research proposal in applied mathematics

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Applied Mathematics

Important information for proposers.

All proposals must be submitted in accordance with the requirements specified in this funding opportunity and in the NSF Proposal & Award Policies & Procedures Guide (PAPPG) that is in effect for the relevant due date to which the proposal is being submitted. It is the responsibility of the proposer to ensure that the proposal meets these requirements. Submitting a proposal prior to a specified deadline does not negate this requirement.

Supports mathematics research motivated by or having an effect on problems arising in science and engineering.

The Applied Mathematics program supports mathematics research motivated by or having an effect on problems arising in science and engineering. Mathematical merit and novelty, as well as breadth and quality of impact on applications, are important factors. Proposals to develop critical mathematical techniques from individual investigators as well as from interdisciplinary teams are encouraged.

Proposals whose primary applications are in the biological sciences are inappropriate for Applied Mathematics, and should be submitted elsewhere; see the synopsis of the DMS Mathematical Biology program on that program's webpage for further guidance.

Conferences

Proposals to the Applied Mathematics program for conferences or workshops should be submitted through the program solicitation "Conferences and Workshops in the Mathematical Sciences" (link below).  Principal Investigators should carefully read the program solicitation to obtain important information regarding the substance of proposals for conferences, workshops, summer/winter schools, and similar activities.

To facilitate timely notification of the availability of support:

• Proposals for conferences, workshops, etc., to be held in the US must be submitted 8 months in advance of the conference date;
• Proposals to support group travel to meetings outside the US must be submitted 12 months in advance of the meeting date;
• Proposals for conferences, workshops, etc., whose budget request exceeds $50,000 must be submitted during the annual November 1-15 submission window.

Program contacts

Program events.

• October 17, 2022 - DMS Virtual Office Hours
• March 22, 2021 - DMS Virtual Office Hours

Additional program resources

• Conferences and Workshops in the Mathematical Sciences

Awards made through this program

Related programs.

• Focused Research Groups in the Mathematical Sciences (FRGMS)
• Mathematical Biology
• Computational Mathematics
• Algorithms for Threat Detection (ATD)
• Joint DMS/NIGMS Initiative to Support Research at the Interface of the Biological and Mathematical Sciences (DMS/NIGMS)
• Collaborative Research in Computational Neuroscience (CRCNS)
• Major Research Instrumentation Program (MRI)
• Faculty Early Career Development Program
• Research Experiences for Undergraduates (REU)
• Facilitating Research at Primarily Undergraduate Institutions:

Organization(s)

• Directorate for Mathematical and Physical Sciences (MPS)
• Division of Mathematical Sciences (MPS/DMS)

Examples of Successful Grant Applications

The links on this page are only available to viewers with an account in the Department of Mathematics at the University of Arizona

AMS-Simons Travel Grants

Below are examples of successful project descriptions. 

Darlayne Addabbo

Houssam Abdul-Rahman

Paul Carter

Yong Suk Moon

Tracy Stepien

Weinan Wang

Amanda Young

AWM Travel Grants

Example of successful proposal.

NSF Mathematical Sciences Postdoctoral Research Fellowships

Below is an example of a successful research proposal. Additionally, Kevin Lin will share examples of funded and unfunded proposals upon request.

Gabriela Jaramillo (Applied Mathematics)

David Glickenstein will share a successful proposal. Joceline Lega will provide feedback on proposal drafts.

NSF Division of Mathematical Sciences

Below are examples of project descriptions of research proposals that were recently funded by DMS. 

Paul Carter (Applied Mathematics, 2018)

Nick Ercolani (Applied Mathematics, 2015)

Nick Ercolani (Applied Mathematics, 2011)

Below is an example of a conference proposal funded by DMS.

Jim Cushing (Mathematical Biology conference, 2016)

Additionally, a number of faculty will provide feedback on draft project descriptions or share examples of funded or unfunded proposals in a variety of areas.

Computational Mathematics: Kevin Lin

Continuous Mechanics and Materials Science: Joceline Lega

Geometric Analysis: David Glickenstein

Mathematical Biology: Joceline Lega

Mathematical Physics: Nick Ercolani

Partial Differential Equations: Nick Ercolani, Joceline Lega

Probability and Applied Probability: Janek Wehr

NSF Robert Noyce Division For Secondary Mathematics Teacher Development

Example of funded proposal shared by Cynthia Anhalt

251+ Math Research Topics [2024 Updated]

Mathematics, often dubbed as the language of the universe, holds immense significance in shaping our understanding of the world around us. It’s not just about crunching numbers or solving equations; it’s about unraveling mysteries, making predictions, and creating innovative solutions to complex problems. In this blog, we embark on a journey into the realm of math research topics, exploring various branches of mathematics and their real-world applications.

How Do You Write A Math Research Topic?

Writing a math research topic involves several steps to ensure clarity, relevance, and feasibility. Here’s a guide to help you craft a compelling math research topic:

• Identify Your Interests: Start by exploring areas of mathematics that interest you. Whether it’s pure mathematics, applied mathematics, or interdisciplinary topics, choose a field that aligns with your passion and expertise.
• Narrow Down Your Focus: Mathematics is a broad field, so it’s essential to narrow down your focus to a specific area or problem. Consider the scope of your research and choose a topic that is manageable within your resources and time frame.
• Review Existing Literature: Conduct a thorough literature review to understand the current state of research in your chosen area. Identify gaps, controversies, or unanswered questions that could form the basis of your research topic.
• Formulate a Research Question: Based on your exploration and literature review, formulate a clear and concise research question. Your research question should be specific, measurable, achievable, relevant, and time-bound (SMART).
• Consider Feasibility: Assess the feasibility of your research topic in terms of available resources, data availability, and research methodologies. Ensure that your topic is realistic and achievable within the constraints of your project.
• Consult with Experts: Seek feedback from mentors, advisors, or experts in the field to validate your research topic and refine your ideas. Their insights can help you identify potential challenges and opportunities for improvement.
• Refine and Iterate: Refine your research topic based on feedback and further reflection. Iterate on your ideas to ensure clarity, coherence, and relevance to the broader context of mathematics research.
• Craft a Title: Once you have finalized your research topic, craft a compelling title that succinctly summarizes the essence of your research. Your title should be descriptive, engaging, and reflective of the key themes of your study.
• Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap for your study and justify the significance of your research topic.

By following these steps, you can effectively write a math research topic that is well-defined, relevant, and poised to make a meaningful contribution to the field of mathematics.

251+ Math Research Topics: Beginners To Advanced

• Prime Number Distribution in Arithmetic Progressions
• Diophantine Equations and their Solutions
• Applications of Modular Arithmetic in Cryptography
• The Riemann Hypothesis and its Implications
• Graph Theory: Exploring Connectivity and Coloring Problems
• Knot Theory: Unraveling the Mathematics of Knots and Links
• Fractal Geometry: Understanding Self-Similarity and Dimensionality
• Differential Equations: Modeling Physical Phenomena and Dynamical Systems
• Chaos Theory: Investigating Deterministic Chaos and Strange Attractors
• Combinatorial Optimization: Algorithms for Solving Optimization Problems
• Computational Complexity: Analyzing the Complexity of Algorithms
• Game Theory: Mathematical Models of Strategic Interactions
• Number Theory: Exploring Properties of Integers and Primes
• Algebraic Topology: Studying Topological Invariants and Homotopy Theory
• Analytic Number Theory: Investigating Properties of Prime Numbers
• Algebraic Geometry: Geometry Arising from Algebraic Equations
• Galois Theory: Understanding Field Extensions and Solvability of Equations
• Representation Theory: Studying Symmetry in Linear Spaces
• Harmonic Analysis: Analyzing Functions on Groups and Manifolds
• Mathematical Logic: Foundations of Mathematics and Formal Systems
• Set Theory: Exploring Infinite Sets and Cardinal Numbers
• Real Analysis: Rigorous Study of Real Numbers and Functions
• Complex Analysis: Analytic Functions and Complex Integration
• Measure Theory: Foundations of Lebesgue Integration and Probability
• Topological Groups: Investigating Topological Structures on Groups
• Lie Groups and Lie Algebras: Geometry of Continuous Symmetry
• Differential Geometry: Curvature and Topology of Smooth Manifolds
• Algebraic Combinatorics: Enumerative and Algebraic Aspects of Combinatorics
• Ramsey Theory: Investigating Structure in Large Discrete Structures
• Analytic Geometry: Studying Geometry Using Analytic Methods
• Hyperbolic Geometry: Non-Euclidean Geometry of Curved Spaces
• Nonlinear Dynamics: Chaos, Bifurcations, and Strange Attractors
• Homological Algebra: Studying Homology and Cohomology of Algebraic Structures
• Topological Vector Spaces: Vector Spaces with Topological Structure
• Representation Theory of Finite Groups: Decomposition of Group Representations
• Category Theory: Abstract Structures and Universal Properties
• Operator Theory: Spectral Theory and Functional Analysis of Operators
• Algebraic Number Theory: Study of Algebraic Structures in Number Fields
• Cryptanalysis: Breaking Cryptographic Systems Using Mathematical Methods
• Discrete Mathematics: Combinatorics, Graph Theory, and Number Theory
• Mathematical Biology: Modeling Biological Systems Using Mathematical Tools
• Population Dynamics: Mathematical Models of Population Growth and Interaction
• Epidemiology: Mathematical Modeling of Disease Spread and Control
• Mathematical Ecology: Dynamics of Ecological Systems and Food Webs
• Evolutionary Game Theory: Evolutionary Dynamics and Strategic Behavior
• Mathematical Neuroscience: Modeling Brain Dynamics and Neural Networks
• Mathematical Physics: Mathematical Models in Physical Sciences
• Quantum Mechanics: Foundations and Applications of Quantum Theory
• Statistical Mechanics: Statistical Methods in Physics and Thermodynamics
• Fluid Dynamics: Modeling Flow of Fluids Using Partial Differential Equations
• Mathematical Finance: Stochastic Models in Finance and Risk Management
• Option Pricing Models: Black-Scholes Model and Beyond
• Portfolio Optimization: Maximizing Returns and Minimizing Risk
• Stochastic Calculus: Calculus of Stochastic Processes and Itô Calculus
• Financial Time Series Analysis: Modeling and Forecasting Financial Data
• Operations Research: Optimization of Decision-Making Processes
• Linear Programming: Optimization Problems with Linear Constraints
• Integer Programming: Optimization Problems with Integer Solutions
• Network Flow Optimization: Modeling and Solving Flow Network Problems
• Combinatorial Game Theory: Analysis of Games with Perfect Information
• Algorithmic Game Theory: Computational Aspects of Game-Theoretic Problems
• Fair Division: Methods for Fairly Allocating Resources Among Parties
• Auction Theory: Modeling Auction Mechanisms and Bidding Strategies
• Voting Theory: Mathematical Models of Voting Systems and Social Choice
• Social Network Analysis: Mathematical Analysis of Social Networks
• Algorithm Analysis: Complexity Analysis of Algorithms and Data Structures
• Machine Learning: Statistical Learning Algorithms and Data Mining
• Deep Learning: Neural Network Models with Multiple Layers
• Reinforcement Learning: Learning by Interaction and Feedback
• Natural Language Processing: Statistical and Computational Analysis of Language
• Computer Vision: Mathematical Models for Image Analysis and Recognition
• Computational Geometry: Algorithms for Geometric Problems
• Symbolic Computation: Manipulation of Mathematical Expressions
• Numerical Analysis: Algorithms for Solving Numerical Problems
• Finite Element Method: Numerical Solution of Partial Differential Equations
• Monte Carlo Methods: Statistical Simulation Techniques
• High-Performance Computing: Parallel and Distributed Computing Techniques
• Quantum Computing: Quantum Algorithms and Quantum Information Theory
• Quantum Information Theory: Study of Quantum Communication and Computation
• Quantum Error Correction: Methods for Protecting Quantum Information from Errors
• Topological Quantum Computing: Using Topological Properties for Quantum Computation
• Quantum Algorithms: Efficient Algorithms for Quantum Computers
• Quantum Cryptography: Secure Communication Using Quantum Key Distribution
• Topological Data Analysis: Analyzing Shape and Structure of Data Sets
• Persistent Homology: Topological Invariants for Data Analysis
• Mapper Algorithm: Method for Visualization and Analysis of High-Dimensional Data
• Algebraic Statistics: Statistical Methods Based on Algebraic Geometry
• Tropical Geometry: Geometric Methods for Studying Polynomial Equations
• Model Theory: Study of Mathematical Structures and Their Interpretations
• Descriptive Set Theory: Study of Borel and Analytic Sets
• Ergodic Theory: Study of Measure-Preserving Transformations
• Combinatorial Number Theory: Intersection of Combinatorics and Number Theory
• Additive Combinatorics: Study of Additive Properties of Sets
• Arithmetic Geometry: Interplay Between Number Theory and Algebraic Geometry
• Proof Theory: Study of Formal Proofs and Logical Inference
• Reverse Mathematics: Study of Logical Strength of Mathematical Theorems
• Nonstandard Analysis: Alternative Approach to Analysis Using Infinitesimals
• Computable Analysis: Study of Computable Functions and Real Numbers
• Graph Theory: Study of Graphs and Networks
• Random Graphs: Probabilistic Models of Graphs and Connectivity
• Spectral Graph Theory: Analysis of Graphs Using Eigenvalues and Eigenvectors
• Algebraic Graph Theory: Study of Algebraic Structures in Graphs
• Metric Geometry: Study of Geometric Structures Using Metrics
• Geometric Measure Theory: Study of Measures on Geometric Spaces
• Discrete Differential Geometry: Study of Differential Geometry on Discrete Spaces
• Algebraic Coding Theory: Study of Error-Correcting Codes
• Information Theory: Study of Information and Communication
• Coding Theory: Study of Error-Correcting Codes
• Cryptography: Study of Secure Communication and Encryption
• Finite Fields: Study of Fields with Finite Number of Elements
• Elliptic Curves: Study of Curves Defined by Cubic Equations
• Hyperelliptic Curves: Study of Curves Defined by Higher-Degree Equations
• Modular Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Number Theory
• Zeta Functions: Analytic Functions with Special Properties
• Analytic Number Theory: Study of Number Theoretic Functions Using Analysis
• Dirichlet Series: Analytic Functions Represented by Infinite Series
• Euler Products: Product Representations of Analytic Functions
• Arithmetic Dynamics: Study of Iterative Processes on Algebraic Structures
• Dynamics of Rational Maps: Study of Dynamical Systems Defined by Rational Functions
• Julia Sets: Fractal Sets Associated with Dynamical Systems
• Mandelbrot Set: Fractal Set Associated with Iterations of Complex Quadratic Polynomials
• Arithmetic Geometry: Study of Algebraic Geometry Over Number Fields
• Diophantine Geometry: Study of Solutions of Diophantine Equations Using Geometry
• Arithmetic of Elliptic Curves: Study of Elliptic Curves Over Number Fields
• Rational Points on Curves: Study of Rational Solutions of Algebraic Equations
• Galois Representations: Study of Representations of Galois Groups
• Automorphic Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Automorphic Forms
• Selberg Trace Formula: Tool for Studying Spectral Theory and Automorphic Forms
• Langlands Program: Program to Unify Number Theory and Representation Theory
• Hodge Theory: Study of Harmonic Forms on Complex Manifolds
• Riemann Surfaces: One-dimensional Complex Manifolds
• Shimura Varieties: Algebraic Varieties Associated with Automorphic Forms
• Modular Curves: Algebraic Curves Associated with Modular Forms
• Hyperbolic Manifolds: Manifolds with Constant Negative Curvature
• Teichmüller Theory: Study of Moduli Spaces of Riemann Surfaces
• Mirror Symmetry: Duality Between Calabi-Yau Manifolds
• Kähler Geometry: Study of Hermitian Manifolds with Special Symmetries
• Algebraic Groups: Linear Algebraic Groups and Their Representations
• Lie Algebras: Study of Algebraic Structures Arising from Lie Groups
• Representation Theory of Lie Algebras: Study of Representations of Lie Algebras
• Quantum Groups: Deformation of Lie Groups and Lie Algebras
• Algebraic Topology: Study of Topological Spaces Using Algebraic Methods
• Homotopy Theory: Study of Continuous Deformations of Spaces
• Homology Theory: Study of Algebraic Invariants of Topological Spaces
• Cohomology Theory: Study of Dual Concepts to Homology Theory
• Singular Homology: Homology Theory Defined Using Simplicial Complexes
• Sheaf Theory: Study of Sheaves and Their Cohomology
• Differential Forms: Study of Multilinear Differential Forms
• De Rham Cohomology: Cohomology Theory Defined Using Differential Forms
• Morse Theory: Study of Critical Points of Smooth Functions
• Symplectic Geometry: Study of Symplectic Manifolds and Their Geometry
• Floer Homology: Study of Symplectic Manifolds Using Pseudoholomorphic Curves
• Gromov-Witten Invariants: Invariants of Symplectic Manifolds Associated with Pseudoholomorphic Curves
• Mirror Symmetry: Duality Between Symplectic and Complex Geometry
• Calabi-Yau Manifolds: Ricci-Flat Complex Manifolds
• Moduli Spaces: Spaces Parameterizing Geometric Objects
• Donaldson-Thomas Invariants: Invariants Counting Sheaves on Calabi-Yau Manifolds
• Algebraic K-Theory: Study of Algebraic Invariants of Rings and Modules
• Homological Algebra: Study of Homology and Cohomology of Algebraic Structures
• Derived Categories: Categories Arising from Homological Algebra
• Stable Homotopy Theory: Homotopy Theory with Stable Homotopy Groups
• Model Categories: Categories with Certain Homotopical Properties
• Higher Category Theory: Study of Higher Categories and Homotopy Theory
• Higher Topos Theory: Study of Higher Categorical Structures
• Higher Algebra: Study of Higher Categorical Structures in Algebra
• Higher Algebraic Geometry: Study of Higher Categorical Structures in Algebraic Geometry
• Higher Representation Theory: Study of Higher Categorical Structures in Representation Theory
• Higher Category Theory: Study of Higher Categorical Structures
• Homotopical Algebra: Study of Algebraic Structures in Homotopy Theory
• Homotopical Groups: Study of Groups with Homotopical Structure
• Homotopical Categories: Study of Categories with Homotopical Structure
• Homotopy Groups: Algebraic Invariants of Topological Spaces
• Homotopy Type Theory: Study of Foundations of Mathematics Using Homotopy Theory

In conclusion, the world of mathematics is vast and multifaceted, offering endless opportunities for exploration and discovery. Whether delving into the abstract realms of pure mathematics or applying mathematical principles to solve real-world problems, mathematicians play a vital role in advancing human knowledge and shaping the future of our world.

By embracing diverse math research topics and interdisciplinary collaborations, we can unlock new possibilities and harness the power of mathematics to address the challenges of today and tomorrow. So, let’s embark on this journey together as we unravel the mysteries of numbers and explore the boundless horizons of mathematical inquiry.

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Mathematics at MIT is administratively divided into two categories: Pure Mathematics and Applied Mathematics. They comprise the following research areas:

Pure Mathematics

• Algebra & Algebraic Geometry
• Algebraic Topology
• Analysis & PDEs
• Mathematical Logic & Foundations
• Number Theory
• Probability & Statistics
• Representation Theory

Applied Mathematics

In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications.

• Combinatorics
• Computational Biology
• Physical Applied Mathematics
• Computational Science & Numerical Analysis
• Theoretical Computer Science
• Mathematics of Data

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• Knowledge Base
• Starting the research process
• How to Write a Research Proposal | Examples & Templates

How to Write a Research Proposal | Examples & Templates

Published on October 12, 2022 by Shona McCombes and Tegan George. Revised on November 21, 2023.

A research proposal describes what you will investigate, why it’s important, and how you will conduct your research.

The format of a research proposal varies between fields, but most proposals will contain at least these elements:

Introduction

Literature review.

• Research design

Reference list

While the sections may vary, the overall objective is always the same. A research proposal serves as a blueprint and guide for your research plan, helping you get organized and feel confident in the path forward you choose to take.

Table of contents

Research proposal purpose, research proposal examples, research design and methods, contribution to knowledge, research schedule, other interesting articles, frequently asked questions about research proposals.

Academics often have to write research proposals to get funding for their projects. As a student, you might have to write a research proposal as part of a grad school application , or prior to starting your thesis or dissertation .

In addition to helping you figure out what your research can look like, a proposal can also serve to demonstrate why your project is worth pursuing to a funder, educational institution, or supervisor.

Research proposal length

The length of a research proposal can vary quite a bit. A bachelor’s or master’s thesis proposal can be just a few pages, while proposals for PhD dissertations or research funding are usually much longer and more detailed. Your supervisor can help you determine the best length for your work.

One trick to get started is to think of your proposal’s structure as a shorter version of your thesis or dissertation , only without the results , conclusion and discussion sections.

Download our research proposal template

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

• Academic style
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See an example

Writing a research proposal can be quite challenging, but a good starting point could be to look at some examples. We’ve included a few for you below.

• Example research proposal #1: “A Conceptual Framework for Scheduling Constraint Management”
• Example research proposal #2: “Medical Students as Mediators of Change in Tobacco Use”

Like your dissertation or thesis, the proposal will usually have a title page that includes:

• The proposed title of your project
• Your supervisor’s name
• Your institution and department

The first part of your proposal is the initial pitch for your project. Make sure it succinctly explains what you want to do and why.

Your introduction should:

• Introduce your topic
• Give necessary background and context
• Outline your  problem statement  and research questions

To guide your introduction , include information about:

• Who could have an interest in the topic (e.g., scientists, policymakers)
• How much is already known about the topic
• What is missing from this current knowledge
• What new insights your research will contribute
• Why you believe this research is worth doing

As you get started, it’s important to demonstrate that you’re familiar with the most important research on your topic. A strong literature review  shows your reader that your project has a solid foundation in existing knowledge or theory. It also shows that you’re not simply repeating what other people have already done or said, but rather using existing research as a jumping-off point for your own.

In this section, share exactly how your project will contribute to ongoing conversations in the field by:

• Comparing and contrasting the main theories, methods, and debates
• Examining the strengths and weaknesses of different approaches
• Explaining how will you build on, challenge, or synthesize prior scholarship

Following the literature review, restate your main  objectives . This brings the focus back to your own project. Next, your research design or methodology section will describe your overall approach, and the practical steps you will take to answer your research questions.

To finish your proposal on a strong note, explore the potential implications of your research for your field. Emphasize again what you aim to contribute and why it matters.

For example, your results might have implications for:

• Improving best practices
• Informing policymaking decisions
• Strengthening a theory or model
• Challenging popular or scientific beliefs
• Creating a basis for future research

Last but not least, your research proposal must include correct citations for every source you have used, compiled in a reference list . To create citations quickly and easily, you can use our free APA citation generator .

Some institutions or funders require a detailed timeline of the project, asking you to forecast what you will do at each stage and how long it may take. While not always required, be sure to check the requirements of your project.

Here’s an example schedule to help you get started. You can also download a template at the button below.

Download our research schedule template

If you are applying for research funding, chances are you will have to include a detailed budget. This shows your estimates of how much each part of your project will cost.

Make sure to check what type of costs the funding body will agree to cover. For each item, include:

• Cost : exactly how much money do you need?
• Justification : why is this cost necessary to complete the research?
• Source : how did you calculate the amount?

To determine your budget, think about:

• Travel costs : do you need to go somewhere to collect your data? How will you get there, and how much time will you need? What will you do there (e.g., interviews, archival research)?
• Materials : do you need access to any tools or technologies?
• Help : do you need to hire any research assistants for the project? What will they do, and how much will you pay them?

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

Methodology

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

Once you’ve decided on your research objectives , you need to explain them in your paper, at the end of your problem statement .

Keep your research objectives clear and concise, and use appropriate verbs to accurately convey the work that you will carry out for each one.

I will compare …

A research aim is a broad statement indicating the general purpose of your research project. It should appear in your introduction at the end of your problem statement , before your research objectives.

Research objectives are more specific than your research aim. They indicate the specific ways you’ll address the overarching aim.

A PhD, which is short for philosophiae doctor (doctor of philosophy in Latin), is the highest university degree that can be obtained. In a PhD, students spend 3–5 years writing a dissertation , which aims to make a significant, original contribution to current knowledge.

A PhD is intended to prepare students for a career as a researcher, whether that be in academia, the public sector, or the private sector.

A master’s is a 1- or 2-year graduate degree that can prepare you for a variety of careers.

All master’s involve graduate-level coursework. Some are research-intensive and intend to prepare students for further study in a PhD; these usually require their students to write a master’s thesis . Others focus on professional training for a specific career.

Critical thinking refers to the ability to evaluate information and to be aware of biases or assumptions, including your own.

Like information literacy , it involves evaluating arguments, identifying and solving problems in an objective and systematic way, and clearly communicating your ideas.

The best way to remember the difference between a research plan and a research proposal is that they have fundamentally different audiences. A research plan helps you, the researcher, organize your thoughts. On the other hand, a dissertation proposal or research proposal aims to convince others (e.g., a supervisor, a funding body, or a dissertation committee) that your research topic is relevant and worthy of being conducted.

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Mathematics Research Proposals Samples For Students

24 samples of this type

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Research Proposal On Whiteboard on Mathematics Classroom

Virtual architecture model, smashing research proposal about research questions, impacts of interactive boards in mathematics classrooms..

- What are the effects of white board technology on mathematics student’s performance and attention? - Do mathematics students engage better while using interactive white boards than without the white board?

Research description

Purpose statement research proposals example, impact of interactive board in mathematics classroom.

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Example Of Research Proposal On The Correlation Between Student Anxiety And Academic Performance In Low-Level College

This paper examines the correlative effects of stress levels on examination results, particularly in areas of academic study where students are already struggling. The research examines the test scores and stress levels of remedial and basic-level mathematics students in the undergraduate level, tracking their changes in stress level over time and the effects that changes in stress level has on a student’s academic performance in in-class mathematics examinations.

Introduction

Research proposal on research hypotheses:, education research proposal samples, free math group studying discourse community research proposal sample, common core standards in education: research proposal research proposal sample, introduction, free research proposal on the relationship between preschool programs and kindergarten readiness, the research aim research proposal template for faster writing, research outline proposal: development of geometry by the hippocrates of chios.

Introduction Hippocrates made mathematical advancement during the Golden Age in which fundamental concepts of geometry began thriving in the social dynamics (Huffman, and Filolaos 197). Some of the two core mathematic techniques that occurred during this era include axiomatic techniques to geometry and introduction of paradoxes by the Zeno of Elea (Bell 138). Principally, the paradoxes were concerned with the determination of infinite and infinitesimal mathematic concepts (Klette, and Azriel 455).

Good Research Proposal About Project-Based Learning

This research proposal will employ a longitudinal experimental design to investigate student learning using Project-based learning for middle school literature classrooms within the same school. The results will be measured by IOWA testing every term over a 3 year time period and compared to the results of the students from traditional classroom setting. Assessment scores will be the dependent variables. The literature review of six peer-reviewed articles is included. The purpose of the study, hypotheses, methodology, participants, procedure, instruments and data analysis will be described.

Radiation Detector Failures Research Proposals Examples

Proper research proposal example about the impact of computers on individual learning, unknown cumulative distribution function research proposal, problem statement research proposal example.

Dropping Out or Pushed Out: The Impact of High School Dropout Rate Relative To High Stakes Testing Policy In The State Of Michigan

The Research Project Research Proposal Examples

Doctor candidate:.

Philosophy of Transformation: Differentiation or Subtraction Summary in Key Words Philosophy of transformation; Deleuze; Badiou; differentiation, subtraction, (re-, de-) territorialization; folding; plane of consistency; events (interventions); truth procedure; subject; the capitalism; the democratic materialism

Summary of the Theme and the Aim of the Project

Research questions: a sample research proposal for inspiration & mimicking, exemplar research proposal on winston educational foundation to write after, improvements in public education.

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Anaheim, California

818.432.2465

Dear City Councilman Roberts:

Example of components of a computer research proposal.

Introduction The application of computers is widespread in the current generation. Computers form a fundamental part of our daily lives as well as activities. The application of computers ranges from simple mathematical computations in devices like calculators to complex mathematical computations in industries. Virtually everything depends on computers for operation and completion of various tasks and processes in equal measure. The use of computer presents a variety of advantages over other alternative methods of accomplishing tasks (Krishnamoorthy, et al, 2009).

Background Research

Good recidivism among paroled inmates: discussion research proposal example.

(Institute)

Returning to prison for paroled inmates: Introduction

Good research proposal on p(g,s,r)= p(g/s,r)p(s/r)p(r), good research proposal about gcu: res 880.

Dropping Out or Pushed Out: The Impact of High School Dropout Rate Relative to High Stakes Testing Policy in Wayne County, State of Michigan

Dissertation Prospectus Dropping Out or Pushed Out: The Impact of High School Dropout Rate Relative to High Stakes Testing Policy in Wayne County, State of Michigan <Insert Chair Name>

Dissertation Prospectus

Preparing design and technology students for the future research proposal, research proposal on nursing homes, statement of the problem.

Old age is associated with several mental illnesses, which culminate into other psychosocial issues. For example, dementia and other related conditions such as the Creutzfeudz Jacob’s disease – as caused by advanced senility – have become common in the modern world. Usually, these diseases affect old people, which become more and more problematic as the age advances. The role of caring for the old people has therefore become very vital, usually requiring increased care and special treatment to these people.

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An research proposal examples on mathematics is a prosaic composition of a small volume and free composition, expressing individual impressions and thoughts on a specific occasion or issue and obviously not claiming a definitive or exhaustive interpretation of the subject.

Some signs of mathematics research proposal:

• the presence of a specific topic or question. A work devoted to the analysis of a wide range of problems in biology, by definition, cannot be performed in the genre of mathematics research proposal topic.
• The research proposal expresses individual impressions and thoughts on a specific occasion or issue, in this case, on mathematics and does not knowingly pretend to a definitive or exhaustive interpretation of the subject.
• As a rule, an essay suggests a new, subjectively colored word about something, such a work may have a philosophical, historical, biographical, journalistic, literary, critical, popular scientific or purely fiction character.
• in the content of an research proposal samples on mathematics , first of all, the author’s personality is assessed - his worldview, thoughts and feelings.

The goal of an research proposal in mathematics is to develop such skills as independent creative thinking and writing out your own thoughts.

Writing an research proposal is extremely useful, because it allows the author to learn to clearly and correctly formulate thoughts, structure information, use basic concepts, highlight causal relationships, illustrate experience with relevant examples, and substantiate his conclusions.

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How to Compose a Quality Research Proposal for Mathematics

Best tips on what will make your research proposal for mathematics stand out.

What is a Research Proposal in Mathematics Education?

This one is an official document representing the significance of the study. It’s a kind of plan you submit to the supervisors or the funding committee to share information about your research goals, as well as investigation issues, objectives, and methods related to teaching, learning, program development, or assessment in mathematics education.

Crafting an impactful research proposal for mathematics is extremely hard, although utterly exciting. Most students’ problems begin when choosing mathematics research areas . Other issues are often related to a lack of fundamental knowledge and complexity of particular topics & concepts, predicting the potential study influence, or suggesting effective issue solutions. Ordinary time management issues may also create a lot of hassle.

Except for the difficulty factor, there’s the need to follow strict structural and formatting guidelines. Obviously, writing professionals can easily compose a good text. Learners, on the other hand, are often doing this for the first time. Despite all the different approaches to crafting proposals, almost always, mathematics research encompasses the following parts:

• Problem overview.
• (Potential) solutions.
• Costs (both in human efforts and budgetary ones).
• Possible benefits.

Of course, the action research proposal in mathematics content will change according to the specific mathematics research topics and corresponding college guidelines. We believe it is completely obvious that writing such a complex task requires extraneous amounts of effort and time. As a result, many learners decide to delegate these assignments to seasoned experts, freeing up their time for more important responsibilities.

How to Write Best Research Proposal in Mathematics Easily

Despite all the different approaches, almost always, a mathematical survey encompasses the following parts:

• Choosing a Specific Topic. Formulate clearly the problem you are going to solve, explain its relevance, and articulate a concise, well-structured question or hypothesis your study aims to answer. If you have several research proposal in mathematics topics, try to choose a specific one that interests you and have enough materials to study.
• Highlighting Importance: Formulate the significance of your investigation and its possible implications on the mathematics field. Justify why it is significant and how it enhances knowledge.
• Tailoring to Audience: Adapt your engineering proposal to your target audience, whether it’s an academic committee, potential advisors, or funding agencies. Take into account their interests, worries, and expectations.
• Conducting a Literature Review: Thoroughly examine existing literature related to your chosen topic and prepare the theoretical background for your action research proposal in mathematics.
• Outlining Your Methodology: Describe the methods and techniques you plan to use to investigate the chosen mathematics issue. Explain why these methods are appropriate and how you will apply them.
• Proposing a Timeline: Create a realistic timeline that outlines your mathematics project’s key milestones and stages.
• Budget and Resources: Estimate the necessary research resources, including materials, software, equipment, and any potential travel. Justify the budget allocation based on the requirements of your work.
• Writing a Clear and Compelling Paper: Craft a well-structured and engaging research proposal in mathematics education following the guidelines provided by your institution or funding agency.
• Citations: Properly cite all sources you reference in your paper using the appropriate citation style (e.g., APA, MLA, Chicago).
• Proofreading and Formatting: Check the text for grammatical errors, typos, and formatting issues. Ensure consistency in style and formatting throughout the document.

Review Our Sample of Action Research Proposal in Mathematics

We recommend you check the following sample of action research proposal in mathematics to see for yourself the quality of the work. It includes such parts as:

• Introduction
• Background of the Study
• Statement of the Research
• Limitation of the Study
• References.

Click and DOWNLOAD FULL  Research Proposal for PhD in Mathematics

Some topics for action research proposal in mathematics.

In case you lack inspiration, we’ve listed a few mathematics topics to give you some inspiration.

In addition, many experts recommend moving away from traditional research proposal topics in mathematics and looking more broadly. Mathematical theoretical concepts are at the core of various fields, covering many engineering, architectural, and business industries. You can also find good ideas by checking out studies in information and computer technology.

Quite a few finance and accounting fields also involve mathematics concepts. The same can be said about logistics, social and political sciences, business, and management. Perhaps some ideas are not on the surface, and you will have to dig deeper. However, as a result, you will be able to identify several worthy solutions that can not only take your research proposal to the next level but also make it more relevant, valuable, and effective.

How to Start Writing Mathematics Research Proposal?

Sometimes, it may be difficult to get started because of the abovementioned factors. Nevertheless, we recommend a few techniques to help you get a grip on your writing.

• Set goals you are sure to accomplish and move step by step, sticking to a certain schedule ( e.g., use the Pomodoro technique).
• Take some ready-made examples of proposals dedicated to working with theoretical frameworks, as a mathematics research proposal may have different approaches to presenting your research than any others related to applied solutions.
• Acquire the support of your supervisor – any writing prompts, guidance, one-to-one conversations, etc. Getting help isn’t a weakness but a testament to your desire to develop a better project proposal.

You can also try to start a mathematics research proposal by preparing a theoretical base and additional materials, visuals, graphs, diagrams, etc. First, it will allow you to focus and choose a direction for your work. Secondly, having a variety of ready-made materials is ideal for combating the fear of a blank sheet. In addition, a well-designed research proposal involving many mathematics visuals has greater value and, in all likelihood, will be better received by the target audience.

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