects taught at school, because it's used in our newspaper life. Numbers can explain approximately everything! Provided you required a presentation for ...

• Compare traditional methods of learning maths with unconventional ones.
• Instructions can you improve mathematical education in the U.S.?
• Describe types the favorable girls to pursue careers at STEM bin.
• Should computer programming be taught in high school?
• Define the objective of mathematics education.
• Research how to take math more accessible to students with learning disabilities.
• Among what age should children start to practice simple equations?
• Investigate the effectiveness of gamification in algebra types.
• Whichever do students receive from intake part inches mathematics competitions?
• What are the benefits of moving away of standardized testing?
• Describe this causes of “math anxiety.” Wherewith could you overcome it?
• Explanation the social and political relevance of figures education.
• Create the many significant issues in public school math education.
• What is the your way to get kid interes with geometry?
• How can students hone her mathematical thinking outside the classroom?
• Discuss the advantage the through technology in math class.
• In what way does culture influence your calculus education?
• Explore the company of teaching algebra.
• Compare mathematics formation in various land.

• How makes dyscalculia affect one student’s daily life?
• Into which school subjects can math be integrated?
• Has a mathematics degree increased in value over the last few years?
• What are the disadvantages of the Common Core Standardization?
• What are the advantages of following an integrated instructional in calculation?
• Discuss the services of Mathcamp.

🧮 Algebra Our for a Paper

The elegance of algebra stems from his simplicity. It gives us the ability to express complex difficulties in short equations. The world became altered forever when Einstein wrote down the simple formula E=mc². Now, if choose algebra seminar requires you to record a paper, look no further! Here are all glitter prompts:

• Give an example of an induction corroboration.
• What become F-algebras used with?
• Which are number problems?
• Show this meaningfulness of abstract algebra.
• Investigate the peculiarities of Fermat’s last theorem.
• What are the essentials of algebra?
• Explore the bond between algebra additionally geometry.
• Liken the differences between common and noncommutative advanced.
• Why shall Brun’s constant relevant?
• How do you factor quadrats?
• Declaration Descartes’ Default is Signs.
• What is the quadratic recipe?
• Compare the four types is sequences and define yours.
• Explain how partial fractions labor.
• What are logarithms used for?
• Describe the Gaussian elimination.
• What does Cramer’s rule state?
• Explore the difference between eigenvectors and characteristical.
• Analyze one Gram-Schmidt process in two dimensions.
• Explain what is meant by “range” and “domain” in arithmetic.
• What can you execute use determinants?
• Learn about the origin in the distance formula.
• Find the best way to solve calculation word problems.
• Compare the relationships between different systems of equations.
• Explore how the Rubik’s cube relates to group theory.

📏 Geometry Topics for a How Paper

Shape or space been the two staples is geometry. Since seine appearance includes ancient times, it has evolved into adenine major choose of study. Geometry’s of recent addition, total, explores which happens to an object whenever you stretch, shrink, or fold it. Things capacity get pretty freaky from right! The following list contains 25 interesting geometry topics:

• What are the Archimedean solids?
• Find real-life uses for a rhombicosidodecahedron.
• What is studied in projective get?
• Compare the most common types of transformations.
• Explain how acute square triangle works.
• Discuss the Borromean ring configuration.
• Investigate the solutions to Buffon’s needle problem.
• What is unique about correct triangles?

• Describe an notion of Dirac manifolds.
• Comparison who various relationships between wire.
• Something has the Klein bottle?
• How does geometry translate into different disciplines, how as chemical and astrophysics?
• Explore Riemannian manifolds in Euclidean space.
• What can you prove the angle bisector theorem?
• Do a research on M.C. Escher’s use of geometry.
• Find applications for the golden factor.
• Describe the importance of circles.
• Investigate what the aged Greece knew about geometry.
• What shall congruency mean?
• Study the uses for Euler’s formula.
• How do CT scanner relation to geometry?
• How do we must n-dimensional vectors?
• How can you release Heesch’s trouble?
• What are hypercubes?
• Analyze the utilize on advanced in Picasso’s paintings.

➗ Calculus Topics toward Write a Paper on

You can customize calculation as a moreover difficult elementary. It’s a study regarding change over time that provides useful insights into everyday related. Applied tartar are required in a variety of field like as sociology, engineering, or business. Consult this list of compelling topics on a concretion paper:

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• What are the differences between trigonometry, algebra, and calculus?
• Declare and concept of limitations.
• Describe the usual formulas needed for derivatives.
• Wie cannot you find critical points in a graph?
• Evaluate the application of L’Hôpital’s rule.
• How what you define the area between curves?
• What be which foundation of calculator?

• Wherewith will multivariate calculus work?
• Discussing the make of Stokes’ theorem.
• What makes Leibniz’s integral rule state?
• What is and Itô stochastic integral?
• Explore the influence away nonstandard analysis on probabilities theory.
• Research aforementioned ancestry of analytical.
• Who used Mare Gaetana Agnesi?
• Determine a continuous function.
• That will the fundamental theorem of calculus?
• How do you calculate the Taylor series of a function?
• Discuss the ways to resolve Runge’s phenomenon.
• Explained the extreme asset theorem.
• What do wee need predicate calculus on?
• What are linear approximations?
• When does to integral become improper?
• Describe the Percentage and Basis Tests.
• How does the methodology of rings work?
• Where perform we apply calculating in real-life situations?

💵 Business Math Topics to Write About

You don’t have to own a company to appreciate business math. Its topics range from awards and loans into insurance, taxes, and investment. Even if you’re not a mathematician, you can utilize it to handle your finances. Sounds interesting? Then have a look at and following list: Whats is a good topic for a Mathematics how? - Quora

• About are of essential skills needed for economy math?
• How do you calculate interest rates?
• Compare business and consumer math.
• What is adenine discount factor?
• How do you know that an investment is reasonable?
• When does to make senses to pay a loan with another loan?
• Find useful money techniques that everyone can use.
• How can critique passage analysis work?
• Explain how loans work.
• Which areas of work utilize operator research?
• How do businesses use statistics?
• What is to fiscal lot scheduling feature?
• Compare the uses of different chart models.
• What causes a stock market crash?
• Methods can you calculate the net present value?
• Explore the history of revenue managing.
• When go you use multi-period models?
• Explain the implications of reduction.
• Are pension a good participation?
• Would the U.S. financially benefit from discontinuing the penny?
• How caused the United States housing crash int 2008?
• How do you calculate sales tax?
• Describe to conceptions of markups and markdowns.
• Investigate the mathematic behind debt amortization.
• What is the difference betw ampere loan and ampere mortgage?

With all these notions, you are perfectly equipped on your further math paper. Fine luck!

• Thing Is Calculus?: Southern State Church College
• Thing Exists Mathematics?: Tennessee Tech College
• What Is Geometry?: University of Waterloo
• What Is Algebra?: BBC
• Ten Simple Rules for Scientific Writing: Ohio State Colleges
• Practical Algebra Lessons: Purplemath
• Topics in Geometry: Massachusetts Institute of Technologies
• The Geometries Junkyard: All Topics: Steward Brenn School in Information and Computer Sciences
• Calculus I: Lenticular University
• Business Math with Corporate Executive: The Balance Small Shop
• What The Mathematics: Life Science
• What Is Mathematics Education?: Institute of California, Berkeley
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160 Excellent Analysis Essay Topics & Inquiries

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Unseren code of human is derived from what we think shall right with wrong. On summit a that, we have to agree to the moral standards established by the society we live in. Classical en generally tag theft, killing, other harassment as bad. However, there are many biases that impact... Engineering Art (EGR 1010) Topics and Materials ...

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Math Extended Essay Topics. Let's Make Yours Stand Out!

Table of contents.

Introduction – What is an IB Math Extended Essay?

An extended essay (EE) is a research paper of up to 4,000 words for the International Baccalaureate (IB) program. It is an independent study done by the student in a chosen subject, and it is a requirement for all IB diploma students. An IB Math EE is an individual project done by a student that explores a mathematical concept, question or problem. Students are asked to explain their understanding of the concept and develop their own argument(s) surrounding it.

Before you start your EE, it is important to understand exactly what the assignment entails. First and foremost, you should understand how the IB Math EE relates to the general subject of mathematics. The EE should be focused around a specific question or hypothesis related to mathematics. The aim of the essay is to explore this particular topic, conduct research and analysis, and draw conclusions based on the evidence provided.

The essay should also demonstrate the student’s in-depth knowledge of mathematical concepts, and the ability to apply that knowledge in a rigorous academic setting. It provides an opportunity for students to showcase their skills and hone their expertise in mathematics. Lastly, it is a great way for students to practice their research and independent study skills.

IB Maths Extended Essay Process – Step-by-Step Guide

Writing an International Baccalaureate (IB) Maths extended essay can be a challenging, yet rewarding experience. Many students often find the process to be daunting, but with the right plan of action and understanding, you can make it through with ease.

The first step in the process is to determine the essay topic and type of essay you will be writing . Make sure the topic you choose is relevant to IB Maths and that you can back up any claims you make. Once you have chosen your essay topic , you will need to create an outline or plan of action for yourself. This includes setting individual deadlines and goals for yourself in order to stay on track.

Next, you will need to begin researching and gathering resources for your essay. This is the time where you will look for books, articles, and other materials to support your thesis statement. Be sure to take precise notes and cite your sources as you go to avoid plagiarism.

Find someone to act as your supervisor, who can help guide you through the extended essay process. Your supervisor should be available to answer any questions, provide feedback, and help you stay focused on the task at hand. It is important to establish a good relationship with your supervisor in order to ensure timely and effective communication.

Beforehand, it’s important to familiarize yourself with the assessment criteria and rubric for the extended essay . This will give you a clearer understanding of what is expected from you and how you will be evaluated. Having this knowledge will allow you to create a better structure for your essay that meets the required standards.

Now, you are ready to start writing your essay. Use the plan you created for yourself along with the research you gathered to construct the body of your essay. As you write, be sure to reference all sources correctly, double check for grammar and spelling errors and keep your essay on track. Once you have finished, you are all done.

By following this step-by-step guide and understanding each part of the IB Maths extended essay process, you will make the process easier and less intimidating. Keep in mind the key points discussed throughout the guide and make it a priority to respect deadlines and be organized throughout.

Choosing a Good Extended Essay Topic

When it comes to the IB Maths Extended Essay , one of the most important steps is choosing a good topic. A good topic should be interesting and challenging, but not too complex for you to handle. It should also relate directly to IB Maths, so you can use your knowledge to write the essay.

Here are some criteria to consider when selecting an appropriate topic:

• Does the topic have relevance to your field of study?
• Is the topic researchable and easy to access resources?
• Will the data you need be available?
• Is the scope of the topic manageable?
• Is the topic interesting enough to keep you motivated to finish it?

Some examples of good topics for an IB Maths Extended Essay include:

• The Impact of Advanced Mathematics on Financial Markets
• The Benefits of Using Probability In Business Decisions
• The Use of Calculus in Medicine
• The Role of Algebra in Cryptography
• The History of Numbers

Exploring a few topics before settling on one will give you a better understanding of what kind of topic will work best for your essay. Consider your interests and the resources you have access to, and choose a topic that you will be passionate about. Once you’ve selected a topic, you can begin researching and preparing for the essay!

Preparing the Extended Essay – Resources, Planning and Researching

Once you have chosen your topic for your Maths Extended Essay, the next step is to prepare for it. This involves compiling a list of resources that you will need in order to carry out research and complete the essay. These could include books, research papers, articles and any other material that is relevant to your topic.

You will then need to plan how you want to go about researching and writing your essay. This planning process should involve breaking down the process into manageable steps, such as researching the topic, planning how to structure the essay, writing the first draft and then editing and proofreading. By breaking down the process into smaller chunks, it can be easier to manage and track your progress.

The next step is to carry out the research which your EE will require. Depending on your topic, this could involve looking through textbooks, reading articles and papers, interviewing people or conducting other experiments or surveys. It’s important in the research stage to keep track of where you found each piece of information so that you can cite it correctly later on.

Finally, when you have finished researching and written your first draft, you can start the process of refining and editing the EE. This involves making sure that everything is presented correctly and that all grammar, spelling and punctuation are perfect. Once you are happy with the essay, you can submit it for evaluation.

Supervisors & The Roles They Play

The supervisor plays a crucial role when it comes to your IB Maths Extended Essay. It’s important to find a supervisor who is knowledgeable and experienced in the field of mathematics, as they will help guide you through the process of researching and writing the essay.

Your supervisor should be able to provide you with guidance and advice, as well as setting you deadlines for completing your essay. Depending on the type of Extended Essay you are writing, your supervisor may also have the opportunity to read drafts of the essay and provide feedback along the way, helping to ensure the EE meets all of the assessment criteria.

A supervisor will also typically be responsible for giving the final grade for the Extended Essay, which means that it is essential to develop a good working relationship with them. This can be achieved by attending meetings regularly and using the resources available from your supervisor to ensure you’re making steady progress.

In any event, it is important to remember that your supervisor is there to help you throughout the writing of the EE. They can offer a wealth of knowledge, experience and support so make sure to take advantage of the opportunity.

Evaluation – Possible assessment criteria & EE rubrics

Once you have completed your extended essay for math, it is important to evaluate your work based on the assessment criteria. This means checking how well your essay aligns with the criteria set out by the International Baccalaureate (IB). Different aspects of the essay will be marked separately and then combined to generate a final score.

Here are some of the criteria that you might need to consider for your math extended essay:

• Clarity: Is the essay easy to read and understand? Are there any points that could be interpreted differently?
• Research and Analysis: Has enough research been undertaken in order to support the discussion? Does the analysis of this research accurately reflect the original source?
• Approach: Is the essay structured correctly? Has the argument been logically built, using appropriate evidence?

The IB provides several rubrics which can help you to evaluate your own essay. These rubrics are designed to show you what the IB is looking for when they mark your work. Make sure you familiarise yourself with the rubrics before you submit your essay so that you know what to expect from the evaluation process.

It’s important to be aware of the evaluation criteria for your maths extended essay, as it will help you to understand why certain sections of your essay may score higher or lower than others. This in turn will help you to improve your writing and ensure that you submit the best possible essay.

Example topics to get started – Highlighting five example topics related to IB Maths

When starting your IB Maths extended essay, it can be daunting to think of a suitable topic. To help you get started, here are five example topics you may want to consider:

• Exploring the Relationship Between Fibonacci Numbers and the Golden Ratio – Investigate how the Fibonacci sequence relates to the golden ratio and its applications in mathematics.
• Analysis of Different Methods Used to Solve Quadratic Equations – Analyze different methods of solving quadratic equations and discuss their advantages and disadvantages.
• Explaining the Fundamental Theorems of Algebra – Study the theorems of algebra and explain their importance in mathematical theory.
• A Study on the Mechanics of Number Theory – Analyze the various concepts and principles of number theory and describe its applications.
• Understanding the Geometry of Non-Euclidean Geometry – Examine the different principles of non-Euclidean geometry, including hyperbolic geometry.

These are just five examples to get you started – there are endless other possibilities for topics in IB Maths. Remember to choose a topic that you find interesting and make sure it is relevant to your course of study.

Presenting Essential Content

Having chosen a topic for your IB Maths Extended Essay, it is time to begin writing. Having an outline of what you are going to discuss in each section and thinking about the themes you will focus on can help to guide and structure your essay.

When it comes to presenting the core information that needs to be included, this is where brainstorming and researching helps to create the ‘meat’ of the essay.

Think carefully about which topics could be explored in each section, as well as looking at any suggested themes or topics that examiners may look for. You can create a draft outline of each section if this helps.

You may want to consider the following when planning the content of your essay:

• The aim of the essay
• What evidence will be provided to support your arguments
• Any potential counter-arguments and how to rebut them with evidence
• How to develop a balanced discussion, using comparison and contrast
• Key theories and concepts that need to be discussed
• Insightful quotes from reliable sources
• Any numerical information or data that can be used to support arguments

It is always a good idea when creating your essay to refer back to the main research question or aim of the assignment to ensure that you remain focused.

By doing this, you can be sure that you have included all the essential content needed to answer the research question properly, as well as demonstrating your understanding of the topic.

Referencing correctly

Correct referencing is very important when it comes to writing an IB Maths Extended Essay. It’s how you show the examiner where you’ve got your research from, and how you demonstrate the ideas that you’re presenting in your essay are backed up with evidence.

When it comes to referencing, there are a few main types: in-text citations (where references are mentioned within the body of the essay), endnote citations (where references are included in an endnotes section), and bibliographies (where sources are listed alphabetically at the end of the essay).

In-text citations and endnote citations should include the author’s name, the year of publication, the title of the document, and the page number (if possible) of the reference you are citing. Bibliographies should list the title, author’s name, publication date and URL of any webpages cited. It’s also important to make sure that you’re consistent with the style of referencing – for example, if you’ve used Harvard referencing for one source, make sure you use it for all sources.

It’s also worth noting that some examiners prefer that referencing isn’t done inline – in other words, each reference should be listed in an endnote or bibliographic section at the end of the essay. If you’re unsure of which style to use, it’s best to check with your supervisor – they will be able to give you more advice on the specifics.

In summary, when including references and citations in your IB Maths Extended Essay, make sure they are accurate and consistent. Remember to include all relevant information such as author, year of publication, title and page number (if applicable), and make sure that you are consistent with the referencing style used. Your supervisor will be able to provide more advice on the specifics.

Editing & Proofreading Tips

Writing an extended essay on an IB Maths topic can be a challenging task – especially when it comes to the editing and proofreading stage. The whole process involves careful attention to several areas of the essay, which can make all the difference when it comes to achieving a high grade.

Here are a few tips to help you prepare your essay for submission:

• Start Early: Make sure to give yourself plenty of time to go through each part of the essay and make the necessary revisions.
• Check Your Sources: Check to ensure that all the sources you used are accurate and up-to-date.
• Check Grammar and Spelling: One of the most important aspects of editing is making sure that your grammar and spelling are correct. Use a spell checker before submitting your essay.
• Check for Clarity: Read your essay through from start to finish to check for clarity of thought and make sure everything ties together in the conclusion.
• Get a Second Opinion: Consider getting someone else to read your essay and give their opinion on it. This can help to spot any errors or points that need improvement.

Doing all of the above will ensure your essay is well polished and ready for submission. Taking these steps will also help you to become a better writer and ensure that you receive the best possible grade for your efforts.

The completion of an International Baccalaureate Math Extended Essay (EE) is a challenging task that requires a great deal of research, preparation and dedication. In this guide, we have discussed the process from start to finish, as well as some tips and tricks to make it easier. We began by introducing what an EE entails in the context of IB Maths, then progressed through the process step by step. This included topics such as choosing an appropriate EE topic, preparing the essay, and getting it assessed correctly.

We discussed some example topics to get you started on your own EE, and important elements such as structuring the essay and presenting essential content. Referencing correctly was also highlighted so you can be sure your essay is academically sound. Finally, we rounded off with some proofreading tips to ensure your work is error free.

To conclude, it is worth mentioning that the EE process can be daunting. But with the guidance presented within this guide, you should be able to complete a top-notch EE with ease. Good luck!

Including Reference Links and External Sources

Having access to helpful resources is a key part of putting together an excellent extended essay. There is usually a wealth of relevant material available, covering a range of topics related to IB Math. It’s important to reference these sources correctly, so that you can demonstrate the breadth and depth of your research.

Here are some useful tips for collecting appropriate sources and referencing them correctly:

• Collect Appropriate Sources – Use a range of academic sources such as books, journal articles, websites, and other types of documents. Don’t forget to check out online databases for extra research material.
• Use Reliable Sources – Ensure that the sources you use are reliable and up-to-date. Try to use recent published sources where possible.
• Cite Accurately – When citing the sources you use, be sure to include the author’s name, year of publication, and the page number (if relevant).
• Avoid Plagiarism – As mentioned above, it’s important to cite any sources you use. Plagiarism should be avoided at all costs as it can result in a loss of points.

By following these tips, you can ensure that your extended essay makes good use of external sources, and that you cite and reference them correctly. Taking the time to look through a range of materials will also help you to form a well-informed opinion, which is essential for a successful paper.

FAQs about IB Math Extended Essay Topics

• Q: What is an IB Mathematics Extended Essay? A: An IB Mathematics Extended Essay (EE) is an in-depth, project-based essay, which requires a student to explore a topic and present their findings. The Extended Essay should be related to and reflect the knowledge of Mathematics learned in the IB program.
• Q: How difficult is a Mathematics EE? A: Writing an EE is no small task. It requires considerable commitment and hard work as well as dedication to the research, writing and presentation process. However, with adequate preparation, guidance, and support, a student will be able to create a successful extended essay.
• Q: What steps are involved in the process of creating a Mathematics EE? A: The process of crafting a Mathematics EE involves the following steps: selecting a topic, conducting the research, gathering evidence, writing an outline and the draft, proofreading and editing, planning for submission.
• Q: How does one select a suitable topic for a Mathematics EE? A: When selecting a topic for a Mathematics EE, students should consider their interests, display their mathematical knowledge, and choose something that can be researched thoroughly. Additionally, they may find it helpful to review example topics and assess their suitability and feasibility.
• Q: Who is responsible for supervising the Mathematics EE? A: An experienced teacher should provide supervision throughout the EE process and guide the student in proper methodology, accuracy in content, format and presentation of the completed essay.
• Q: How are Mathematics EEs evaluated? A: A Mathematics EE is generally evaluated on the student’s ability to demonstrate relevant content and thorough research, as well as their mastery of the subject, attention to detail and accuracy, originality and creativity.
• Q: What structure is typically used when writing a Mathematics EE? A: A MathematicsEE typically has a conventional structure, which includes the introduction, body and conclusion. In the body, the research problem and approach, main focus and findings should be addressed.
• Q: What type of information is needed to include in a Mathematics EE? A: Mathematical EEs should include mathematical terms and formulas, clear explanations of processes, correct notation and symbols, as well as authentic research.
• Q: What tips can help a student prepare for the EE submission? A: A student can edit and proofread their EE to ensure that all sections are accurate, concise and organized. They should double check all numbers, formulas, citations and references. Moreover, they may want to get feedback from their supervisor and peers.
• Q: How can external sources help a student create a successful EE? A: External sources may provide up-to-date information regarding formatting, research methods, mathematical tools, etc., which a student can use to expand their knowledge and create a comprehensive EE.

Valerie Green

Valerie Green is a dedicated educator who spends her time helping high school and college students succeed. She writes articles and guides for various online education projects, providing students with the tools they need to excel in their studies. Friendly and approachable, she is committed to making a difference in the lives of students.

Tips for Creating a Compelling Research Question for Your IB EE

By following these tips, you can create a research question that not only meets the criteria of the IB Extended Essay, but also sets you up for a rewarding research experience. Remember that a well-conceived research question is the first step towards a successful and insightful Extended Essay.

How Do You Select the Perfect Supervisor for Your Extended Essay?

Choosing the perfect Extended Essay supervisor is a crucial step in your IB path, offering a blend of academic insight, moral support and critical feedback. This article will guide you through the essential criteria for choosing a supervisor who can inspire, challenge, and guide you toward a high-quality Extended Essay. Learn how expertise, commitment, and a supportive relationship can transform your EE writing experience.

What Is IB Reflective Project?

The Reflective Project is an in-depth study where students select an ethical issue related to their career-related studies to research and analyze through various lenses. This research is not a mere academic exercise; it is a rigorous, reflective process that encourages students to connect their findings with their own beliefs, values, and experiences.

What’s the Ideal Number of Sources for Your IB EE?

What’s the ideal number of sources for my EE? The answer, nuanced and subject-specific, depends on striking the perfect balance between breadth and depth of research. As a seasoned IB writer, I’ve seen how this balance varies across disciplines — a History EE might thrive on many sources to construct a well-rounded argument, while a Math EE might depend on a few texts for its foundational theory.

How Much Does It Cost to Order a Custom Extended Essay Online?

When tackling the International Baccalaureate program, students often wonder about the cost of ordering a custom extended essay online. As an experienced IB writer, I can tell you that several factors influence this cost. These include the essay’s length, its complexity, the urgency of your deadline, and the writer’s expertise.

Pros and Pitfalls of Using Internet-Sourced EE Topics

In the ever-evolving landscape of academic research, the Internet has emerged as a significant resource for students undertaking the challenging task of the IB Extended Essay (EE). As an experienced IB writer, I’ve observed the transformative impact of Internet-sourced EE topics. This article aims to highlight both the benefits and challenges of this modern approach to research.

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50 IB Maths IA Topic Ideas

IB Maths is a struggle for most people going through their diploma. To make matters worse, on top of just doing the dreaded maths exam, we’re also expected to write a Maths IA exploration into a topic of our choice! Where do you even begin such a task? How do you even choose a topic? To make things easier, we have plenty of free Maths resources! Firstly though, we’ve compiled 50 common Maths IA topics that may spark some creative juices and set you on your way to conquering one of the hardest assignments of the diploma!

Once you have chosen your topic, you may want to check out our other posts on how to structure and format your Maths IA or how to write your IA .

NOTE: These topics are purely meant as inspiration and are not to be chosen blindly. Even though many of these topics led to high scores for some of our graduates in the past, it is important that you listen to the advice of your subject teacher before choosing any topic!

• Pascal’s triangle : Discovering patterns within this famous array of numbers
• Pythagorean triples : Can you find patterns in what numbers form a pythagorean triple?
• Monty Hall problem : How does Bayesian probability work in this real-life example, and can you add a layer of complexity to it?
• The Chinese Remainder Theorem : An insight into the mathematics of number theory
• Sum of all positive integers is -1/12? Explore this fascinating physics phenomenon through the world of sequences and series
• Birthday paradox : Why is it that in a room of people probability dictates that people are very likely to share a birthday? 
• Harmonic series : Explore why certain notes/chords in music sound dissonant, and others consonant, by looking at the ratios of frequencies between the notes.
• Optimizing areas : Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon?
• Optimizing volumes : Explore the mathematics of finding a maximum volume of a cuboid subject to some constraint
• Flow of traffic : How does mathematics feed into our traffic jams that we endure every morning?
• Football statistics : Does spending a lot of cash during the transfer window translate to more points the following year? Or is there a better predictor of a team’s success like wages, historic performance, or player valuation?
• Football statistics #2 : How does a manager sacking affect results? 
• Gini coefficient : Can you use integration to derive the gini coefficient for a few countries, allowing you to accurately compare their levels of economic inequality?
• Linear regressions : Run linear regressions using OLS to predict and estimate the effect of one variable on another.
• The Prisoner’s Dilemma : Use game theory in order to deduce the optimal strategy in this famous situation
• Tic Tac Toe : What is the optimal strategy in this legendary game? Will my probability of winning drastically increase by some move that I can make?
• Monopoly : Is there a strategy that dominates all others? Which properties should I be most excited to land on?
• Rock Paper Scissors : If I played and won with rock already, should I make sure to change what I play this time? Or is it better to switch? 
• The Toast problem : If there is a room of some number of people, how many toasts are necessary for everyone to have toasted with everyone?
• Cracking a Password : How long would it take to be able to correctly guess a password? How much safer does a password get by adding symbols or numbers?
• Stacking Balls : Suppose you want to place balls in a cardboard box, what is the optimal way to do this to use your space most effectively?
• The Wobbly Table : Many tables are wobbly because of uneven ground, but is there a way to orient the tables to make sure they are always stable?
• The Stable Marriage Problem : Is there a matching algorithm that ensures each person in society ends up with their one true love? What is the next best alternative if this is not viable?
• Mathematical Card Tricks : Look at the probabilities at play in the famous 3 card monte scam. 
• Modelling the Spread of a Virus : How long would it take for us all to be wiped out if a deadly influenza spreads throughout the population?
• The Tragedy of the Common s : Our population of fish is dwindling, but how much do we need to reduce our production by in order to ensure the fish can replenish faster than we kill?
• The Risk of Insurance : An investigation into asymmetric information and how being unsure about the future state of the world may lead us to be risk-averse
• Gabriel’s Horn : This figure has an infinite surface area but a finite volume, can you p rove this?
• Modelling the Shape of an Egg : Although it may sound easy, finding the surface area or volume of this common shape requires some in-depth mathematical investigation
• Voting Systems : What voting system ensures that the largest amount of people get the official that they would prefer? With 2 candidates this is logical, but what if they have more than 2?
• Probability : Are Oxford and Cambridge biased against state-school applicants?
• Statistics : With Tokyo 2020 around the corner, how aboutmodelling change in record performances for a particular discipline?
• Analysing Data : In the 200 meter dash, is there an advantage to a particular lane in track? 
• Coverage : Calculation of rate of deforestation, and afforestation. How long will our forests last?
• Friendly numbers, Solitary numbers, perfect numbers : Investigate what changes the condition of numbers
• Force : Calculating the intensity of a climber’s fall based upon their distance above where they last clamped in
• Königsberg bridge problem : Using networks to solve problems. 
• Handshake problem : How many handshakes are required so that everyone shakes hands with all the other people in the room? 
• The mathematics of deceit : How con artists use pyramid schemes to get rich quick!
• Modelling radioactive decay : The maths of Chernobyl – when will it be safe to live there?
• Mathematics and photography : Exploring the relationship between the aperture of a camera and a geometric sequence
• Normal Distribution : Using distributions to examine the 2008 financial crisis
• Mechanics : Body Proportions for Track and Field events
• Modelling : How does a cup of Tea cool?
• Relationships : Do BMI ratings and country wealth share a significant relationship?
• Modelling : Can we mathematically model musical chords and concepts like dissonance?
• Evaluating limits : Exploring L’Hôpital’s rule
• Chinese postman problem : How do we calculate shortest possible routes?
• Maths and Time : Exploring ideas regarding time dilation
• Plotting Planets : Using log functions to track planets!

So there we have it: 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework ! We also have similar ideas for Biology , Chemistry , Economics , History , Physics , TOK … and many many more tips and tricks on securing those top marks on our free resources page – just click the ‘Maths resources’ button!

Still feeling confused, or want some personalised help? We offer online private tuition from experienced IB graduates who got top marks in their Maths IA. 

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TOM ROCKS MATHS

Maths, but not as you know it…, oxford university maths essay competition 2024.

The Tom Rocks Maths Essay Competition is back – with a new home at the Oxford University Department of Continuing Education. Full details and entry form here .

This exciting competition asks students of all ages and abilities to explain their favourite mathematical topic in an essay aimed at a non-specialist audience. Originally launched in 2020 as a partnership between Tom Rocks Maths and St Edmund Hall, the competition aims to provide the participants with the opportunity to communicate complex ideas in an understandable manner, and to encourage them to engage with maths beyond any curriculum.

There are no eligibility requirements, all you need is a passion for maths and a flair for writing to participate! The closing date is Monday 1st April 2024 and the showcase of entries (including the announcement of the winners) will take place throughout summer 2024.

There are two strands of entry: 1. Under 18’s (student); and 2. Over 18’s (adult) Please note: A ‘student’ is defined as anyone who is still studying full-time at school or college, university students fall into the ‘adult’’ category.

There is no word limit for the essays, but as a guideline 1000-2000 words is sufficient. All entries must be submitted using the online form as PDF or Microsoft Word documents. The submission form can be accessed here .

The winners will be selected by Dr Tom Crawford, Public Engagement Lead and Departmental Lecturer, and the creator of the award-winning ’Tom Rocks Maths’. All entries will be published on the Tom Rocks Maths website as part of the essay showcase.

The student prizewinner will receive a cash prize of £100 alongside the publication of their winning essay on the University website.

The adult prizewinner will receive free registration to an online live-time weekly class (WOW) of their choosing and the publication of their winning essay on the University website. The full list of courses available can be found here .

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Guest Essay

J.D. Vance: The Math on Ukraine Doesn’t Add Up

By J. D. Vance

Mr. Vance, a Republican, is the junior senator from Ohio.

President Biden wants the world to believe that the biggest obstacle facing Ukraine is Republicans and our lack of commitment to the global community. This is wrong.

Ukraine’s challenge is not the G.O.P.; it’s math. Ukraine needs more soldiers than it can field, even with draconian conscription policies. And it needs more matériel than the United States can provide. This reality must inform any future Ukraine policy, from further congressional aid to the diplomatic course set by the president.

The Biden administration has applied increasing pressure on Republicans to pass a supplemental aid package of more than $60 billion to Ukraine. I voted against this package in the Senate and remain opposed to virtually any proposal for the United States to continue funding this war. Mr. Biden has failed to articulate even basic facts about what Ukraine needs and how this aid will change the reality on the ground.

The most fundamental question: How much does Ukraine need and how much can we actually provide? Mr. Biden suggests that a $60 billion supplemental means the difference between victory and defeat in a major war between Russia and Ukraine. That is also wrong. This $60 billion is a fraction of what it would take to turn the tide in Ukraine’s favor. But this is not just a matter of dollars. Fundamentally, we lack the capacity to manufacture the amount of weapons Ukraine needs us to supply to win the war.

Consider our ability to produce 155-millimeter artillery shells. Last year, Ukraine’s defense minister estimated that the country’s base-line requirement for these shells was over four million per year but that it could fire up to seven million if that many were available. Since the start of the conflict, the United States has gone to great lengths to ramp up production of 155-millimeter shells. We’ve roughly doubled our capacity and can now produce 360,000 per year — less than a tenth of what Ukraine says it needs. The administration’s goal is to get this to 1.2 million — 30 percent of what’s needed — by the end of 2025. This would cost the American taxpayers dearly while yielding an unpleasantly familiar result: failure abroad.

Just this week, the top American military commander in Europe argued that absent further security assistance, Russia could soon have a 10-to-1 artillery advantage over Ukraine. What didn’t gather as many headlines is that Russia’s current advantage is at least 5 to 1, even after all the money we have poured into the conflict. Neither of these ratios plausibly leads to Ukrainian victory.

Proponents of American aid to Ukraine have argued that our approach has been a boon to our own economy, creating jobs here in the factories that manufacture weapons. But our national security interests can be — and often are — separate from our economic interests. The notion that we should prolong a bloody and gruesome war because it’s been good for American business is grotesque. We can and should rebuild our industrial base without shipping its products to a foreign conflict.

The story is the same when we look at other munitions. Take the Patriot missile system — our premier air defense weapon. It’s of such importance in this war that Ukraine’s foreign minister has specifically demanded them. That’s because in March alone, Russia reportedly launched over 3,000 guided aerial bombs, 600 drones and 400 missiles at Ukraine. To fend off these attacks, the Ukrainian president, Volodymyr Zelensky, and others have indicated they need thousands of Patriot interceptors per year. The problem is this: The United States only manufactures 550 per year. If we pass the supplemental aid package currently being considered in Congress, we could potentially increase annual production to 650, but that’s still less than a third of what Ukraine requires.

These weapons are not only needed by Ukraine. If China were to set its sights on Taiwan, the Patriot missile system would be critical to its defense. In fact, the United States has promised to send Taiwan nearly $900 million worth of Patriot missiles, but delivery of those weapons and other essential resources has been severely delayed, partly because of shortages caused by the war in Ukraine.

If that sounds bad, Ukraine’s manpower situation is even worse. Here are the basics: Russia has nearly four times the population of Ukraine. Ukraine needs upward of half a million new recruits, but hundreds of thousands of fighting-age men have already fled the country. The average Ukrainian soldier is roughly 43 years old , and many soldiers have already served two years at the front with few, if any, opportunities to stop fighting. After two years of conflict, there are some villages with almost no men left. The Ukrainian military has resorted to coercing men into service, and women have staged protests to demand the return of their husbands and fathers after long years of service at the front. This newspaper reported one instance in which the Ukrainian military attempted to conscript a man with a diagnosed mental disability.

Many in Washington seem to think that hundreds of thousands of young Ukrainians have gone to war with a song in their heart and are happy to label any thought to the contrary Russian propaganda. But major newspapers on both sides of the Atlantic are reporting that the situation on the ground in Ukraine is grim.

These basic mathematical realities were true, but contestable, at the outset of the war. They were obvious and incontestable a year ago, when American leadership worked closely with Mr. Zelensky to undertake a disastrous counteroffensive. The bad news is that accepting brute reality would have been most useful last spring, before the Ukrainians launched that extremely costly and unsuccessful military campaign. The good news is that even now, a defensive strategy can work. Digging in with old-fashioned ditches, cement and land mines are what enabled Russia to weather Ukraine’s 2023 counteroffensive. Our allies in Europe could better support such a strategy, as well. While some European countries have provided considerable resources, the burden of military support has thus far fallen heaviest on the United States.

By committing to a defensive strategy, Ukraine can preserve its precious military manpower, stop the bleeding and provide time for negotiations to commence. But this would require both the American and Ukrainian leadership to accept that Mr. Zelensky’s stated goal for the war — a return to 1991 boundaries — is fantastical.

The White House has said time and again that it can’t negotiate with President Vladimir Putin of Russia. This is absurd. The Biden administration has no viable plan for the Ukrainians to win this war. The sooner Americans confront this truth, the sooner we can fix this mess and broker for peace.

J.D. Vance ( @JDVance1 ), a Republican, is the junior senator from Ohio.

The Times is committed to publishing a diversity of letters to the editor. We’d like to hear what you think about this or any of our articles. Here are some tips . And here’s our email: [email protected] .

Follow the New York Times Opinion section on Facebook , Instagram , TikTok , WhatsApp , X and Threads .

What is the difference between a solar eclipse and a lunar eclipse?

It almost time! Millions of Americans across the country Monday are preparing to witness the once-in-a-lifetime total solar eclipse as it passes over portions of Mexico, the United States and Canada.

It's a sight to behold and people have now long been eagerly awaiting what will be their only chance until 2044 to witness totality, whereby the moon will completely block the sun's disc, ushering in uncharacteristic darkness.

That being said, many are curious on what makes the solar eclipse special and how is it different from a lunar eclipse.

The total solar eclipse is today: Get the latest forecast and everything you need to know

What is an eclipse?

An eclipse occurs when any celestial object like a moon or a planet passes between two other bodies, obscuring the view of objects like the sun, according to NASA .

What is a solar eclipse?

A total solar eclipse occurs when the moon comes in between the Earth and the sun, blocking its light from reaching our planet, leading to a period of darkness lasting several minutes. The resulting "totality," whereby observers can see the outermost layer of the sun's atmosphere, known as the corona, presents a spectacular sight for viewers and confuses animals – causing nocturnal creatures to stir and bird and insects to fall silent.

Partial eclipses, when some part of the sun remains visible, are the most common, making total eclipses a rare sight.

What is a lunar eclipse?

A total lunar eclipse occurs when the moon and the sun are on exact opposite sides of Earth. When this happens, Earth blocks the sunlight that normally reaches the moon. Instead of that sunlight hitting the moon’s surface, Earth's shadow falls on it.

Lunar eclipses are often also referred to the "blood moon" because when the Earth's shadow covers the moon, it often produces a red color. The coloration happens because a bit of reddish sunlight still reaches the moon's surface, even though it's in Earth's shadow.

Difference between lunar eclipse and solar eclipse

The major difference between the two eclipses is in the positioning of the sun, the moon and the Earth and the longevity of the phenomenon, according to NASA.

A lunar eclipse can last for a few hours, while a solar eclipse lasts only a few minutes. Solar eclipses also rarely occur, while lunar eclipses are comparatively more frequent. While at least two partial lunar eclipses happen every year, total lunar eclipses are still rare, says NASA.

Another major difference between the two is that for lunar eclipses, no special glasses or gizmos are needed to view the spectacle and one can directly stare at the moon. However, for solar eclipses, it is pertinent to wear proper viewing glasses and take the necessary safety precautions because the powerful rays of the sun can burn and damage your retinas.

Contributing: Eric Lagatta, Doyle Rice, USA TODAY