mathematics degree coursework

Department of Mathematics

The mathematics major.

This page has a few notes that may be helpful to mathematics majors. Other useful sources of information: 

• For details about math major requirements, please see the current edition of YCPS.
• For more information, take a look at our extensive  Math major FAQ.
• For detailed information about introductory courses and assistance choosing your path through them, please visit our  first year student resources site . 
• A list of recent textbooks for our courses is available. 

In summary: 

The introductory sequence into the mathematics major consists of linear algebra (Math 225 or 226), analysis (Math 255 or 256), and multvariable analysis / calculus (Math 302 or 120). 

Each Mathematics Major must take the senior seminar, Math 480 or Math 481, or the senior essay, Math 475. 

In total, mathematics majors must complete ten mathematics courses numbered 200 or higher (counting the introductory sequence and the senior seminar). 

There are two distributional requirements, categories and core areas.

There are five categories: algebra, combinatorics and number theory; logic and foundations; analysis; geometry and topology; applied mathematics. From three of the five categories, at least two courses in each must be completed. Yale course search provides current listing and descriptions of the courses. It lists the attributes for each course, and can be used to search for courses with a particular attribute. (A sample list of courses that could be offered, by category, can be found below.) 

For the second distributional requirement, students are required to take courses from at least two of the three core areas (all three are recommended): Algebra (Math 350 or higher), Real Analysis (Math 305 or higher) and Complex Analysis (Math 310 or higher). These courses form the core of the undergraduate major. 

The requirements for the Degree of Bachelor of Science in Mathematics include those for the B.A. degree, plus two additional advanced science courses approved by the DUS. A list of approved courses can be found in the  Math major FAQ .

Pure mathematics majors can count up to two courses from related departments. Some of these courses are listed below; a full list can be found in the  Math major FAQ . ( Joint majors may not substitute courses from other departments - a course to be counted toward the math requirements must have a math number - reasons for this policy are explained in our Math major FAQ .) 

Below is a list of courses that tend to belong to each category. Some of these courses are not offered every year, new ones may be added, and our offering may change in other ways in any given year. For a current list of courses that count toward a particular category, with up-to-date prerequisites, we encourage you to use the attribute search on YCS.

Algebra, Combinatorics, and Number Theory

(Math 350 and Math 370 are often taken as a 2-term sequence. Math 380 may also be taken for graduate credit, by students who have a graduate course requirement in the intensive major or the B.S./M.S. program. )

225 or 226 Linear Algebra 

244 Discrete Mathematics

340 Advanced linear algebra

345 Modern Combinatorics

350 Introduction to Abstract Algebra (also carries core area algebra attribute)

353 Introduction to Representation Theory (typically offered every other year)

354 Number Theory

370 Fields and Galois Theory (also carries core area algebra attribute)

373 Algebraic number theory (typically offered every other year)

380 Modern Algebra  (also carries core area algebra attribute)

440 Introduction to Algebraic Geometry (typically offered every other year)

Logic and Foundations

Math 270  Set Theory

Phil 267  Mathematical L ogic   (may count for pure math major only, with limit as noted above)

Phil 427 Computability and Logic (may count for pure math major only, with limit as noted above)

(Math 320-325 and Math 310-315 are generally taken as two term sequences; Math 315, 320, and 325 may also be taken for graduate credit, by students who have a graduate course requirement in the intensive major or the B.S./M.S. program.)

255 or 256 Analysis I

246  Ordinary Differential Equations 

302 Multivariable Analysis

305 Real Analysis (also carries core area real analysis attribute)

310 Introduction to Complex Analysis (also carries core area complex analysis attribute)

315 Intermediate Complex Analysis (also carries core area complex analysis attribute)

320 Measure Theory and Integration (also carries core area real analysis attribute)

325 Introduction to Functional Analysis (also carries core area real analysis attribute)

447 Partial differential equations  (typically offered every other year)

Geometry and Topology

360 Introduction to Lie Groups

430 Introduction to Algebraic Topology  (typically offered every other year)

435 Differential Geometry (typically offered every other year)

544 Introduction to algebraic topology (This is the only graduate course that carries an attribute.)

Applied Mathematics

241  Probability Theory

242  Theory of Statistics

246 Ordinary Differential Equations 

247 Partial Differential Equations

251 Stochastic Processes

310 Complex Analysis

330 Advanced probability

345 Modern combinatorics

421 Mathematics of Data Science (typically offered every other year)

Other courses that may be of interest

As noted above, these only count for pure math majors (not joint-math), and there is a maximum of two that may be counted. They carry no attributes. For the full list of courses that can be counted as outside electives for pure math majors, please see the math major FAQ . 

AMTH 437  Optimization Techniques

CPSC 365 or 366  (Intensive) Algorithms

(and other CPSC classes, such as 267, 427, 440, 460, 468)

ECON 135 or 136 (these may not be counted along with MATH 241 or 242)

ECON 351 Mathematical economics: game theory

S&DS 364 Information theory

S&DS 410 Statistical inference

What You Need to Know About Becoming a Mathematics Major

Mathematics majors can study pure mathematics or applied mathematics and go on to work in areas like finance, biotech and academia.

Becoming a Math Major

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Because mathematics is a fairly broad field, you’ll want to make sure you have an affinity for the breadth of the major.

Mathematics majors study the relationships between numbers, structures and patterns. Their classes range from algebra to statistics, and the concepts build on one another. Students learn skills like logic, analysis, abstract thinking and problem-solving, which are valuable to future employers.

What Is a Mathematics Major?

Math majors study algebra, calculus, geometry and the different equations needed to solve mathematical problems. They also learn how to think and apply that foundation to an array of larger, more complex problems. German mathematician Carl Friedrich Gauss called mathematics “the queen of the sciences” since it sheds so much light on the physical reality.

Some schools differentiate between pure mathematics and applied mathematics. One way to describe the difference between these two types of mathematics majors is that applied mathematics is math put to practical use, while pure mathematics is more of what you might see in the films "Good Will Hunting" or "A Beautiful Mind." Put another way, pure mathematics is the study of mathematics without the primary motivation of outside applications.

Mathematics vs. statistics major: What’s the difference?

While both majors require a lot of coursework involving numbers, the main difference between a mathematics major and a statistics major is what they do with these numbers. A mathematics major can generally take two directions: pure mathematics and applied mathematics. Students majoring in pure mathematics focus on the relationship between numbers and their values. Applied mathematics majors learn how to transfer their knowledge and computational thinking to other fields, like data encryption.

Where pure mathematics is about calculating numbers and applied math is about employing that knowledge of numbers in real-world scenarios, statistics focuses more on analyzing numbers and understanding their patterns or trends. Some schools offer statistics as a major, while others offer it as a concentration or specialization within the math major.

Common Coursework Mathematics Majors Can Expect

Many mathematics majors start their undergraduate degree program by taking an array of liberal arts classes, from psychology to English literature. But they also take a lot of mathematics courses. Programs typically require pure mathematics majors to take several courses of algebra that build upon one another. The same could go for calculus, analysis, geometry, logic, number theory, probability and statistics, and topology.

Students majoring in applied mathematics will take different courses, possibly including combinatorics, computer science , economics and finance, and statistics and data science. In the summers, some mathematics majors intern at companies and organizations to learn on-the-job skills in areas like risk modeling at banks or financial institutions, accounting at accounting firms, or analysis anywhere from financial firms to hospitals.

How to Know if This Major Is the Right Fit for You

Students who enjoyed math classes in high school and performed well in them, particularly in higher level and advanced placement courses, will likely be good candidates for math majors in college. This major involves a lot of time in study groups or meeting with teaching assistants to master especially tricky concepts. Because mathematics is a fairly broad field, with topics ranging from trigonometry to statistics to number theory, you’ll want to make sure you have an affinity for the breadth of the major, or at least an interest in its many forms.

Pick the Perfect Major

Discover the perfect major for you based on your innate wiring. The Innate Assessment sets you up for success by pairing you with majors, colleges and careers that fit your unique skills and abilities.

What Can I Do with a Mathematics Major?

Because so many aspects of life involve math or numbers, students who major in mathematics ultimately can pursue a number of jobs in the public or private sectors. The Bureau of Labor Statistics projects faster than average growth for some roles that mathematics degree holders can pursue, some of which have six-figure average annual salaries.

Data is sourced from the U.S. Bureau of Labor Statistics .

Students may wish to tailor their studies to their field of interest. Pure mathematics concentrates on theory and research, and is good for students who want to teach math or work in academia. An applied mathematics major focuses more on the real-world application of mathematical concepts and might be a better fit for students who hope to work in fields like business or technology.

Whether math majors pursue further education after earning a bachelor’s degree can depend on each individual’s career goals. For some roles, like data scientist, mathematician, statistician or operations research analyst, an advanced degree in math or a related field may be required or can help expand job opportunities. Math degree-holders who wish to pursue teaching may need a graduate degree to teach at the college level, or a state-issued license to teach at the grade school level.

While actuaries can enter their field with a bachelor’s degree in mathematics, they also must be certified by either the Casualty Actuarial Society or the Society of Actuaries , depending on the insurance field in which they plan to work.

What Mathematics Majors Say

“Choosing mathematics as a major can entail a rigorous academic journey, but it should not dissuade you from pursuing this path if it aligns with your passions and interests. A bachelor’s degree in mathematics holds relevance across various professional industries, such as Finance, the Federal Government, Education, Insurance, and in my case, Actuarial Consulting. Your undergraduate coursework will likely expose you to the fundamental and theoretical aspects of mathematics, alongside their practical application to real-world challenges and scenarios. Mathematics can also increase your critical thinking and analytical abilities, skills valued across many professions. A degree in mathematics is a journey very few people choose to take part in, but it can lead you to a fulfilling career with many opportunities.”

— Maia Goldstein , Auburn University, class of '24,

“Being a math major is like being an artist, using your mind to visualize abstract concepts and fitting them together to get the final piece. This final piece might even lead to more questions that you could potentially research on in the future. To anyone considering math, you are always learning something new in math, so it is ok to not know everything at first glance. Just keep practicing and you will eventually get a better understanding of the concepts you are working on.”

— Brayan Gutierrez , University of Houston, class of '24.

“As a mathematics major, you’ll develop problem-solving skills that are applicable in various career paths. My advice is to be curious, open-minded, and willing to learn. Mathematics is vast and you might discover a passion for an area you never considered before. I have come across several interesting subject areas in mathematics in which I really enjoy working out the problems.”

— David Torrent, Mississippi College, class of '24.

“The mathematics major starts out with a transition from high school level math by still following the model of a more-computation based curriculum, while also adding in some mathematical proofs to get students more comfortable with the classes to come. Around the second and third years, more proof-based classes become available, which is the core of the major. Proving theorems and propositions is what makes math ‘math’ after all! The material you learn in the upper-level courses brings this level of understanding and reasoning that can be applied to several fields outside of math - I myself find computer science classes a lot easier to understand having a background in mathematical logic and thinking. The best advice I can give to prepare prospective students is to note that math in college is not like math in high school. There is much more structure in college-level math classes that comes along with the field, and requires a deeper understanding of vocabulary that some may otherwise have taken for granted in high school math classes.”

— Alex Yelovich, University of Maryland, class of '25.

“One thing I do get questions about is what I actually do. This is a fair question as before college I could not tell you what a math major does. Basically for each foundational class, we start with nothing, just a few assumptions and definitions about mathematical objects. Then you build the universe from that stardust, you learn theorems, results, and more definitions until you have a foundational concept of the field, often building on an understanding that took centuries for the past mathematicians to get to. And then you can decide to do it all again the next semester or keep building on the universe you just made. One nice thing about getting a Math degree is that everyone will assume you are smart, as you have proved you can handle abstractions upon abstractions and while everything you learn may not be that applicable, your intuition is.”

— Matthew Walloch , Georgia Institute of Technology, class of '25.

Schools Offering a Mathematics Major

Check out some schools below that offer mathematics majors and find the full list of schools here that you can filter and sort.

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Undergraduate

Undergraduate students  welcome to the Harvard Mathematics Department! Check out the left sidebar and navigation bar above to navigate through this website and find all the information you need about our courses, concentration, and events!

First Year Students: Please Click Here for information on courses and your Math Placement Test

Math Major Roadmaps

This document outlines “roadmaps” of course options for undergraduates interested in particular fields and applications of mathematics. Each roadmap consists of three stages:

• Stage 1: Introductory courses with few prerequisites, accessible to a typical sophomore.
• Stage 2: More advanced classes for students who have mastered several stage-1 classes.
• Stage 3: The most advanced classes, often beginning graduate-level subjects, for students who have mastered many stage-1 and stage-2 classes. (Many math majors will never take a stage-3 course, and that’s okay!)

The stages also reflect priorities —for example, students interested in pursuing analysis probably want to take 18.100 as early as possible, whereas a student pursuing mathematical finance might take it later to deepen their understanding.

In each specialized field or application of mathematics below, we list courses that could be relevant for a career in that field —not just courses narrowly in that specialization, but also useful courses in broadly related areas. On the other hand, these specific courses are not requirements to pursue that field.

Note that a math degree requires 18.06/18.C06/18.700/701 (or approved substitutions thereof), but these are not necessarily listed in every roadmap below, nor do we list GIRs like 18.02.

Pure Mathematics

General comments: Below is a list of research areas. As an undergraduate, however, you should not conceive of yourself as specializing in one or another of these areas . A much better idea is to gain experience in several of them. You may find yourself taking more courses in one or another area, but all of these fields of study reinforce each other.

Stage 2, but not specific to any particular area: 18.821 (Project Lab in Mathematics) is a great introduction to some essential skills (research, teamwork, and communication).

• Stage 1: 18.090 , 18.700 + 18.703 , 18.700 + 18.701 + 18.702 or 18.701 + 18.702
• Stage 2: 18.704 , 18.715 , 18.721 , 18.782
• Stage 3: 18.705 , 18.706 , 18.725 , 18.745 , 18.755 , 18.783

Analysis & Geometry

• Stage 1: 18.090 , 18.100 , 18.700 / 18.701
• Stage 2: 18.101 , 18.102 , 18.103 , 18.104 , 18.112 , 18.152 , 18.950 , 18.994
• Stage 3: 18.125 , 18.155 , 18.156 , 18.952 , 18.965 , 18.966
• Stage 1: 18.090 , 18.510 , 18.701 or 18.700 + 18.703
• Stage 2: 18.400 , 18.404 , 18.504
• Stage 3: 18.515 (not offered regularly)

The MIT Philosophy department also offers subjects in logic: 24.241–24.245 and 24.711 . Also consider logic classes at Harvard .

Number Theory

• Stage 1: 18.090 , 18.700 + 18.703 or 18.701 + 18.702 , 18.781
• Stage 2: 18.704 , 18.721 , 18.782 , 18.784
• Stage 3: 18.705 , 18.725 , 18.783 , 18.785

Probability & Statistics

• Stage 1: 18.090 , 18.065 , 18.100 , 18.600 , 18.700 / 18.701
• Stage 2: 18.102 , 18.103 , 18.112 , 18.200 , 18.211 , 18.615 , 18.642 , 18.650
• Stage 3: 18.125 , 18.675 , 18.676 , 18.677 , 18.338 , 18.416 , 18.424 , 18.655 , 18.657

Topology & Geometry

• Stage 1: 18.090 , 18.100 , 18.112 , 18.701 + 18.702 or 18.700 + 18.703 , 18.900 , 18.950
• Stage 2: 18.101 , 18.102 , 18.901 , 18.904 , 18.952 , 18.994
• Stage 3: 18.116 , 18.155 , 18.721 , 18.755 , 18.782 , 18.905 , 18.906 , 18.965 , 18.966

Applied Mathematics

Combinatorics.

• Stage 1: 18.090 , 18.100 , 18.200 , 18.400 , 18.600 , 18.701 + 18.702 or 18.700 + 18.703 , 18.900
• Stage 2: 18.204 , 18.211 , 18.212 , 18.112 , 18.404 , 18.410 , 18.453 , 18.721 , 18.781 , 18.901 , 18.950
• Stage 3: 18.217 , 18.218 , 18.225 , 18.226 , 18.338 , 18.455 , 18.615 , 18.705 , 18.715 , 18.725 , 18.745

Computer Science

• Stage 1: 18.06 / 18.C06 / 18.700 , 18.062 , 18.090 , 18.200 , 18.330 , 18.600 , 18.650 , 18.701
• Stage 2: 18.204 , 18.211 , 18.400 , 18.404 , 18.410 , 18.424 , 18.434 , 18.453
• Stage 3: 18.337 , 18.415 , 18.416 , 18.425 , 18.435 , 18.437 , 18.455 , 18.783

Students in this area should strongly consider supplementing their math courses with several courses in computer science; see the 18c major requirements for typical choices.

Economics and Finance

• Stage 1: 18.03 , 18.05 , 18.06 / 18.C06 / 18.700 , 18.065 , 18.090 , 18.300 , 18.330 , 18.600 , 18.650
• Stage 2: 18.100 , 18.152 , 18.303 , 18.453 , 18.642
• Stage 3: 18.103 , 18.125 , 18.675 , 18.676 , 18.677 , 18.335 , 18.337 , 18.338 , 18.352 , 18.353 , 18.355 , 18.615 , 18.655

Students interested in economics and finance should strongly consider supplementing their math courses with several classes in course 14 and 15, if not a minor or double major.

Computational Science and Engineering

• Stage 1: 18.03 , 18.06 / 18.C06 / 18.700 , 18.04 , 18.05 , 18.062 , 18.065 , 18.090 , 18.200 , 18.303 , 18.330 , 18.600 , 18.650 , 18.S190 , 18.S191
• Stage 2: 18.100 , 18.404 , 18.434 , 18.410 , 18.701
• Stage 3: 18.335 , 18.336 , 18.337 , 18.338 , 18.367 , 18.415 , 18.437

Students in this area should consider supplementing their math courses with several courses in computer science, both for software engineering (e.g. 6.100A , 6.1010 ) and numerical methods or optimization (e.g. 6.7201 , 6.7330 ). For students interested in computational modeling of physical systems, see also the Physical Applied Math classes below.

Physical Applied Math

• Stage 1: 18.03 , 18.04 , 18.06 / 18.C06 / 18.700 , 18.090 , 18.300 , 18.303 , 18.330 , 18.352 , 18.353 , 18.354 , 18.600 , 18.650
• Stage 2: 18.100 , 18.112 , 18.152 , 18.384 , 18.417
• Stage 3: 18.102 , 18.103 , 18.305 , 18.306 , 18.335 , 18.355 , 18.357 , 18.367 , 18.369 , 18.376 , 18.377

Students interested in physical applied mathematics should strongly consider supplementing their math courses with at least 2–3 non-GIR courses in physics and/or engineering, depending on their field of interest, if not a minor or double major.

Statistics and Data Science

• Stage 1: 18.05 , 18.06 / 18.C06 / 18.700 , 18.062 , 18.065 , 18.090 , 18.100 , 18.200 , 18.330 , 18.600 , 18.650 , 18.701
• Stage 2: 18.102 , 18.112 , 18.204 , 18.642
• Stage 3: 18.125 , 18.675 , 18.676 , 18.335 , 18.338 , 18.615 , 18.657

Students in this area should consider supplementing their math courses with courses in computer science on machine learning and courses in economics on econometrics.

Major in Mathematics

First upper-division math courses.

It should be emphasized that the character of mathematics changes sharply between lower and upper-division courses. The role of computation diminishes and there is a greater emphasis on deductive reasoning. While some students find the theoretical approach more congenial, most find upper-division courses more difficult. Because of this, it is strongly recommended that only students who earned grades of B- or better in all of Math 53, Math 54 or Math 56, and Math 55 apply to the major programs in Mathematics or Applied Mathematics. Additionally, the advising staff recommend Mathematics 110 as your first upper-division class. Students are more successful in making the transition with this course. Math 104 is a particularly demanding class and should be taken later in your program. Be aware that top students spend 12 to 15 hours per class beyond the lectures and sections, so plan your course load accordingly.

Eligibility to Declare the Major

You are eligible to declare the major in Mathematics or Applied Mathematics if you have met ALL of the following criteria:

• Completion of Math 1A & Math 1B (or equivalent) with averages grades of at least "C". For our policy on Advanced Placement scores, please see the following  link .
• Completion of Math 53, Math 54 or Math 56, and Math 55 (or equivalent) with minimum grades of "C" in each, or completion of two of those three courses (with minimum grades of "C" in each) and currently enrolled in the third.  If declaring while currently enrolled in the final lower-division requirement, that course will need to be completed with a letter grade of at least "C".  Please note that we will only accept Computer Science 70 in lieu of Math 55 if you are declared major in Computer Science or Electrical Engineering and Computer Science and declare Mathematics/Applied Mathematics as an additional major.
• If you have already taken one or more upper division math courses, you should have a grade point average of at least 2.0 from those courses completed at the time of declaration. Note, however, that you do not need to have completed an upper division math course in order to declare.

Any alterations to the above requirements must be authorized (in writing) by the Head Major Advisor, upon referral from an Undergraduate Advisor in 964 or 965 Evans Hall.

Major Declaration Procedures

Submit an Application for the Major in Mathematics/Applied Mathematics to our dedicated declaration email address, both of which you can find our our  declaration webpage . 

Note that double majors require signatures from both your departments. If we are the first to sign your Double Major Petition, we will send it back to you to take to your second department. If your Double Major Petition is already signed by your first department, we can forward it to L&S Advising for final approval.)

Honors Program

See our  Honors page  for information about graduating with honors in Math or Applied Math.

Course Enrollment and CalCentral

Each semester advising holds are placed on math and applied math majors who have been declared for more than one semester. Mathematics and Applied Mathematics majors must consult with their Faculty Advisor for their first CalCentral registration period after declaring the major.  In subsequent semesters, they may meet with the Staff Advisors. Meeting the Faculty or Staff Advisors should take place prior to the student's enrollment appointment to ensure removal of the hold in a timely manner. Before meeting with the Advisor, the student should plan a tentative program for the coming semester, and have an overall plan for completing the major. Enrollment packets consisting of a Course Approval Form (green) and a Major Checklist (white) which shows your completed courses and grades will be available in the Main Office (970 Evans) two weeks prior to the start of Phase I enrollment appointments. Faculty Advisors hold regular  office hours  during the academic year. These hours are also posted on the bulletin board outside 964 Evans. It is best to allow time for more than one meeting in case decisions depend on information not available at the first visit. When the Advisor and the student have agreed on a program of study, the Advisor will sign the Course Approval Form (green). Approved electives should be indicated on the bottom of the program form and initialed by the Advisor. Major holds are released by the Staff Advisors in 964 and 965 Evans Hall. Admitted transfer students should participate in orientation programs during the Summer preceding their first semester at Cal. Returning students should see their faculty advisor or the Undergraduate Advisor during the semester prior to their readmitted term. Although students are formally required to see their Faculty Advisors only when they first declare the major, they are strongly encouraged to consult with them, or seek the advice of any faculty member, at any time. If the Advisor's  office hours  conflict with the student's classes, the student should schedule an appointment with via email.

Credit by Examination

Outstanding  lower-division  students may choose to fulfill one or more of the lower-division requirements via credit-by-exam. Although the University awards only P/NP grades for credit-by-exam, credit-by-exam in any of the lower division prerequisite classes is acceptable for entry into the major. The Credit by Examination Petition is available through the following  link  on the Office of the Registrar's forms website. In order to file the petition, the student must acquire the approval of: (a) an instructor willing to administer the examination, and (b) the Major Advisor, ( only if already declared ).  The list of eligibility criteria for Credit by Examination can be found on page two of the petition. (Note: you must be registered in the term in which the examination is to be taken; you may only take Credit by Exam in Fall and Spring terms; you must already have a 2.0 or better UC GPA - meaning it can be taken only after at least one term at UC.)

Course Equivalency

Equivalency of courses taken at other colleges and universities should be determined early in the application process. Articulation agreements with the California Community Colleges can be found on assist.org and non-California Community College coursework will be individually evaluated by a Non-Major Faculty Advisor prior to the student declaring the major or minor. For more information about this process, visit our  Course Equivalency website .

Program Changes

Students can add or drop courses via CalCentral through the WEDNESDAY of the FOURTH week of classes. Grading option changes from letter grade to Pass/No Pass or from Pass/No Pass to letter grade can be done via CalCentral through the TENTH week of classes. Any student with fewer than 13 units needs permission from L&S Undergraduate Advising, located on the 2nd floor of Evans Hall, for a reduced study load.

Minimum and Maximum Limits of Number of Mathematics Courses Taken

Majors must take a minimum of four upper-division courses to establish residency in either of the math majors. The only limitation on the maximum number of upper-division and graduate mathematics courses a major may take is a College of Letters and Science regulation which states that students cannot register beyond the semester in which s/he surpasses their 130th unit. Advance planning can result in hitting 130 units and having an additional semester available, should you need it. An Undergraduate Advisor in 964 or 965 Evans can assist you.

Passed/Not Passed Grading (P/NP)

Courses taken to fulfill major requirements must be taken for a letter grade. The one exception is four units of Mathematics 199 (offered pass/not pass only) which may be used if approved by one's Faculty Advisor. Mathematics 199 cannot be used to study material covered in standard courses. To be eligible for enrollment, a student must have completed 60 units and have a minimum cumulative grade point average of 2.0. Additional regulations concerning 199 courses are outlined in the College of Letter and Science Earning Your Degree Guide. Staff in 970 Evans can assist students with the enrollment procedure.

Probation and Dismissal

A mathematics major whose cumulative grade-point average in the upper-division major taken at Berkeley falls below 2.0 will be placed on departmental probation. The departmental grade-point average computation includes both required courses in the major and approved electives. Any additional upper-division or graduate mathematics courses which are not used to satisfy major requirements are exempted. Students are expected to check their grades at the end of each semester. A student on probation will be subject to dismissal from the major if the grade-point average is not brought up to 2.0 within the following term. Questions concerning probation and dismissal may be directed to an Undergraduate Advisor in 964 or 965 Evans or the College of Letters and Science Advising, 206 Evans Hall.

Additional Academic Assistance

The Undergraduate Program Office, 970 Evans Hall, maintains a  list of tutors  for students seeking assistance. There are tutors listed for mathematics courses at all levels, from the most basic, precalculus courses, through upper-division, and even including basic graduate level courses. Students make arrangements with tutors on an individual basis. The  Student Learning Center , located in the Cesar Chavez Center, offers group and drop-in tutoring for the basic lower division classes: Mathematics 1A-1B, and 53-54. Call (510) 642-7332 for scheduling and other information. There are also Academic Centers located at the dorms that provide drop-in tutoring during the evenings.

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The Mathematics courses we offer are designed to help prepare you for a career in education, engineering, data analysis, and scientific research, providing a strong foundation in mathematical concepts and their practical applications in various fields.

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Searches related to mathematics

In summary, here are 10 of our most popular mathematics courses.

• Introduction to Mathematical Thinking :   Stanford University
• Introduction to Calculus :   The University of Sydney
• Basic Mathematics :   Birla Institute of Technology & Science, Pilani
• Mathematics for Machine Learning and Data Science :   DeepLearning.AI
• Math Prep: College & Work Ready :   University of North Texas
• Algebra: Elementary to Advanced :   Johns Hopkins University
• Mathematics for Machine Learning :   Imperial College London
• Introduction to Statistics :   Stanford University
• Mathematics for Engineers :   The Hong Kong University of Science and Technology
• Data Science Math Skills :   Duke University

Learn Mathematics Online

Delve into the fascinating world of mathematics with our courses, carefully designed to accommodate learners at every stage of mathematical understanding. Starting with fundamental concepts like algebra and geometry, our curriculum smoothly transitions into more complex areas such as calculus, statistics, and beyond. Throughout your learning journey, you'll encounter real-world applications demonstrating the practicality and beauty of mathematical theories. Guided by esteemed educators from top universities and leading industry professionals, you will cultivate a deeper appreciation for the discipline and a robust analytical toolkit. Our mathematics courses are ideal for students seeking academic growth, professionals enhancing their quantitative skills, or anyone curious about the patterns that underpin our world. Engage with us for a comprehensive and enriching educational experience that empowers you to unlock the mysteries of mathematics and apply them across various aspects of life and work.

Frequently Asked Questions about Mathematics

What is mathematics ‎.

Simply put, mathematics is the study of numbers, but it's so much more than that. Mathematics deals with quantity, shape, and arrangement. Ancient civilizations contributed to the science of math as we know it today, yet scientists are making new discoveries using mathematics in the present. Mathematics can be as simple as addition and subtraction, or it can be as complex as calculus and other higher level studies. Mathematicians study and solve both theoretical problems and issues with real-world applications. ‎

Why study mathematics? ‎

Skills in mathematics can benefit you no matter what career path you're in, but learning math can also benefit you in other ways. In the course of your day, chances are you're going to use math, whether you're developing a computer program or balancing a checking account, so having those skills at your fingertips will make your job easier. Mathematics also helps you strengthen your cognitive functions and problem-solving skills. Math gives you a better understanding of the world around you as well, because it's the foundation of scientific study and transcends culture and language. ‎

What are typical careers that use mathematics? ‎

You use math in some way or another in any workplace, but there are specific career paths that rely on mathematics for success. Some mathematics careers are in demand and pay high salaries, such as statisticians, data scientists, and software engineers. If you love helping people make and invest money, turn that passion along with your math skills into a career as an accountant or investment planner. Actuaries help determine the costs of financial risk, while economists look at math and finance at a larger scale. You can even help companies understand the accuracy of their financial records as an auditor. ‎

How can online courses on Coursera help me learn mathematics? ‎

Online courses on Coursera can help you gain the understanding and application you need to learn the concepts in mathematics that can help you take the next step in your career. You have the opportunity to learn about data modeling, computer programming, and differential equations, for example. Depending on your interests, you can also learn about algebra, game theory, statistics, machine learning, and precalculus. ‎

What are the benefits of taking an online Mathematics course? ‎

Online Mathematics courses offer a convenient and flexible way to enhance your knowledge or learn new Mathematics skills. Choose from a wide range of Mathematics courses offered by top universities and industry leaders tailored to various skill levels. ‎

What Mathematics courses are best for training and upskilling employees or the workforce? ‎

When looking to enhance your workforce's skills in Mathematics, it's crucial to select a course that aligns with their current abilities and learning objectives. Our Skills Dashboard is an invaluable tool for identifying skill gaps and choosing the most appropriate course for effective upskilling. For a comprehensive understanding of how our courses can benefit your employees, explore the enterprise solutions we offer. Discover more about our tailored programs at Coursera for Business here . ‎

Other topics to explore

Mathematics

Undergraduate Program

Mathematics is the science of order, and mathematicians seek to identify instances of order and to formulate and understand concepts that enable us to perceive order in complicated situations. The concentration in Mathematics is designed to acquaint the student with the most important general concepts underlying the three branches of modern mathematics. Concentration in mathematics will provide an adequate basis for further study in either pure or applied mathematics. Students are also eligible to apply for an A.B./A.M. degree program.

The graduate Mathematics Program at Harvard is designed for students who hope to become research mathematicians and show definite promise in this direction. Once the student has demonstrated a command of basic mathematical concepts by passing the qualifying examination, the emphasis is on getting to the frontiers of some field by independent reading, advanced courses, and seminars. The Cambridge area is one of the most active centers of mathematics in the world. Harvard, Brandeis, and Northeastern Universities and the Massachusetts Institute of Technology have an especially close association in mathematics, and the Harvard University Center of Mathematical Sciences and Applications hosts conferences, seminars, and workshops.

Secondary Menu

• Math Intranet

We offer both a bachelor of science and a bachelor of arts in math. Students who plan to attend graduate school in mathematics or the sciences should consider working towards the bachelor of science degree.

Prerequisites

Recommended: Students without computer experience are encouraged to take COMPSCI 101: Program Design and Analysis I

Note:  Students considering a math major are strongly encouraged to take MATH 221, which teaches linear algebra along with the skills of rigorous  mathematical reasoning needed by math majors. However,  an alternative route is to take MATH 218 along with MATH 240, 242, or 245 in order to develop the skills of writing mathematical proofs. The combination of 218 with 240, 242, or 245 may be counted as the prerequisite for any course that requires MATH 221. (Many students who took MATH 221 may also benefit from these courses as well.)

In particular, Pratt students considering a math major should  not  take  the engineering sequence MATH 218/353; they should instead take MATH 221 followed by MATH 356 for a first course in differential equations. This alternative sequence has been approved by Pratt for engineers.

Note:  A student interested in the math major who has already taken MATH 202 (and therefore is ineligible to enroll in MATH 212, 219, or 222) should consult with the Director of Undergraduate Studies as soon as possible.

Math Courses

Science courses.

• Students who choose the PHYSICS 161D/162D sequence are encouraged to supplement it with at least one semester of the half-credit sequence PHYSICS 161L/162L, Introductory Experimental Physics.
• Students who choose STAT 210 are encouraged to supplement it with the half-credit course STAT 211.
• Students who wish to substitute a more advanced course for one of the above science courses (such as a graduate version of one of the courses above) should contact the Director of Undergraduate Studies with their specific request.
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• Mathematical questions arising from the COVID epidemic
• Exploring minimal surfaces modulo p
• Modeling the dynamics of filter fouling
• Smoothness of subspace-valued maps
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• Characterizing emerging features in cell dynamics
• Parameter interference in epidemiological models
• Calculus of variations and notions of convexity
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Online Math Degree Bachelor's in Mathematics

Add a Math Degree to your Resume

• $330/credit (120 total)
• Transfer up to 90 credits
• Earn math credits for what you already know
• 24/7 online access to the classroom
• No application fee or SAT/ACT
• Prepares you for many jobs in quantitative and analytical fields

Online Math Degree Program Overview

Earn your Bachelor of Arts (BA) in Mathematics online and develop a strong mathematical skill set, including an advanced ability in mathematical methods, reasoning and problem solving.

Earn math credits for what you already know: Save time and tuition with our Pathways to Math Success assessments. Depending on your scores, you could earn up to 12 math credits – the equivalent of 4 courses – toward your degree for less than $50 per assessment. For additional information, or to register for a Pathways to Math Success assessment, contact your admission counselor or academic advisor today.

What You'll Learn

• Analyze and solve problems across a broad range of mathematical areas
• Construct, evaluate and present mathematical solutions
• Use mathematical reasoning to solve real-world problems
• Create logical mathematical proofs

How You'll Learn

At SNHU, you'll get support from day 1 to graduation and beyond. And with no set class times, 24/7 access to the online classroom, and helpful learning resources along the way, you'll have everything you need to reach your goals.

Concentration Options

Join thousands of SNHU students who’ve saved time and money by earning credits and having courses waived – simply by demonstrating what you already know.

Mathematics Career Outlook

An online math degree can provide you with the foundation for career opportunities in a broad range of fields. However, some fields or specializations may require additional training or credentials.

Use mathematics, statistics and financial theory to assess financial risk for businesses.

Operations Research Analyst

Statistician, financial analyst.

Assess the performance of stocks, bonds and other investments to determine the best financial strategies for your clients.

Management Analyst

Computer programmer.

Bring life to the ideas software developers create by writing the code that gives computer applications functionality.

You'll be able to apply what you've learned to a variety of real-world problems in almost any field, from pharmaceuticals to sports statistics. Wherever there's a need for quantitative analysis or modeling, you'll have an opportunity to use your online math degree in real, impactful ways.

"Throughout high school I made it a point to help my fellow classmates understand what was frustrating them in math and would always strive for the moment when they got a big smile on their faces and started enjoying themselves … There is nothing more pure than math; it's the core basic universal truth. Science is a theory that somewhere down the line might be disproven by some improbable possibility. I love science, but no matter what, math ties into everything," Benet said.

A math degree helped Luanne Dexter '18 change jobs entirely.

"Towards the end of my degree program, I began working with someone from the SNHU career center, because I wanted to transition out of an industry that I was no longer passionate about," she said. "I also wanted to find a company with a better culture. During this time, I was laid off and because I was already working towards transitioning, it made the situation a lot less stressful than it would have been under normal circumstances."

Dexter credits the combination of her math degree and SNHU's career services to leading her to her employer.

"I learned so much from this program and it was a great experience," she said. "I am so thankful for the opportunities it brought me. ... This degree allowed me to complete my goal and it inspired me to go for my master's degree (an MS in Data Analytics, class of 2020) with SNHU!"

Job Growth and Salary

Although job projections can vary by region and title, careers related to mathematics are generally on the rise.

According to the U.S. Bureau of Labor Statistics, job prospects for actuaries are set to soar 23% through 2032, 23% for operations research analysts, 30% for statisticians and 10% for management analysts. All considerably faster than the national average of 3% for all occupations. 1

In 2022, the median annual wage for actuaries was $113,990, $85,720 for operations research analysts, $98,920 for statisticians and $95,570 for financial analysts. 1 Along with promising career outlook projections, the median annual salary for management analysts was $95,080. 1

Understanding the Numbers When reviewing job growth and salary information, it’s important to remember that actual numbers can vary due to many different factors — like years of experience in the role, industry of employment, geographic location, worker skill and economic conditions. Cited projections do not guarantee actual salary or job growth.

Start Your Journey Toward an Online Mathematics Degree

Why snhu for your math degree flexible with no set class meeting times, you can learn on your schedule and access online course materials 24/7. affordable as part of our mission to make higher education more accessible, we’re committed to keeping our tuition rates low. in fact, we offer some of the lowest online tuition rates in the nation. prior coursework could also help you save time and money. snhu’s transfer policy  allows you to transfer up to 90 credits toward your bachelor's degree and 45 credits for an associate degree from your previous institutions—that means you could save up to 75% off the cost of tuition. you could also save time and money by getting college credit for previous work experience , or by taking advantage of military discounts and employer tuition assistance if available to you. respected founded in 1932 , southern new hampshire university is a private, nonprofit institution with over 160,000 graduates across the country. snhu is accredited by the new england commission of higher education (neche), a regional accreditor, which advocates for institutional improvement and public assurance of quality.  recently, snhu has been nationally recognized for leading the way toward more innovative, affordable and achievable education: u.s. news & world report named snhu the 2021 most innovative university in the north and one of the nation's "best regional universities" awarded the 21st century distance learning award for excellence in online technology by the united states distance learning association (usdla) a $1 million grant from google.org to explore soft skills assessments for high-need youth network at southern new hampshire university, you'll have access to a powerful network of more than 300,000 students, alumni and staff that can help support you long after graduation. our instructors offer relevant, real-world expertise to help you understand and navigate the field. plus, with our growing, nationwide alumni network, you'll have the potential to tap into a number of internship and career opportunities. 93.6% of online students would recommend snhu (according to a 2022 survey with 17,000+ respondents). discover why snhu may be right for you . admission requirements expanding access to quality higher education means removing the barriers that may stand between you and your degree. that’s why you can apply at any time and get a decision within days of submitting all required materials: completed free undergraduate application prior transcripts, which we can retrieve at no cost to you test scores are not required as part of your application acceptance decisions are made on a rolling basis throughout the year for our 6 (8-week) undergraduate terms . how to apply if you’re ready to apply, follow these simple steps to get the process going: complete a free undergraduate application submit any additional documents required work with an admission counselor  to explore financial options  and walk through the application process if you have questions or need help filling out your application, call 1.888.387.0861 or email [email protected] . if (typeof accordiongroup === "undefined") { window.accordiongroup = new accordion(); } accordiongroup.init(document.getelementbyid('78c1fc7d472542b6b4f9946816540589')); learn from industry experts.

"The instructors at SNHU not only brought classroom experience but most of them brought in real-world experience. They really helped me to understand how the concepts are used and also how to find additional resources if I needed them."

Courses & Curriculum

If you have a genuine interest in mathematics, you have an ideal way to multiply your skills with the help of instructors in the online BA in Mathematics degree program.

This online math degree provides broad exposure to the key branches of mathematics. In addition, students can strengthen their math skills and marketability through the use of industry-standard programming languages like Python, Matlab and R to solve real-world problems in business, finance – just about any discipline.

You'll complete 14 math courses as you work toward your math degree online – 4 of which are elective courses based on your particular areas of interest. Courses in this program are taught by seasoned faculty with real-world experience as mathematicians and educators across a broad range of fields, including business, economics, technology, natural sciences and social sciences.

"The class that stood out the most to me was Differential Equations," Dexter said. "This was the last in-person course I had taken at a local college ... and the professor told us that most of us would fail. That was the case, and I was really discouraged after that. SNHU was a completely different experience . I was given so many resources and full support of the professor. I was so happy when I completed that course since it signified a new experience, and I knew I was in the right program."

Learn more about how to study math .

Curriculum Requirements & Resources

General education.

All undergraduate students are required to take general education courses , which are part of SNHU's newly redesigned program, The Commons. The goal of The Commons' curriculum is to empower you with some of the most in-demand skills, so you can succeed not only in your academic career, but in your personal and professional life too.

Technology Resources

We provide cloud-based virtual environments in some courses to give you access to the technology you need for your degree – and your career. Learn more about our virtual environments .

Earn Math Credits

Save time and tuition with our Pathways to Math Success assessments. Depending on your scores, you could earn up to 12 math credits – the equivalent of 4 courses – toward your degree for less than $50 per assessment. For additional information, or to register for a Pathways to Math Success assessment, contact your admission counselor or academic advisor today.

Minimum Hardware Requirements Component Type   PC (Windows OS)   Apple (Mac OS)   Operating System  Currently supported operating system from Microsoft.   Currently supported operating system from Apple.  Memory (RAM)  8GB or higher  8GB or higher  Hard Drive  100GB or higher  100GB or higher  Antivirus Software  Required for campus students. Strongly recommended for online students.  Required for campus students. Strongly recommended for online students.  SNHU Purchase Programs  Visit Dell   Visit Apple   Internet/ Bandwidth  5 Mbps Download, 1 Mbps Upload and less than 100 ms Latency  5 Mbps Download, 1 Mbps Upload and less than 100 ms Latency  Notes:   Laptop or desktop?   Whichever you choose depends on your personal preference and work style, though laptops tend to offer more flexibility.  Note:   Chromebooks (Chrome OS) and iPads (iOS) do not meet the minimum requirements for coursework at SNHU. These offer limited functionality and do not work with some course technologies. They are not acceptable as the only device you use for coursework. While these devices are convenient and may be used for some course functions, they cannot be your primary device. SNHU does, however, have an affordable laptop option that it recommends: Dell Latitude 3301 with Windows 10.  Office 365 Pro Plus  is available free of charge to all SNHU students and faculty. The Office suite will remain free while you are a student at SNHU. Upon graduation you may convert to a paid subscription if you wish. Terms subject to change at Microsoft's discretion. Review system requirements for  Microsoft 365 plans  for business, education and government.  Antivirus software:  Check with your ISP as they may offer antivirus software free of charge to subscribers.  if (typeof accordionGroup === "undefined") { window.accordionGroup = new accordion(); } accordionGroup.init(document.getElementById('f756dce5bd874c61855f6f6e92d88470')); Tuition & Fees

As a private, nonprofit university, we’re committed to making college more accessible by making it more affordable. That’s why we offer some of the lowest online tuition rates in the nation.

We also offer financial aid packages to those who qualify, plus a 30% tuition discount for U.S. service members, both full and part time, and the spouses of those on active duty.

Tuition Rates are subject to change and are reviewed annually. *Note: students receiving this rate are not eligible for additional discounts.

Additional Costs No Application Fee, Course Materials ($ varies by course)

Frequently Asked Questions

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Department Website: http://mathematics.uchicago.edu

Program of Study

The Department of Mathematics provides an environment of research and comprehensive instruction in mathematics and applied mathematics at both undergraduate and graduate levels.

At the undergraduate level, we offer four degrees: a Bachelor of Arts (BA) in Mathematics, a Bachelor of Science (BS) in Mathematics, a Bachelor of Science in Applied Mathematics, and a Bachelor of Science in Mathematics with Specialization in Economics. Students in other fields of study may also complete a minor in mathematics; information for the minor follows the description of the major.

The requirements for a degree in mathematics or in applied mathematics express the educational intent of the Department of Mathematics; they are drawn with an eye toward the cumulative character of an education based in mathematics, the present emerging state of mathematics, and the scholarly and professional prerequisites for an academic career in mathematics.

Requirements for each bachelor's degree look to the advancement of students' general education in modern mathematics and their understanding of its relation to the other sciences (BS) or to the other arts (BA).

Descriptions of the detailed requirements that give meaning to these educational intentions follow. Students should understand that any particular degree requirement can be modified if persuasive reasons are presented to the department; petitions to modify requirements are submitted to one of the Co-Directors of Undergraduate Studies. Students should note that only one undergraduate degree may be earned from the Department of Mathematics. 

At what level does an entering student begin mathematics at the University of Chicago? The College and the Department of Mathematics offer several placement exams to help determine the appropriate starting point for each entering student. During the summer and through Orientation Week, there are three such exams:

• The Online Mathematics Placement Test (must be taken by all entering students)
• The Higher-Level Mathematics Placement Exam
• The Calculus Accreditation Exam

The Online Mathematics Placement Test must be taken (once) by each  entering student in the summer prior to matriculation. The other two exams are offered later in the summer, and students may be invited to take one or the other on the basis of their success on the Online Mathematics Placement Test.

All students are eligible to take MATH 11200 Studies In Mathematics I or MATH 11300 Studies In Mathematics-2 (or various other courses in Statistics and Computer Science) in order to satisfy the general education requirement in the mathematical sciences.

For students interested in taking Calculus, the following placements are possible based on the Online Mathematics Placement Test:

• MATH 10500 Fundamental Mathematics I
• MATH 13100 Elem Functions and Calculus I
• MATH 15100 Calculus I
• MATH 15200 Calculus II
• MATH 15300 Calculus III , or MATH 15250 Mathematical Methods for Economic Analysis , or MATH 18300 Mathematical Methods in the Physical Sciences I , or MATH 19620 Linear Algebra

Completing the first two quarters of Calculus (MATH 13100-13200 or MATH 15100-15200 or MATH 16100-16200 or MATH 16110-16210) satisfies the general education requirement, as does completing any higher-level course, which then confers back credit for the first two quarters of Calculus. Additionally, completing MATH 15200 confers back credit for MATH 15100.

MATH 10500 is recommended for students who need MATH 13100-13200 in their degree programs but do not place into MATH 13100. Such students should take MATH 10500-13100-13200 in their first year. MATH 10500 counts as a general elective and does not count toward the general education requirement in the mathematical sciences.

MATH 13100-13200-13300 and MATH 15100-15200-15300 are the standard Calculus sequences. The former is intended for students with little or no Calculus background, and the course has thrice-weekly lectures and twice-weekly tutorials as required parts of the course. The latter is intended for students with some Calculus background who demonstrate adequate readiness on the placement test.

For social sciences students interested in economics, the Economics Department recommends taking MATH 15250 after MATH 15200 and before MATH 15300. Thus, economics students with the highest-level Online placement should begin in MATH 15250 (unless they are also interested in one of the physical sciences majors listed below). Economics students with a MATH 13100 placement should take the full MATH 13100-13200-13300 sequence before taking MATH 15250.

Physical sciences students interested in the chemistry, biochemistry, physics, astrophysics, molecular engineering, and/or statistics majors should not take MATH 15250 or MATH 15300 or MATH 19620; instead, they should take the MATH 18300-18400-18500-18600 sequence. To take MATH 18300, a student should have completed MATH 15200 or have earned the highest-level Online placement. Students with an AP Calculus BC score of 5 or an International Baccalaureate Mathematics HL score of 7 will also be invited to begin in MATH 18300, but these scores do not supersede the Online placement, and the MATH 18300 invitation is not equivalent to the (higher) MATH 15300/15250/18300/19620 placement.

Additionally, students who receive a sufficiently high score on the Online Mathematics Placement Test, as well as students who earn a score of 5 on the AP Calculus BC exam or a score of 7 on the International Baccalaureate HL exam, will also receive an invitation to enroll in MATH 16100 Honors Calculus I  or  MATH 16110 Honors Calculus I (IBL) . These are the first courses in the  MATH 16100-16200-16300 Honors Calculus I-II-III  and  MATH 16110-16210-16310 Honors Calculus I (IBL); Honors Calculus II (IBL); Honors Calculus III (IBL)  sequences, which are highly theoretical courses that best prepare students for further study in pure mathematics, although they are also taken by many students other than mathematics majors. Students who begin in  MATH 16100 Honors Calculus I  or  MATH 16110 Honors Calculus I (IBL)  forgo credit for  MATH 15100 Calculus I  and/or  MATH 15200 Calculus II .

On the basis of the Online Mathematics Placement Test results, namely, by achieving the highest-level Online placement, students may also be invited to take one of the other two exams.

The Calculus Accreditation Exam is for students who do not plan to take  further  mathematics at the University of Chicago but who wish to earn credit for  MATH 15100-15200 Calculus I-II . Most students with Online placement of MATH 15300/15250/18300/19620 earn back credit for MATH 15100 and 15200 by their successful completion of the higher course. But, if such a course is not part of a student's academic plan, they can nevertheless earn back credit for MATH 15100 and 15200 by passing the Calculus Accreditation Exam.

The Higher-Level Mathematics Placement Exam is for students who would like to begin their mathematics coursework at the University of Chicago in a higher-level course than MATH 15300/15250/18300/19620. On the basis of this exam, a student may receive placement into:

• MATH 15910 Introduction to Proofs in Analysis
• MATH 20250 Abstract Linear Algebra
• MATH 20300 Analysis in Rn I , or MATH 20310 Analysis in Rn I (accelerated) , or MATH 20320 Analysis in Rn I (IBL)

A small number of students each year receive an invitation to enroll in MATH 20700 Honors Analysis in Rn I . Admission to this course is by invitation only to those first-year students with superior performance on the Higher-Level Mathematics Placement Exam or to those second-years with an excellent record in MATH 16100-16200-16300 Honors Calculus I-II-III or MATH 16110-16210-16310 Honors Calculus I (IBL); Honors Calculus II (IBL); Honors Calculus III (IBL) .

Students who are granted three quarters of calculus placement on the basis of the Higher-Level Mathematics Placement Exam and who do not qualify for admission to MATH 20700 Honors Analysis in Rn I will place into one of the courses in the list above. Such students may also consult with one of the Co-Directors of Undergraduate Studies about the option of beginning with MATH 16100 Honors Calculus I or MATH 16110 Honors Calculus I (IBL) , so that they would be eligible for admission to Honors Analysis the following year.

Students who submit a score of 5 on the Calculus AB Advanced Placement exam in mathematics receive placement into MATH 15100 Calculus I . Students who submit scores of 4 or 5 on the AP Calculus BC exam or a 7 on the International Baccalaureate Higher Level Calculus exam receive placement into MATH 15200 Calculus II . Currently, we do not offer course credit or placement for British A-level or O-level examinations.

Program Requirements

Undergraduate programs.

Four bachelor's degrees are available in the Department of Mathematics: the BA in mathematics, the BS in mathematics, the BS in applied mathematics, and the BS in mathematics with specialization in economics. Programs qualifying students for the BA degree provide more elective freedom. Programs qualifying students for the BS degrees require more emphasis on the physical sciences, while the BS in mathematics with specialization in economics has its own set of specialized courses with more electives in economics in place of electives in the physical sciences. All degree programs, whether qualifying students for a degree in mathematics or in applied mathematics, require fulfilling the College's general education requirements. The general education sequence in the physical sciences must be selected from either first-year chemistry or first-year physics.

Except for the BS in mathematics with specialization in economics, each degree requires at least five courses outside mathematics. (Detailed descriptions follow for each degree.) These courses must be within the Physical Sciences Collegiate Division (PSCD).

• One of these courses must complete the three-quarter sequence in basic chemistry or basic physics.
• Astrophysics (ASTR 20500 or above, except not 21700, 22060, or 23500)
• Computer Science (CMSC 12100 or above, except not 29512)
• Data Science (DATA 21100 or above)
• Geophysical Sciences (all GEOS courses not cross-listed as PHSC, except also not 27300 or 29600)
• Molecular Engineering (all MENG courses except 20300, 22200, 22400, 23140, 23150, or 23500)
• Statistics (STAT 22000 or above)
• Graduate courses from these departments may also be used to fulfill these requirements.

Please note in particular the different requirements outside of mathematics described below in the degree program for the BS in mathematics with specialization in economics.

Degree Programs in Mathematics

All students who are majoring in mathematics are required to complete the following courses, with additional requirements that are specific to the four degrees offered:

• A three-quarter Calculus sequence or equivalent competence as demonstrated on the Higher-Level placement exam
• Either  MATH 16300 Honors Calculus III  or  MATH 16310 Honors Calculus III (IBL)  as the third quarter of the calculus sequence or  MATH 15910 Introduction to Proofs in Analysis
• The linear algebra course  MATH 20250 Abstract Linear Algebra
• ​ MATH 20300-20400-20500 Analysis in Rn I-II-III
• MATH 20310-20410-20510 Analysis in Rn I (accelerated); Analysis in Rn II (accelerated); Analysis in Rn III (accelerated)
• MATH 20320-20420-20520 Analysis in Rn I-II-III (IBL)
• MATH 20700-20800-20900 Honors Analysis in Rn I-II-III
• MATH 25400-25500 Basic Algebra I-II
• MATH 25700-25800-25900 Honors Basic Algebra I-II-III

Students may not use both  MATH 15910 Introduction to Proofs in Analysis  and  MATH 16300 Honors Calculus III / MATH 16310 Honors Calculus III (IBL)  to satisfy major or minor requirements.

For students whose first mathematics course at the University of Chicago is  MATH 20700 Honors Analysis in Rn I , the MATH 15910 Introduction to Proofs in Analysis / MATH 16300 Honors Calculus III / MATH 16310 Honors Calculus III (IBL) requirement is waived entirely.

Candidates for the BA and BS in mathematics take at least one course in basic algebra. BA candidates may opt for the first quarter of either the regular or the honors sequence ( MATH 25400-25500 Basic Algebra I-II or MATH 25700-25800-25900 Honors Basic Algebra I-II-III ), whereas candidates for the BS degree must take the first two quarters of one of the two sequences.

The remaining mathematics courses needed in the programs (three for the BA, two for the BS) must be selected, with due regard for prerequisites, from the following list of approved mathematics courses. Note that STAT 25100 Introduction to Mathematical Probability or STAT 25150 Introduction to Mathematical Probability-A also meet the requirement. BA candidates may include MATH 25500 Basic Algebra II or MATH 25800 Honors Basic Algebra II  as one of these three. All three mathematics courses in the Paris Mathematics program each Spring Quarter also meet this requirement.

List of Approved Courses

With an exception (see below) in the BS in mathematics with specialization in economics, no course from any professional school or program—including the University of Chicago Booth School of Business, the University of Chicago Harris School of Public Policy, Toyota Technological Institute at Chicago, and Financial Mathematics—may be used to satisfy requirements for an undergraduate degree in mathematics.

BS candidates are further required to select a minor field, which consists of three additional courses that are outside the Department of Mathematics and are within the same department in the Physical Sciences Collegiate Division (PSCD). Please see the second paragraph under "Program Requirements" above for more details.

Summaries of Requirements

Summary of requirements: mathematics ba, summary of requirements: mathematics bs, degree program in applied mathematics.

Candidates for the BS in applied mathematics all take prescribed courses in numerical analysis, algebra, complex variables, ordinary differential equations, and partial differential equations. In addition, candidates are required to take six courses outside of Mathematics but within the Physical Sciences Collegiate Division (PSCD), with three of these six comprising a secondary field in a single PSCD department.

Summary of Requirements: BS in Applied Mathematics

Degree program in mathematics with specialization in economics.

This program is a version of the BS in mathematics. The BS degree is in mathematics with the designation "with specialization in economics" included on the final transcript. Candidates are required to complete a yearlong sequence in calculus, MATH 15910 Introduction to Proofs in Analysis if the calculus sequence did not terminate with MATH 16300 Honors Calculus III / MATH 16310 Honors Calculus III (IBL) , the one-quarter course  MATH 20250 Abstract Linear Algebra , a yearlong sequence in analysis ( MATH 20300-20400-20500 Analysis in Rn I-II-III or MATH 20310-20410-20510 Analysis in Rn I (accelerated); Analysis in Rn II (accelerated); Analysis in Rn III (accelerated) or MATH 20700-20800-20900 Honors Analysis in Rn I-II-III ), and one quarter of abstract algebra ( MATH 25400 Basic Algebra I or MATH 25700 Honors Basic Algebra I ), and earn a grade of at least C– in each course. Students must also take STAT 25100 Introduction to Mathematical Probability or STAT 25150 Introduction to Mathematical Probability-A . The remaining two mathematics courses must be among the following six: MATH 27000 Basic Complex Variables , MATH 27100 Measure and Integration ,  MATH 27200 Basic Functional Analysis , MATH 27300 Basic Theory of Ordinary Differential Equations ,  MATH 23500 Markov Chains, Martingales, and Brownian Motion , or MATH 26200 Point-Set Topology . A C average or higher must be earned in these two courses.

In addition to the third quarter of basic chemistry or basic physics, the eight courses required outside the Department of Mathematics must include STAT 23400 Statistical Models and Methods or STAT 24400 Statistical Theory and Methods I . The remaining seven courses should be in the Department of Economics and must include ECON 20000-20100-20200 The Elements of Economic Analysis I-II-III or ECON 20010 - ECON 20110 - ECON 20210 The Elements of Economic Analysis: Honors I-II-III and either ECON 21020 Econometrics or ECON 21030 Econometrics - Honors . The remaining three courses may be chosen from any undergraduate economics course numbered higher than ECON 20210 The Elements of Economic Analysis III Honors , except for ECON 21010 Statistical Methods in Economics . Courses with an ECMA designation may also be counted among these. A University of Chicago Booth School of Business course may be considered for elective credit if the course requires the equivalent of ECON 20100 as a prerequisite and is numbered as Chicago Booth 40000 or higher. Additionally, the course must pertain to the application of economic theory to a course subject that is not offered by the Department of Economics. Courses such as accounting, investments, and entrepreneurship will not be considered for economics elective credit. Consideration for elective credit must be done by petition before a student registers for the course. There will be no retroactive consideration for credit. Students must earn a grade of C or higher in each course taken in economics to be eligible for this degree.

It is recommended that students considering graduate work in economics use some of their electives to include at least one programming course ( CMSC 15100 Introduction to Computer Science I is strongly recommended) and an additional course in statistics ( STAT 24400-24500 Statistical Theory and Methods I-II or STAT 24410 Statistical Theory and Methods Ia and STAT 24500 Statistical Theory and Methods II are appropriate two-quarter sequences). Students planning to apply to graduate economics programs are strongly encouraged to meet with one of the economics undergraduate program directors before the beginning of their third year.

Summary of Requirements: BS in Mathematics with Specialization in Economics

Pass/fail grades.

Subject to College grading requirements and grading requirements for the major and with consent of instructor, students may take any mathematics course beyond the second quarter of Calculus for either a quality grade or for P/F grading. In mathematics, a grade of Pass is given only for work of C- quality or higher. Pass/Fail grading must be requested by the Friday of the ninth week of classes. The request should be in writing, and it must be communicated to the instructor. Once requested, a grade of Pass cannot be changed into a quality grade. It is the responsibility of the student to be sure that a grade of Pass is in compliance with their degree requirements. 

Courses in the Mathematics Major

All courses taken to meet requirements in the mathematics major must be taken for quality grades. A grade of C- or higher must be earned in each Calculus, analysis, or algebra course (including MATH 20250); and an overall grade average of C or higher must be earned in the remaining mathematics courses that a student uses to meet requirements for the major. Students must earn a grade of C or higher in each course taken in economics for the degree in mathematics with a specialization in economics. Mathematics or applied mathematics students may take any 20000-level mathematics courses elected beyond program requirements for P/F grading.

Incomplete Grades

Grades of Incomplete are given in the Department of Mathematics only to those students who have completed the large majority of the course work at passing quality and who are unable to complete some small portion of the course work by the end of the quarter. Arrangements are made between the instructor and the student in coordination with College Advising.

Withdrawals

Requests for Withdrawal grades should be submitted through College Advising and do not require the permission of the instructor. The request must be made by 5 p.m. the Monday of the ninth week of instruction or before the final work of the course is due, whichever is earlier.

The BA or BS with honors is awarded to students who, while meeting requirements for one of the mathematics degrees, also meet the following requirements: (1) a GPA of 3.25 or higher in mathematics courses and a 3.0 or higher overall; (2) no grade below C- and no grade of W in any mathematics course; (3) completion of at least one honors sequence (either MATH 20700-20800-20900 Honors Analysis in Rn I-II-III or MATH 25700-25800-25900 Honors Basic Algebra I-II-III ) with grades of B- or higher in each quarter; and (4) completion with a grade of B- or higher of at least five mathematics courses chosen from the list that follows so that at least one course comes from each group (i.e., algebra, analysis, and topology). No course may be used to satisfy both requirement (3) and requirement (4). If both honors sequences are taken, one sequence may be used for requirement (3) and one sequence may be used for up to three of the five courses in requirement (4).

Algebra Courses

Analysis courses, topology courses.

With departmental approval, MATH 29700 Proseminar in Mathematics , or any course(s) in the Paris Mathematics Program, may be chosen so that it falls in one of the three groups. One of the three Paris courses each year will be designated as a replacement for MATH 25500 Basic Algebra II / MATH 25800 Honors Basic Algebra II for students wishing to complete the BS degree. Additionally, one of the three Paris courses each year will be designated as a replacement for MATH 25900 Honors Basic Algebra III for candidates who are working toward graduation with honors.

Courses taken for the honors requirements (3) and (4) also may be counted toward courses taken to meet requirements for the major. Students do not need to apply for an honors degree, as all degree programs are automatically checked. However, a student who is concerned about meeting the requirements for honors should consult with one of the Co-Directors of Undergraduate Studies. 

Minor Program in Mathematics

The minor in mathematics requires a total of six or seven courses in mathematics, depending on whether or not MATH 15910 Introduction to Proofs in Analysis , MATH 16300 Honors Calculus III or MATH 16310 Honors Calculus III (IBL) is required in another degree program. If it is not used elsewhere, MATH 15910 Introduction to Proofs in Analysis , MATH 16300 Honors Calculus III or MATH 16310 Honors Calculus III (IBL) must be included in the minor, for a total of seven courses.

The remaining six courses must include the following courses:

• MATH 20300-20400-20500 Analysis in Rn I-II-III
• MATH 20320-20420-20520 Analysis in Rn I-II-III (IBL)  
• The first course in one of the algebra sequences ( MATH 25400 Basic Algebra I or MATH 25700 Honors Basic Algebra I )
• The sixth course may be chosen from either the second course in one of the algebra sequences ( MATH 25500 Basic Algebra II or MATH 25800 Honors Basic Algebra II ) or a mathematics course numbered 23000 or higher chosen in consultation with one of the Co-Directors of Undergraduate Studies

Under special circumstances and to avoid double counting, students may also use mathematics courses numbered 23000 or higher to substitute for up to two quarters of analysis or algebra, if these are required in another degree program.

No course in the minor can be double counted with the student's major(s) or with other minors; nor can it be counted toward general education requirements. Students must earn a grade of at least C- in each of the courses in the mathematics minor. More than one-half of the requirements for a minor must be met by registering for courses bearing University of Chicago course numbers.

Students should plan to meet with one of the Co-Directors of Undergraduate Studies by Spring Quarter of their third year to declare their intention to complete a minor program in mathematics and to obtain approval for the minor on the Consent to Complete a Minor Program form obtained online or from their College adviser.

Paris Mathematics Program

Each Spring Quarter, the Department of Mathematics offers a study abroad opportunity for students to take upper-level mathematics electives at the University's Center in Paris. Departmental faculty offer three successive three-week courses in specialized topics, and students also take a French language course from local French faculty. Students should have completed one of the analysis sequences ( MATH 20300-20400-20500 Analysis in Rn I-II-III or MATH 20310-20410-20510 Analysis in Rn I (accelerated); Analysis in Rn II (accelerated); Analysis in Rn III (accelerated) or MATH 20320-20420-20520 Analysis in Rn I-II-III (IBL) or MATH 20700-20800-20900 Honors Analysis in Rn I-II-III ) and at least one quarter of one of the algebra sequences ( MATH 25400 Basic Algebra I or MATH 25700 Honors Basic Algebra I ) before attending the Paris program. First round applications are due the prior Spring Quarter and should be submitted to the Study Abroad office. If the program does not reach maximum capacity, second round applications will also be accepted in the Autumn Quarter.

BA/MS or BS/MS in Mathematics

Qualified College students may receive both a bachelor's and a master's degree in mathematics concurrently at the end of their studies in the College. Qualification consists of satisfying all requirements of both degrees in mathematics. To be eligible for the joint program, a student should begin  MATH 20700 Honors Analysis in Rn I in the Autumn Quarter of the student's first year. By following a program of prescribed undergraduate course sequences in mathematics and succeeding in all courses with grades no lower than A–, the student becomes eligible to enroll in graduate courses in mathematics in the student's third year. While only a few students complete the joint bachelor's/master's program, many undergraduates enroll in graduate-level mathematics courses. Admission to all mathematics graduate courses requires prior written consent of the Director of Undergraduate Studies. This consent is based on an assessment by the director that it is in the student's best interest to enroll in the graduate course.

Students should submit their application for the joint program to one of the Co-Directors of Undergraduate Studies in the Department of Mathematics as soon as possible, but no later than the Winter Quarter of their third year.

Mathematics Courses

MATH 10500. Fundamental Mathematics I. 100 Units.

Students who place into this course must take it in their first year in the College. Must be taken for a quality grade. MATH 10500 will count only as one elective. This course does NOT meet the Core requirement in the mathematical sciences. This course covers basic precalculus topics with an emphasis on their use in Calculus. It is concerned with elements of algebra, coordinate geometry, and elementary functions, including trigonometric, and exponential functions.

Terms Offered: Autumn Prerequisite(s): Performance on the mathematics placement test Note(s): Recommended for students who need MATH 13100-13200 in their degree programs but who did not place into MATH 13100 originally. Such students should plan to take MATH 10500-13100-13200 in their first year.

MATH 11200-11300. Studies in Mathematics I-II.

MATH 11200 AND 11300 cover the basic conceptual foundations of mathematics by examining the ideas of number and symmetry. MATH 11200 addresses number theory, including a study of the rules of arithmetic, integral domains, primes and divisibility, congruences, and modular arithmetic. MATH 11300’s main topic is symmetry and geometry, including a study of polygons, Euclidean construction, polyhedra, group theory, and topology. These courses emphasize the understanding of ideas and the ability to express them through rigorous mathematical arguments. While students may take MATH 11300 without having taken MATH 11200, it is recommended that MATH 11200 be taken first. Either course in this sequence meets the general education requirement in mathematical sciences. These courses are at the level of difficulty of the MATH 13100-13200-13300 calculus sequence.

MATH 11200. Studies In Mathematics I. 100 Units.

MATH 11200 AND 11300 cover the basic conceptual foundations of mathematics by examining the ideas of number and symmetry. MATH 11200 addresses number theory, including a study of the rules of arithmetic, integral domains, primes and divisibility, congruences, and modular arithmetic. These courses emphasize the understanding of ideas and the ability to express them through rigorous mathematical arguments. While students may take MATH 11300 without having taken MATH 11200, it is recommended that MATH 11200 be taken first. Either course in this sequence meets the general education requirement in mathematical sciences. These courses are at the level of difficulty of the MATH 13100-13200-13300 calculus sequence.

Terms Offered: Autumn

MATH 11300. Studies In Mathematics-2. 100 Units.

Terms Offered: Winter Prerequisite(s): MATH 11200 recommended

MATH 13100-13200-13300. Elementary Functions and Calculus I-II-III.

MATH 13100-13200-13300 is a sequence in calculus for students who need some precalculus reinforcement. The sequence completes the necessary background and covers basic calculus in three quarters. This is achieved through three regular one-hour class meetings and two mandatory one-and-one-half-hour tutorial sessions each week. A class is divided into tutorial groups of about eight students each, and these meet with an undergraduate junior tutor for problem solving related to the course. Students completing MATH 13100-13200-13300 have a command of calculus equivalent to that obtained in MATH 15100-15200-15300. Students may not take the first two quarters of this sequence for P/F grading. MATH 13100-13200 meets the general education requirement in the mathematical sciences.

MATH 13100. Elem Functions and Calculus I. 100 Units.

MATH 13100 gives a careful treatment of limits, the continuity and differentiability of algebraic functions, and applications of the derivative.

Terms Offered: Autumn Winter Prerequisite(s): MATH 10500 or adequate performance on the mathematics placement test

MATH 13200. Elem Functions and Calculus II. 100 Units.

Topics examined in MATH 13200 include applications of differentiation; exponential, logarithmic, and trigonometric functions; the definite integral and the Fundamental Theorem of Calculus, and applications of the integral.

Terms Offered: Spring Winter Prerequisite(s): MATH 13100

MATH 13300. Elementary Functions and Calculus III. 100 Units.

In MATH 13300, subjects include more applications of the definite integral, improper integrals, and an introduction to infinite sequences and series and Taylor expansions. MATH 13300 also includes an introduction to multivariable calculus, such as functions of several real variables and integration of functions of several variables.

Terms Offered: Spring Prerequisite(s): MATH 13200

MATH 15100-15200-15300. Calculus I-II-III.

This is the regular calculus sequence in the department. Students entering this sequence are to have mastered appropriate precalculus material and, in many cases, have had some previous experience with calculus in high school or elsewhere. All Autumn Quarter offerings of MATH 15100, 15200, and 15300 begin with a rigorous treatment of limits and limit proofs. Students may not take the first two quarters of this sequence for P/F grading. MATH 15100-15200 meets the general education requirement in mathematical sciences.

MATH 15100. Calculus I. 100 Units.

This is the first course in the regular calculus sequence in the department. Students entering this sequence are to have mastered appropriate precalculus material and, in many cases, have had some previous experience with calculus in high school or elsewhere. MATH 15100 undertakes a careful treatment of limits, the differentiation of algebraic and transcendental functions, applications of differentiation, and the Mean Value Theorem. All Autumn Quarter offerings of MATH 15100 begin with a rigorous treatment of limits and limit proofs. Students may not take the first two quarters of this sequence for P/F grading. MATH 15100-15200 meets the general education requirement in mathematical sciences.

Terms Offered: Autumn Prerequisite(s): Placement based on the mathematics placement test(s) or appropiate AP score or IB score

MATH 15200. Calculus II. 100 Units.

This is the second course in the regular calculus sequence in the department. Students entering this sequence are to have mastered appropriate precalculus material and, in many cases, have had some previous experience with calculus in high school or elsewhere. MATH 15200 covers integration, techniques of integration, applications of the integral, and transcendental functions. All Autumn Quarter offerings of MATH 15200 begin with a rigorous treatment of limits and limit proofs. Students may not take the first two quarters of this sequence for P/F grading. MATH 15100-15200 meets the general education requirement in mathematical sciences.

Terms Offered: Autumn Winter Prerequisite(s): MATH 15100; or placement based on the mathematics placement test(s) or appropriate AP score or IB score

MATH 15300. Calculus III. 100 Units.

This is the third course in the regular calculus sequence in the department. MATH 15300 covers an introduction to infinite sequences and series and Taylor expansions, indeterminate forms and improper integration, and an introduction to multivariable integral calculus including functions of several real variables, double and triple integrals, integration of polar functions, change of variables, and applications of integration. All Autumn Quarter offerings of MATH 15300 begin with a rigorous treatment of limits and limit proofs.

Terms Offered: Autumn Spring Winter Prerequisite(s): MATH 15200; or placement based on the mathematics placement test(s)

MATH 15250. Mathematical Methods for Economic Analysis. 100 Units.

This is a course in mathematical techniques covers the basic topics of multivariable differential calculus including vectors and vector functions, partial derivatives, gradients, total derivative, and Lagrange multipliers. It also covers an introduction to optimization, including linear programming, the simplex method, the duality theorem, and the Kuhn-Tucker theorem. The tools and techniques covered in this course build the foundation for the Elements of Economic Analysis sequence offered by the Griffin Department of Economics.

Terms Offered: Autumn Spring Winter Prerequisite(s): MATH 15200 or MATH 13300 or placement

MATH 15910. Introduction to Proofs in Analysis. 100 Units.

This course is intended for students who are making the transition from MATH 13300 or 15300 to MATH 20250 and MATH 20300, or for students who need more preparation in learning to read and write proofs. This course covers the fundamentals of theoretical mathematics and prepares students for upper-level mathematics courses beginning with MATH 20250 and MATH 20300. Topics include the axioms for the real numbers, completeness and the least upper bound property, the topology of the real line, and sequences and series of real and complex numbers. Students who are majoring or minoring in mathematics may not use both MATH 15910 and MATH 16300 to meet program requirements.

Terms Offered: Autumn Spring Winter Prerequisite(s): MATH 15300 or MATH 13300 or MATH 18300 or superior performance on the mathematics placement test(s)

MATH 16100-16200-16300. Honors Calculus I-II-III.

MATH 16100-16200-16300 is an honors version of MATH 15100-15200-15300. A student with a strong background in the problem-solving aspects of one-variable calculus may be invited to register for MATH 16100-16200-16300. This sequence emphasizes the theoretical aspects of one-variable analysis and, in particular, the consequences of completeness in the real number system. MATH 16300 also includes an introduction to multivariable calculus. Students may not take the first two quarters of this sequence for P/F grading. MATH 16100-16200 meets the general education requirement in mathematical sciences.

MATH 16100. Honors Calculus I. 100 Units.

MATH 16100 emphasizes the theoretical aspects of one-variable analysis and, in particular, the consequences of completeness in the real number system. Topics include a rigorous treatment of the real numbers and the least upper bound property, limits, continuity, uniform continuity, and differentiation.

Terms Offered: Autumn Prerequisite(s): Invitation only based on superior performance on the mathematics placement test(s) or appropriate AP score or IB score

MATH 16200. Honors Calculus II. 100 Units.

MATH 16200 covers integration, the Fundamental Theorem of Calculus, transcendental functions, and other topics.

Terms Offered: Winter Prerequisite(s): MATH 16100

MATH 16300. Honors Calculus III. 100 Units.

MATH 16300 covers sequences and series, power series, and Taylor series. It also includes an introduction to multivariable calculus, such as functions of several real variables, partial derivatives, gradients, and the total derivative, and integration of functions of several variables.

Terms Offered: Spring Prerequisite(s): MATH 16200

MATH 16110-16210-16310. Honors Calculus I (IBL); Honors Calculus II (IBL); Honors Calculus III (IBL)

This sequence is an Inquiry Based Learning version of MATH 16100-16200-16300 Honors Calculus I-II-III. In this alternate version of Honors Calculus, rather than having lectures from instructors, students are given "scripts" of carefully ordered theorems whose proofs they prepare outside of class and then present in class for comment and discussion. MATH 16110-16210 meets the general education requirement in mathematical sciences and may not be taken for P/F grading.

MATH 16110. Honors Calculus I (IBL) 100 Units.

MATH 16110 gives a rigorous axiomatic treatment of the continuum and its topological properties.

MATH 16210. Honors Calculus II (IBL) 100 Units.

MATH 16210 puts an arithmetic structure on the continuum, and constructs the real numbers via Dedekind cuts. There follows a rigorous treatment of limits, continuity, differentiability, integrability, and the Fundamental Theorem of Calculus.

Terms Offered: Winter Prerequisite(s): MATH 16110

MATH 16310. Honors Calculus III (IBL) 100 Units.

MATH 16310 continues the rigorous treatment of single-variable Calculus with a discussion of infinite series. There follows an introduction to the main ideas of multivariable Calculus, including functions of several real variables, partial derivatives, gradients, the total derivative, and integration of functions of several variables.

Terms Offered: Spring Prerequisite(s): MATH 16210

MATH 17500. Basic Number Theory. 100 Units.

This course covers basic properties of the integers following from the division algorithm, primes and their distribution, and congruences. Additional topics include existence of primitive roots, arithmetic functions, quadratic reciprocity, and transcendental numbers. The subject is developed in a leisurely fashion, with many explicit examples.

Terms Offered: Autumn. Offered every other year Prerequisite(s): MATH 16300 or MATH 16310 or MATH 15910 or MATH 15900 or MATH 19900

MATH 17600. Basic Geometry. 100 Units.

This course covers advanced topics in geometry, including Euclidean geometry, spherical geometry, and hyperbolic geometry. We emphasize rigorous development from axiomatic systems, including the approach of Hilbert. Additional topics include lattice point geometry, projective geometry, and symmetry.

Terms Offered: Winter. Offered every other year Prerequisite(s): MATH 16300 or MATH 16310 or MATH 15910 or MATH 15900 or MATH 19900

MATH 18300-18400-18500-18600. Mathematical Methods in the Physical Sciences I-II-III-IV.

This is the full four-quarter sequence of mathematics courses for physical sciences majors.

MATH 18300. Mathematical Methods in the Physical Sciences I. 100 Units.

This is the first in a sequence of mathematics courses for physical sciences majors. The first part of the course covers infinite sums: convergence of infinite sequences and series, Maclaurin and Taylor series, complex numbers and Euler's formula. The second part covers elementary linear algebra: linear equations, vectors and matrices, dot products, cross products and determinants, applications to 3D geometry, eigenvectors and diagonalization.

Terms Offered: Autumn Spring Winter Prerequisite(s): MATH 15200 or MATH 13300 or MATH 16200 or MATH 16210 or placement

MATH 18400. Mathematical Methods in the Physical Sciences II. 100 Units.

This is the second in a sequence of mathematics courses for physical sciences majors. It covers multivariable calculus: functions of more than one variable, parameterized curves and vector fields, partial derivatives and vector derivatives (div/grad/curl), double and triple integrals, line and surface integrals, and the fundamental theorems of vector calculus in two and three dimensions (Green/Gauss/Stokes).

Terms Offered: Autumn Spring Winter Prerequisite(s): MATH 18300 or ((MATH 15300 or MATH 13300 or MATH 16300 or MATH 16310) and (MATH 19620 or MATH 20250 or STAT 24300))

MATH 18500. Mathematical Methods in the Physical Sciences III. 100 Units.

This is the third in a sequence of mathematics courses for physical sciences majors. It covers differential equations: first and second order ODE, systems of ODE, damped oscillators and resonance, Fourier series and Fourier transforms, Laplace transforms, and solutions of the heat and wave equations.

MATH 18600. Mathematics of Quantum Mechanics. 100 Units.

This course covers the mathematical foundations of quantum mechanics, including abstract linear algebra (vector spaces, bases, linear operators, inner products and orthogonality) and partial differential equations (with an emphasis on techniques relevant to solving Schrödinger's equation: series solutions of second order ODE, orthogonal functions, eigenfunctions and Sturm-Liouville theory, separation of variables).

Terms Offered: Autumn Spring Winter Prerequisite(s): MATH 18400 and MATH 18500

MATH 19620. Linear Algebra. 100 Units.

This course takes a concrete approach to the basic topics of linear algebra. Topics include vector geometry, systems of linear equations, vector spaces, matrices and determinants, and eigenvalue problems.

Terms Offered: Autumn Spring Winter Prerequisite(s): MATH 13300 or MATH 15200 or MATH 16200 or MATH 16210 or placement Note(s): Recommended sequence for ECON majors: MATH 19620, STAT 23400, ECON 210x0 in consecutive quarters.

MATH 20250. Abstract Linear Algebra. 100 Units.

This is a theoretical course in linear algebra intended for students taking higher level mathematics courses. Topics include vector spaces and linear transformations, matrices and the algebra of matrices, determinants and their properties, the geometry of R^n and C^n, bases, coordinates and change of basis, eigenvalues, eigenvectors, characteristic polynomial, diagonalization, special forms including QR factorization and Singular Value Decomposition, and applications.

Terms Offered: Autumn,Spring,Winter Prerequisite(s): MATH 16300 or MATH 16310 or MATH 15910 or MATH 15900 or MATH 19900

MATH 20300-20400-20500. Analysis in Rn I-II-III.

This three-course sequence is intended for students who plan to major in mathematics or who require a rigorous treatment of analysis in several dimensions. Both theoretical and problem solving aspects of multivariable calculus are treated carefully. All courses in the sequence require experience with a theoretical treatment of the real numbers, and hence MATH 20300 has a prerequisite of either MATH 16300 or MATH 15910. Additionally, MATH 20400 requires a serious treatment of linear algebra, and thus has a prerequisite of either MATH 20250 or STAT 24300. MATH 20300 covers the construction of the real numbers, the topology of R^n including the Bolzano-Weierstrass and Heine-Borel theorems, and a detailed treatment of abstract metric spaces, including convergence and completeness, compact sets, continuous mappings, and more. MATH 20400 covers differentiation in R^n including partial derivatives, gradients, the total derivative, the Chain Rule, optimization problems, vector-valued functions, and the Inverse and Implicit Function Theorems. MATH 20500 covers integration in R^n including Fubini's Theorem and iterated integration, line and surface integrals, differential forms, and the theorems of Green, Gauss, and Stokes. This sequence is the basis for all advanced courses in analysis and topology.

MATH 20300. Analysis in Rn I. 100 Units.

MATH 20300 covers the construction of the real numbers, the topology of R^n including the Bolzano-Weierstrass and Heine-Borel theorems, and a detailed treatment of abstract metric spaces, including convergence and completeness, compact sets, continuous mappings, and more.

Terms Offered: Autumn Spring Winter Prerequisite(s): MATH 16300 or MATH 16310 or MATH 15910 or MATH 15900 or MATH 19900

MATH 20400. Analysis in Rn II. 100 Units.

MATH 20400 covers differentiation in R^n including partial derivatives, gradients, the total derivative, the Chain Rule, optimization problems, vector-valued functions, and the Inverse and Implicit Function Theorems.

Terms Offered: Autumn Spring Winter Prerequisite(s): (MATH 20700 or MATH 20300 or MATH 20310 or MATH 20320) AND (MATH 20250 or STAT 24300)

MATH 20500. Analysis in Rn III. 100 Units.

MATH 20500 covers integration in R^n including Fubini's Theorem and iterated integration, line and surface integrals, differential forms, and the theorems of Green, Gauss, and Stokes

Terms Offered: Autumn Spring Winter Prerequisite(s): MATH 20400 or MATH 20410 or MATH 20800

MATH 20310-20410-20510. Analysis in Rn I (accelerated); Analysis in Rn II (accelerated); Analysis in Rn III (accelerated)

This sequence is an accelerated version of MATH 20300-20400-20500 Analysis in Rn I-II-III.

MATH 20310. Analysis in Rn I (accelerated) 100 Units.

This is an accelerated version of MATH 20300.

Terms Offered: Autumn Winter Prerequisite(s): MATH 16300 or MATH 16310 or MATH 15910 or MATH 15900 or MATH 19900. Students should have received a grade of B+ or better in MATH 16300, 16310, 15900, or 15910 in order to be properly prepared for the accelerated Analysis sequence.

MATH 20410. Analysis in Rn II (accelerated) 100 Units.

This is an accelerated version of MATH 20400.

Terms Offered: Spring Winter Prerequisite(s): (MATH 20700 or MATH 20310 or MATH 20320) AND (MATH 20250 or STAT 24300)

MATH 20510. Analysis in Rn III (accelerated) 100 Units.

This is an accelerated version of MATH 20500.

Terms Offered: Autumn Spring Prerequisite(s): MATH 20800 or MATH 20410

MATH 20320-20420-20520. Analysis in Rn I-II-III (IBL)

This is an Inquiry-Based Learning (IBL) version of MATH 20300-20400-20500.

MATH 20320. Analysis in Rn I (IBL) 100 Units.

This is an Inquiry-Based Learning (IBL) version of Math 20300.

Terms Offered: Autumn Prerequisite(s): MATH 16300 or MATH 16310 or MATH 15910

MATH 20420. Analysis in Rn II (IBL) 100 Units.

This is an Inquiry-Based Learning (IBL) version of MATH 20400.

Terms Offered: Winter Prerequisite(s): (MATH 20700 or MATH 20320) AND (MATH 20250 or STAT 24300)

MATH 20520. Analysis in Rn III (IBL) 100 Units.

This is an Inquiry-Based Learning (IBL) version of MATH 20500.

Terms Offered: Spring Prerequisite(s): MATH 20420

MATH 20700-20800-20900. Honors Analysis in Rn I-II-III.

This highly theoretical sequence in analysis is intended for the most able students. Topics include the real number system, metric spaces, basic functional analysis, and the Lebesgue integral.

MATH 20700. Honors Analysis in Rn I. 100 Units.

This is the first course in a highly theoretical sequence in analysis, and is intended for the most able students. Topics include the real number system, metric spaces, basic functional analysis, and the Lebesgue integral.

Terms Offered: Autumn Prerequisite(s): Invitation only

MATH 20800. Honors Analysis in Rn II. 100 Units.

This is the second course in a highly theoretical sequence in analysis. Topics include the real number system, metric spaces, basic functional analysis, and the Lebesgue integral.

Terms Offered: Winter Prerequisite(s): MATH 20700 and MATH 20250

MATH 20900. Honors Analysis in Rn III. 100 Units.

This is the third course in a highly theoretical sequence in analysis. Topics include the real number system, metric spaces, basic functional analysis, and the Lebesgue integral.

Terms Offered: Spring Prerequisite(s): MATH 20800

MATH 21100. Basic Numerical Analysis. 100 Units.

This course covers direct and iterative methods of solution of linear algebraic equations and eigenvalue problems. Topics include numerical differentiation and quadrature for functions of a single variable, approximation by polynomials and piece-wise polynomial functions, approximate solution of ordinary differential equations, and solution of nonlinear equations.

Terms Offered: Spring Prerequisite(s): MATH 18400 or 20000 or 20250 or 20400 or 20410 or 20420

MATH 21200. Advanced Numerical Analysis. 100 Units.

This course covers topics similar to those of Math 21100 but at a more rigorous level. The emphasis is on proving all of the results. Previous knowledge of numerical analysis is not required. Programming is also not required. The course makes extensive use of the material developed in the analysis sequence (ending in Math 20500 or Math 20900) and provides an introduction to other areas of analysis such as functional analysis and operator theory.

Terms Offered: Autumn Prerequisite(s): MATH 20500 or 20510 or 20520 or 20900

MATH 23500. Markov Chains, Martingales, and Brownian Motion. 100 Units.

This course discusses three of the most important types of stochastic processes: Markov chains (in both discrete and continuous time), martingales (the mathematical model of "fair games"), and Brownian motion (random continuous motion). Applications will include random walk, queueing theory, and branching processes, and may also include other areas such as optimal stopping or stochastic integration.

Terms Offered: Autumn Spring Prerequisite(s): STAT 25100 or STAT 25150 or STAT 24400 or MATH 20500 or MATH 20510 or MATH 20520 or MATH 20900

MATH 23700. Introduction to Modelling. 100 Units.

This class presents applications of mathematics to biology, chemistry, economics, engineering, and physics. Students work in groups to explore mathematical and computation tools. The course consists of a sequence of modules, one for each key concept. Each module consists of roughly three lectures. The first lecture briefly explains the motivation and practical context before quickly moving to describe the methodology and mathematical notions. The second lecture explains the heart of the modelling process. The third lecture solves the problem. Examples of mathematics that will be included are dynamics (discrete, continuous (ode), spatial dependence (pde)), optimization (linear programming, dynamic programming), discrete probability, and statistics (data analysis). Examples of models are problems from biology, ecology, economics, finance, physics (atomistic models, electric circuits), mechanics (bars under tension), car traffic, tracking problems, astronomy, etc.

Terms Offered: Autumn. Offered every other year Prerequisite(s): MATH 20500 or MATH 20510 or MATH 20520 or MATH 20900

MATH 23900. Topics in Analysis. 100 Units.

The aim of this course is to introduce undergraduate students who have already completed the standard analysis sequence to some further, more advanced topics in analysis. Possibly topics include, among many others: Fourier series and Fourier transform, wavelets, uncertainty principle; Hausdorff measure and dimension, fractal geometry; Harmonic functions and their properties, Brownian motion; Geometry of Banach spaces; Descriptive set theory.

Terms Offered: Autumn. Offered every other year Prerequisite(s): MATH 20900 or Consent

MATH 24200. Algebraic Number Theory. 100 Units.

Topics include factorization in Dedekind domains, integers in a number field, prime factorization, basic properties of ramification, and local degree.

Terms Offered: Spring Prerequisite(s): MATH 25500 or 25800

MATH 24400. Introduction to Algebraic Geometry. 100 Units.

This is a first course in algebraic geometry. Topics include: affine and projective varieties; coordinate rings; the Zariski topology; Nullstellensatz; Hilbert basis Theorem; the dictionary between algebraic geometry and commutative algebra; rational functions and morphisms; smoothness; theory of dimension; Other possible topics might include: the classification of plane cubics; elliptic curves; 27 lines on a cubic surface; introduction to the theory of curves (degree, divisors, Bezout's Theorem, etc.). Besides the formal prerequisites, MATH 27000 and MATH 26200 are strongly recommended as preparation.

Terms Offered: Winter Prerequisite(s): (MATH 20500 or MATH 20510 or MATH 20520 or MATH 20900) and (MATH 25500 or MATH 25800)

MATH 25400-25500. Basic Algebra I-II.

This is the sequence in basic algebra. It requires a prior serious treatment of linear algebra and thus has a prerequisite of MATH 20250. MATH 25400 covers groups, subgroups, permutation groups, group actions, and Sylow Theorems. MATH 25500 covers rings and ideals, PIDS, Euclidean domains, UFDs, fields and field extensions, and the fundamentals of Galois theory.

MATH 25400. Basic Algebra I. 100 Units.

This course covers groups, subgroups, permutation groups, group actions, and the Sylow theorems.

Terms Offered: Autumn Winter Prerequisite(s): MATH 20250

MATH 25500. Basic Algebra II. 100 Units.

This course covers rings and ideals, PIDs, Euclidean domains, UFDs, fields and field extensions, modules and canonical forms of matrices, quadratic forms, and multilinear algebra.

Terms Offered: Spring Winter Prerequisite(s): MATH 25400 or MATH 25700

MATH 25700-25800-25900. Honors Basic Algebra I-II-III.

This sequence is an accelerated version of MATH 25400-25500-25600 that is open only to students who have achieved a B- or better in prior mathematics courses. Topics include the theory of finite groups, commutative and noncommutative ring theory, modules, linear and multilinear algebra, and quadratic forms. We also cover basic field theory, the structure of p-adic fields, and Galois theory.

MATH 25700. Honors Basic Algebra I. 100 Units.

Topics in MATH 25700 include the theory of finite groups, up through and including the proofs of the Sylow Theorems.

Terms Offered: Autumn Prerequisite(s): MATH 20250; no entering student may begin this sequence in their first term.

MATH 25800. Honors Basic Algebra II. 100 Units.

Topics in MATH 25800 include commutative and noncommutative ring theory, modules, and field extensions.

Terms Offered: Winter Prerequisite(s): MATH 25700

MATH 25900. Honors Basic Algebra III. 100 Units.

Topics in this course include basic field theory, the structure of p-adic fields, and Galois theory.

Terms Offered: Spring Prerequisite(s): MATH 25800

MATH 26200. Point-Set Topology. 100 Units.

This course examines topology on the real line, topological spaces, connected spaces and compact spaces, identification spaces and cell complexes, and projective and other spaces. With MATH 27400, it forms a foundation for all advanced courses in analysis, geometry, and topology.

Terms Offered: Autumn Winter Prerequisite(s): (MATH 20300 or 20310 or 20320 or 20700) and (MATH 25400 or 25700)

MATH 26300. Introduction to Algebraic Topology. 100 Units.

Topics include the fundamental group of a space; Van Kampen's theorem; covering spaces and groups of covering transformation; existence of universal covering spaces built up out of cells; and theorems of Gauss, Brouwer, and Borsuk-Ulam.

Terms Offered: Spring Prerequisite(s): MATH 26200

MATH 26500. Introduction to Riemannian Geometry. 100 Units.

The study of curves and surfaces is an ideal place to learn the beginnings of Riemannian Geometry. After a basic introduction, topics to be covered include Gaussian curvature, second fundamental form, Gauss's Theorem Egregium, Gauss-Bonnet Theorem, and Rigidity of spheres.

Terms Offered: Winter Prerequisite(s): MATH 20500 or 20510 or 20520 or 20900

MATH 26700. Introduction to Representation Theory of Finite Groups. 100 Units.

This course is an introduction to the representation theory of finite and compact groups. The basic topics covered include irreducible representations, Schur's Lemma, character theory, induced representations and Frobenius Reciprocity. Additional topics may include special topics in, and applications of, representation theory, such as: Burnside's p^aq^b theorem, random walks on groups (applications of Fourier analysis on finite groups), representations of symmetric groups and Young tableaux, and representation theory of compact groups, concentrating on SU(2).

Terms Offered: Autumn Prerequisite(s): MATH 25800 or 25500

MATH 27000. Basic Complex Variables. 100 Units.

Topics include complex numbers, elementary functions of a complex variable, complex integration, power series, residues, and conformal mapping.

Terms Offered: Autumn Spring Winter Prerequisite(s): MATH 20500 or 20510 or 20520 or 20900

MATH 27100. Measure and Integration. 100 Units.

Construction of Lebesgue measure, measurable sets and functions. The Lebesgue integral, convergence theorems. Relationship between Lebesgue and Riemann integral. The L^p spaces, completeness and duality. Other related topics time permitting.

Terms Offered: Winter Prerequisite(s): MATH 20500 or MATH 20510 or MATH 20520

MATH 27200. Basic Functional Analysis. 100 Units.

Review of metric spaces, normed spaces and inner product spaces. Banach spaces and Hilbert spaces. Bounded linear operators. The 3 basic principles of functional analysis: the closed graph theorem, the open mapping theorem and the uniform boundedness principle. Duality and weak topologies. Weak and weak star compactness. Hilbert spaces, orthogonal expansions and spectral theorem. Applications of these concepts.

Terms Offered: Spring Prerequisite(s): MATH 27000 and (MATH 20900 or MATH 27100)

MATH 27300. Basic Theory of Ordinary Differential Equations. 100 Units.

This course is an introduction to the theory of ordinary differential equations in Euclidean space. Topics covered include: first-order equations of one variable, solving higher order systems via reduction of order, linear ODEs in arbitrary dimension, real Jordan form and the matrix exponential, variation of parameters, existence and uniqueness of solutions for Lipschitz vector fields, local analysis near equilibria, stability of solutions, introduction to dynamical systems and the global analysis of flows.

Terms Offered: Autumn Winter Prerequisite(s): MATH 20500 or MATH 20510 or MATH 20520 or MATH 20900 or PHYS 22100

MATH 27400. Introduction to Differentiable Manifolds and Integration on Manifolds. 100 Units.

Topics include exterior algebra; differentiable manifolds and their basic properties; differential forms; integration on manifolds; and the theorems of Stokes, DeRham, and Sard. With MATH 26200, this course forms a foundation for all advanced courses in analysis, geometry, and topology.

MATH 27500. Basic Theory of Partial Differential Equations. 100 Units.

This course covers classification of second-order equations in two variables, wave motion and Fourier series, heat flow and Fourier integral, Laplace's equation and complex variables, second-order equations in more than two variables, Laplace operators, spherical harmonics, and associated special functions of mathematical physics.

Terms Offered: Spring Prerequisite(s): MATH 27000 and MATH 27300

MATH 27600. Dynamical Systems. 100 Units.

An introduction to concepts and examples in the study of dynamical systems. The key notions of recurrence, classification, stability, entropy and chaos will be introduced and illustrated in model examples derived from differential equations, algebra, complex analysis, and modeling. A variety of areas of dynamics will be covered, and may include: topological dynamics, symbolic dynamics, ergodic theory, and smooth and complex dynamics.

Terms Offered: Winter. Offered every other year Prerequisite(s): MATH 20900 OR MATH 27100

MATH 27700-27800. Mathematical Logic I-II.

Mathematical Logic I-II

MATH 27700. Mathematical Logic I. 100 Units.

This course introduces mathematical logic. Topics include propositional and predicate logic and the syntactic notion of proof versus the semantic notion of truth (e.g., soundness, completeness). We also discuss the Gödel completeness theorem, the compactness theorem, and applications of compactness to algebraic problems.

Terms Offered: Autumn Prerequisite(s): MATH 25400 or 25700 Equivalent Course(s): CMSC 27700

MATH 27800. Mathematical Logic II. 100 Units.

Topics include number theory, Peano arithmetic, Turing compatibility, unsolvable problems, Gödel's incompleteness theorem, undecidable theories (e.g., the theory of groups), quantifier elimination, and decidable theories (e.g., the theory of algebraically closed fields).

Terms Offered: Winter Prerequisite(s): MATH 27700 or equivalent Equivalent Course(s): CMSC 27800

MATH 28000. Introduction to Formal Languages. 100 Units.

This course is a basic introduction to computability theory and formal languages. Topics include automata theory, regular languages, context-free languages, and Turing machines.

Prerequisite(s): CMSC 27100 or CMSC 27130 or CMSC 37110 or MATH 15900 or MATH 15910 or MATH 16300 or MATH 16310 or MATH 19900 or MATH 25500 or LING 21010 Equivalent Course(s): CMSC 28000

MATH 28100. Introduction to Complexity Theory. 100 Units.

Computability: Turing machines, Universal Turing machines and the Church-Turing thesis. Undecidability. Reducibilities. Complexity--the study of the amount of resources -- time, space, communication, randomness, etc -- needed in computations: Time and space complexity classes, nondeterministic and probabilistic computations. Complete problems. Lower bounds, and the big open problems: P vs NP, space vs. time, etc. Communication Complexity.

Prerequisite(s): CMSC 27200 or CMSC 27230 or CMSC 37000, or MATH 15900 or MATH 15910 or MATH 16300 or MATH 16310 or MATH 19900 or MATH 25500; experience with mathematical proofs. Equivalent Course(s): CMSC 28100

MATH 28130. Honors Discrete Mathematics. 100 Units.

We emphasize mathematical discovery and rigorous proof, which are illustrated on a refreshing variety of accessible and useful topics. Basic counting is a recurring theme. Further topics include proof by induction; number theory, congruences, and Fermat's little theorem; relations; factorials, binomial coefficients and advanced counting; combinatorial probability; random variables, expected value, and variance; graph theory and trees. Time permitting, material on recurrences, asymptotic equality, rates of growth and Markov chains may be included as well. The honors version of Discrete Mathematics covers topics at a deeper level.

Prerequisite(s): (CMSC 12300 or CMSC 14400 or CMSC 15400) or (MATH 15910 or MATH 16300 or MATH 16310 or MATH 19900 or MATH 20300 or MATH 20310 or MATH 20400 or MATH 20410 or MATH 20700 or MATH 25400 or MATH 25500 or MATH 25700) Equivalent Course(s): CMSC 27130

MATH 28410. Honors Combinatorics. 100 Units.

Methods of enumeration, construction, and proof of existence of discrete structures are discussed in conjunction with the basic concepts of probability theory over a finite sample space. Enumeration techniques are applied to the calculation of probabilities, and, conversely, probabilistic arguments are used in the analysis of combinatorial structures. Other topics include basic counting, linear recurrences, generating functions, Latin squares, finite projective planes, graph theory, Ramsey theory, coloring graphs and set systems, random variables, independence, expected value, standard deviation, and Chebyshev's and Chernoff's inequalities.

Prerequisite(s): MATH 19900 or MATH 15900 or MATH 25400 or MATH 25700, or CMSC 27100 or CMSC 27130 or CMSC 37110. Experience with mathematical proofs. Note(s): This course is offered in alternate years. Equivalent Course(s): CMSC 27410

MATH 28530. Honors Graph Theory. 100 Units.

This course covers the basics of the theory of finite graphs. Topics include shortest paths, spanning trees, counting techniques, matchings, Hamiltonian cycles, chromatic number, extremal graph theory, Turan's theorem, planarity, Menger's theorem, the max-flow/min-cut theorem, Ramsey theory, directed graphs, strongly connected components, directly acyclic graphs, and tournaments. Techniques studied include the probabilistic method.

Prerequisite(s): CMSC 27100, CMSC 27130, or CMSC 37110, or MATH 20400 or MATH 20800. Equivalent Course(s): CMSC 27530

MATH 29700. Proseminar in Mathematics. 100 Units.

Consent of instructor. Students are required to submit the signed College Reading and Research Course Form to the Co-Director of Undergraduate Studies. Must be taken for a quality grade.

Terms Offered: Autumn Spring Winter

MATH 20310-20410-20510 Analysis in Rn I (accelerated); Analysis in Rn II (accelerated); Analysis in Rn III (accelerated) MATH 20320-20420-20520 Analysis in Rn I-II-III (IBL)  or

Undergraduate Primary Contacts

Co-Director of Undergraduate Studies John Boller E 222 773.702.5754 Email

Co-Director of Undergraduate Studies Jitka Stehnova E 228 773.702.7332 Email

Undergraduate Secondary Contact

Director of Undergraduate Studies Robert A. Fefferman Ry 360H 773.702.7377 Email

Administration

Administrator for Undergraduate Studies in Mathematics Hannah Zyung E 214 773.702.7389 Email

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© Stanford University . Stanford , California 94305 .

• Mathematics

College of Letters and Science

• Bachelor of Arts
• Bachelor of Science

Math is everywhere, offering broad career choices. Any complex system can be analyzed using mathematics, which means math arises in health care, business, marketing and even entertainment. Mathematics is much more than simple arithmetic and equations; it is the study of abstract structures, space, change and the interrelations of these concepts. Mathematicians work to address some of science and society's most pressing questions. Their work bridges the gaps between scientific disciplines and provides a framework for considering problems in their purest, most theoretical form.

Major Requirements

Freshmen: You will begin your studies with preparatory courses in mathematics, engineering or computer science, physics and statistics.

Transfer Students: The  UC Transfer Pathway  for this major strongly recommends that all lower-division requirements (equivalent to the first two years of courses) be completed prior to transferring.

At the upper division level, you may choose to focus your studies on one of three areas: preparation for graduate study in mathematics, computational and applied mathematics or mathematics for secondary (middle or high school) teaching. You may choose to earn an A.B. degree, which allows you more flexibility to take courses outside your major, or a B.S. degree, which provides more focused instruction in mathematics.

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• Applied urban science and informatics
• Biomedical engineering

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Course Catalog

Mathematics, BSLAS

for the degree of Bachelor of Science in Liberal Arts & Sciences Major in Mathematics

Students in the Mathematics major can choose one of the following to complete the major:

Mathematics major

Mathematics major, Applied Mathematics concentration

Mathematics major, Data Optimization concentration

Mathematics major, Math Doctoral Preparation concentration

Mathematics major, Mathematics Teaching concentration

Mathematics is a broad discipline that contains a range of areas of specialization within it. The required core courses provide fundamental background for mathematics in general. The concentrations allow the student to broaden this background or begin to specialize. Students must complete the core courses and a concentration.

An entering student in mathematics should have academic preparation to enroll in MATH 220 during the first semester. Admission to MATH 220 requires an acceptable ALEKS score. A student should attain grades of B in calculus in order to complete the advanced courses successfully.

Undergraduate programs in Mathematics

Actuarial Science, BSLAS

Mathematics & Computer Science, BSLAS

for the degree of Bachelor of Science in Liberal Arts and Sciences Major in Mathematics

A Major Plan of Study form, declaring concentration and supporting coursework, must be completed and submitted to the LAS Student Academic Affairs Office except for students in the Teaching of Mathematics concentration.  Please complete this form with an advisor in the Mathematics Undergraduate Office within 1-2 semesters of completing MATH 347 or MATH 348.

Departmental distinction: Distinction will be awarded on the basis of selection of 400-level courses in mathematics and the grade point average. Graduation with High Distinction or Highest Distinction in Mathematics requires participation in the Program for Distinction in Mathematics or Mathematics Education.  Full details are available at the departmental website.

General education: Students must complete the Campus General Education requirements including the campus general education language requirement.

Minimum required major and supporting course work: normally equates to 46-49 hours including 27-35 hours of mathematics beyond calculus, 3-4 hours of computer science, and 12 hours of supporting coursework. twelve (12) hours of 300- and 400-level non-s/u-graded courses in the major must be taken on this campus., minimum hours required for graduation: 120 hours..

Sample Sequence This sample sequence is intended to be used only as a guide for degree completion. All students should work individually with their academic advisors to decide the actual course selection and sequence that works best for them based on their academic preparation and goals. Enrichment programming such as study abroad, minors, internships, and so on may impact the structure of this four-year plan. Course availability is not guaranteed during the semester indicated in the sample sequence.

Students must fulfill their Language Other Than English requirement by successfully completing a fourth level of a language other than English. See the corresponding section on the Degree and General Education Requirements page .

• Ability to construct proofs and recognize when proofs are complete.
• Ability to use theorems in order to solve problems.
• Technical proficiency in calculus and linear algebra
• The ability to apply mathematics; translating real-world problems into mathematical problems and solving them.

Department of Mathematics website Department of Mathematics faculty Mathematics Advising Mathematics Advising email

College of Liberal Arts and Sciences website Overview of Admissions & Requirements for the College of LAS

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What mathematics degrees can you study, what do you need to get onto a mathematics degree, what topics does a mathematics degree cover, how will you be assessed, why study mathematics.

• Are scholarships and bursaries available to students studying a Mathematics degree?

What do Mathematics graduates earn?

What jobs can you get as a mathematics graduate, what are the postgraduate opportunities, similar subjects to mathematics, have any questions.

Mathematics covers three main areas – maths, statistics and operational research. 

Mathematicians are interested in numbers, shape, and space. They simplify complex problems, classify objects, and prove that certain phenomena must, can or can’t happen.

Statistics is also driven by real-world problems. Statisticians examine data to help make predictions and decisions. This could be around drug efficacy or the likeliness of flooding, for instance.

Operational research (OR) is also known as management science. It is the analysis of decision-making processes. Some of its more well-known areas include game theory and the analysis of voting systems.

Take a look at the university league table for Mathematics .

Undergraduate degrees in Mathematics include single honours. You can also study it as a joint honours with a wide range of other subjects. Examples of degrees:

Mathematics BSc/BA/BMath

The BSc (Bachelor of Science) degree is the standard Mathematics degree. The BMath (Bachelor of Mathematics) is similar. The BA (Bachelor of Arts) has a more liberal arts focus, with a broader range of modules available.

Find Mathematics courses .

Actuarial Science and Mathematics BSc

These degree courses tend to combine the study of mathematics, statistics and business. They help you get ready to work as a professional actuary.

Search for Actuarial Science courses .

Applied Mathematics BSc

This degree helps you take theories of maths to apply them to real-world problems. Courses usually include plenty of computer and lab work. In the future, you could find work in fields like engineering, data analysis or technology.

Look through Applied Mathematics courses .

Mathematics, Operational Research, Statistics and Economics (MORSE) BMorse/MMorse

This interdisciplinary degree equips you with a specialist skillset. It prepares you for work where you apply quantitative and analytical methods to solve complex issues. The BMorse is undergraduate, whereas the MMorse includes an integrated master’s year.

Find MORSE courses .

Other options

There are many subject combinations you can study with maths. For instance:

• Economics and Mathematics BSc
• French and Mathematics BA
• Mathematics and Philosophy BSc

Courses may include an integrated foundation year. Some offer opportunities for professional placements and studying abroad. Accelerated study and January start dates are often available too.

See the top 10 universities for Mathematics .

Entry requirements for a Mathematics degree range from 96–165 UCAS points. This could include the qualifications below:

• A Levels: A*A*A–CCC (Further Maths is sometimes an essential requirement)  
• BTECs: D*D*D*–MMM
• Scottish Highers: AAAAA–BBBC (Advanced Highers: AAB–AA)
• International Baccalaureate: 42–30
• Universities will usually ask that you have studied: maths at A Level (or equivalent). Physics is also desirable. 
• Some degrees require a maths admissions test, such as TMUA (Test of Mathematics for University Admission), STEP (Sixth Term Examination Paper), MAT (Mathematics Admissions Test) or Advanced Extension Award (AEA) 
• Interview required by some universities 

Good to have

• Research from books, journals, free lectures online, podcasts or the Maths Careers website (sponsored by the Institute of Mathematics and its Applications) to identify areas of interest
• Work experience in a finance-related role
• Participating in competitions or challenges such as the Senior Mathematical Challenge
• Volunteering to help teach a maths class or tutor a homework club
• STEM Summer schools, if eligible, such as UNIQ or Sutton Trust
• Entry requirements
• About UCAS points
• Alternatives to A Levels

Typical modules for courses in this subject include:

• Algebraic and differential geometry
• Classical mechanics of particles
• Electromagnetism, quantum mechanics and fluid dynamics
• General relativity
• Geometry and dynamics
• Mathematical biology
• Mathematical philosophy
• Multivariate calculus and mathematical models
• Probability and statistics
• The mathematics of machine learning
• Theoretical and statistical mechanics
• Vector spaces 

Read about: what is STEM?

Assessment is mainly by written exam. Some modules may include a mixture of the following:

• Poster presentation
• Project report
• Short written assignments

Mathematicians are needed in many professional contexts, from policymaking to medical research. Study the subject and your career could be involved in solving some of the world's many complex problems.

Career-specific skills:

• Knowledge of the fundamentals of mathematics and topics that could include data science, quantum mechanics, computational modelling, mathematical ecology and epidemiology
• Placements working in finance, statistics or modelling may be available on some courses

Transferable skills:

• Communication
• Creative problem solving
• Decision making
• Logical reasoning and analytical skills
• Numeracy and IT skills
• Presentation
• Team working

Professional accreditation:

• Degrees may be accredited by the Institute of Mathematics and its Applications (IMA). Accreditation leads towards Chartered Mathematician status (CMath)
• Degrees with statistics may be accredited by the Royal Statistical Society (RSS)
• Degrees with accountancy may offer accreditation with professional accountancy bodies. Accreditation leads to exemption from a range of professional accounting exams
• Five reasons to study Mathematics

Are scholarships and bursaries available to students studying a Mathematics degree?  

Some universities offer students specific scholarships, bursaries, or grants to encourage access. It’s worth seeing if you are eligible, how to apply, and what it covers e.g., materials, tuition fees and/or living costs.  

Mathematics graduates can expect an entry-level salary of between £20,000–£28,000.

As your career progresses, your average salary will depend on the field you’ve entered. You could have an income of £55,000 as a senior actuarial analyst, or up to £156,500 as a chief actuary. If you become an operational researcher, you could earn from £40,000–£80,000 with experience.

Read more on what graduates do and earn .

Having specialist knowledge and skills will make you highly employable across many areas. Roles could include: 

• Business analyst
• Chartered accountant
• Data scientist
• Mathematical researcher
• Mathematician
• Radiation protection scientist
• Statistician
• Trainee actuary
• Careers with a Mathematics degree

Graduates with a Mathematics degree need to complete teacher training such as a PGCE if they wish to become a teacher. Other postgraduate study offers the chance to specialise. Examples of postgraduate degrees include:

• Applied Statistics and Datamining PGDip/MSc
• Mathematical Modelling and Scientific Computing MSc
• Mathematics DPhil/MPhil/PhD
• Operational Research with Risk MSc
• Pure Mathematics MSc
• Find postgraduate courses for Mathematics
• Types of postgraduate degrees

Other subject areas that might appeal to you include:

• Accounting & Finance
• Information Technology & Systems
• Physics & Astronomy

Search for undergraduate Mathematics courses now!

If you’ve got any questions about studying Mathematics, you can email our experts at [email protected] . We’ll be happy to hear from you!

• University rankings for Mathematics
• All subject guides

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College of Liberal Arts & Sciences

Department of Mathematics

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Supporting Coursework for Math Majors

All Math majors must complete the Supporting Coursework requirement. We encourage students to start on this requirement early and choose something interesting! The choice of supporting coursework depends upon your interests and professional goals. The Supporting Coursework requirement may be fulfilled in various ways:

1.  Take at least 12 credit hours in a single Math-related area with at least 1-2 advanced courses. Here are some ideas!

• Astronomy:  PHYS 211 and 212; ASTR 210; 404 or 414
• Atmospheric Sciences: ATMS 201; 301; 302; and one of 410 or 411
• Earth, Society & Environmental Sustainability: ESE 200; ESE 320; ESE 379; ESE 445
• Ecology and Conservation Biology: IB 150, 203, 451, 452, 487
• Economics: ECON 102; 103; 302; 303 or 471
• Geography: GEOG 103; 105; 371; 379
• Geology: GEOL 107; 208; 143 or 380; and one of 411, 452 or 470
• Molecular & Cellular Biology: MCB 150; 250 and 252; 300, 317, 401, 402, 461, 462
• Philosophy: PHIL 102 or 103; 202; 270; 453 or 454
• Physics: PHYS 211, 212, 213, 214
• Political Science: PS 101; 230; 231; and one 400- level PS course

2.  Some areas are restricted:

• Statistics: Students must complete, at a minimum, STAT 200 plus nine credit hours of 400-level STAT courses that are not cross-listed with MATH or ASRM.
• Computer Science: Students must complete twelve credit hours of courses different from CS 101 and 125. Courses that are cross-listed with Math, such as MATH 357, cannot be used for this requirement.
• ASRM courses, as well as courses cross-listed with ASRM, may not be used.

3.  Complete any minor (except Statistics or Computer Science, as noted above). For example, complete the Business minor! Please see: https://business.illinois.edu/minor/

4. Complete a double major or dual degree.

BSc Mathematics with Data Science

Introduction, preliminary readings.

This BSc Mathematics with Data Sciences combines rigorous training in mathematics with an in-depth study of data science advancements.

Initially, you’ll study foundational mathematical methods and statistical theory before progressing to more advanced topics such as programming, machine learning and AI.

During your studies, you’ll go well beyond exploring these topics in a theoretical way – you’ll look at the broader social science applications in economics, finance and society.

The programme enables you to develop strong quantitative knowledge and data analysis skills that are highly sought after in employment. Our graduates are in great demand in sectors such as banking, finance, accounting, data analysis, IT, consulting, insurance and research.

Much of university level mathematics is concerned with formal proofs and rigorous mathematical argument, and this is necessary for some of the advanced mathematics required in finance, economics, and other fields of application. For an introduction, we recommend:

• L Alcock How to Study for a Mathematics Degree (Oxford University Press, 2013)
• R Allenby Numbers and Proofs (Butterworth-Heinemann, 1997)
• P Eccles An Introduction to Mathematical Reasoning (Cambridge University Press, 1997)
• T Gowers Mathematics: a very short introduction (Oxford University Press, 2002)
• M Liebeck A Concise Introduction to Pure Mathematics (Chapman & Hall/CRC Mathematics, 2005)

For an introduction to data science, we recommend:

• G Grolemund and Hadley Wickham R for Data Science (O'Reilly Media, 2016)
• JV. Guttag Introduction to Computation and Programming using Python (Second Edition, The MIT Press, 2017)
• James et al An Introduction to Statistical Learning: With applications in R (Springer, 2013)
• N. Silver The signal and the noise: the art and science of prediction (Penguin UK, 2012)

Entry requirements

Here, you can check our entry requirements for GCSEs, A-levels (please read them alongside our information about subject combinations) and the International Baccalaureate (IB) Diploma. We also consider applications from students with a range of other UK qualifications and from overseas. Please select the overseas button below and choose your country from the dropdown list to find the equivalency to A-levels of your qualification.

Additional tests

For GCSEs, you’ll need several GCSE grades at A (or 7) and A* (or 8-9).

As a minimum, we ask for GCSE English Language and Mathematics grades at B (6) or higher. We’ll also consider your overall GCSE subject profile.

A*AA, with an A* in Mathematics

Where it's offered by your school or college, AS- or A-level Further Mathematics is expected to be taken and a grade A achieved.

We also consider your AS grades, if available.

Contextual admissions A-level grades

A*AB with an A* in Mathematics

Read our undergraduate admissions information to learn more about contextual admissions.

A-level subject combinations

• We consider your combination of subjects as well as your grades.
• A broad mix of traditional academic subjects provides the best preparation for studying at LSE. We expect applicants to have at least two full A-levels (or equivalent) in these subjects.
• An A* in Mathematics is required. However, an A* in Further Mathematics and an A grade in Mathematics would be an acceptable alternative.
• We’ll also consider applications from students with a combination of Mathematics, Further Mathematics and one other subject. Other subjects commonly studied include Chemistry and Physics.

Find out more about A-level subject combinations .

38 points overall, including 766 in higher level subjects, with 7 in Mathematics: analysis and approaches.

Contextual admissions IB grades

37 points overall, including 765 in higher level subjects, with 7 in Mathematics: analysis and approaches.

Applicants are encouraged to take the  Test of Mathematics for University Admission (TMUA) . The test is not mandatory, however a good performance on the test may make an application more competitive.

We welcome students from all walks of life at LSE. We want to recruit students with the very best academic merit, potential and motivation. So, whatever your background, please do apply. Get all the details on our general  entry requirements .

Competition for places at LSE is high. We cannot guarantee you an offer of a place even if you’re predicted or achieve our standard entry requirements.

Our standard offer requirements are intended only as a guide and, in some cases, you’ll be asked for different grades.

Programme content

Why study with us.

Discover more about our students and department.

Meet the department

The Department of Mathematics aims to be a leading centre for the study of mathematics in the social sciences.

The department has a vibrant intellectual community, with fantastic students, internationally respected academics and high-achieving alumni. Our department has grown rapidly in recent years, with exciting developments in research and new teaching programmes and courses.

This research encompasses four main overlapping areas:

• discrete mathematics and algorithms
• mathematical game theory
• financial and related mathematics
• operational research.

All aspects of our research were ranked world-leading or internationally excellent in the most recent Research Excellence Framework (2021), submitted jointly with the Department of Statistics.

We embrace the School’s ethos of research-led teaching. Currently, we offer four undergraduate and three postgraduate programmes, as well as doctoral research opportunities on our MPhil/PhD in Mathematics. These programmes are all in high demand – attracting talented students from diverse backgrounds.

Our programmes are highly interdisciplinary and we have close ties with other departments at LSE, including Statistics, Economics, Finance, Management and the Data Science Institute.

Whatever your study route, you’ll benefit from a welcoming, inclusive and friendly learning environment where students and staff are supported to achieve their best.

Learn more about our programmes , recent research and regular events and seminars .

Department of Mathematics

2nd In Europe

5th In the world

1st We're ranked top university in London for the 12th year running

Carbon neutral in 2021 lse became the first carbon neutral verified university in the uk, your application, who attends.

We consider each application carefully, taking into account all the details you’ve included on your UCAS form, such as:

• academic achievement , including predicted and achieved grades (also see specific information about this programme in the "entry requirements" above)
• subjects and subject combinations  (also see specific information about this programme in the "entry requirements" above)
• your personal statement
• your teacher’s reference
• educational circumstances

You may also have to provide evidence of your English proficiency, although this is not needed at the application stage.  See our English language requirements page .

We’re looking for students who demonstrate:

• an equal interest in mathematics and economics
• an understanding of the links between the two disciplines
• involvement in related extra-curricular activities, such as maths competitions or Olympiads
• the ability to think and work independently
• intellectual curiosity and the ability to ask incisive questions
• logical thinking and the ability to follow complex lines of reasoning
• creativity and flexibility in problem-solving
• great organisational and communication skills
• self-motivation and a willingness to work hard.

Fees and funding

The table of fees shows the latest tuition fees for all programmes.

You're charged a fee for each year of your programme. Your tuition fee covers registration and examination fees payable to the School, lectures, classes and individual supervision, lectures given at other colleges under intercollegiate arrangements and, under current arrangements, membership of the Students' Union. It doesn't cover living costs or travel or fieldwork.

Your tuition fees, and eligibility for any financial support, depend on whether you’re classified as a home or an overseas student – known as your fee status. We assess your fee status based on guidelines from the UK Government’s Department for Education.

Learn more about fee status classification .

Scholarships, bursaries and loans

We recognise that the cost of living in London may be higher than in your home town or country. LSE provides generous financial support, in the form of bursaries and scholarships, to UK, EU and overseas students.

Additionally, the UK Government provides loans to UK and some EU students. Some overseas governments also offer funding.

Further information on tuition fees, living costs, loans and scholarships .

Learning and assessment

How you learn, how you're assessed.

Format and contact hours: you’ll usually attend two lectures and one related class for each course per week (eight lectures and four classes). Additionally, you’ll work on exercises in your own time, which are discussed in weekly classes with around 15 students. Hours vary depending on the course. Further details are given in the Calendar within the Teaching section of each course guide .

LSE teaching: all courses include seminars, classes and/or computer workshops to help you develop a deeper understanding of concepts and methods introduced in lectures. In computer workshops, you’ll work on practical data exercises using software and programming languages (mainly Python). Classes and workshops provide a great opportunity to ask questions about the lecture material and other related topics.

LSE is internationally recognised for teaching and research and our academics have wide-ranging expertise. Courses may be taught by our faculty staff, guest teachers and visiting members of staff, LSE teaching fellows and graduate teaching assistants, who may be doctoral research students.

Learn about the teacher responsible for each course in the relevant  course guide .

Academic support

Academic mentor: you’ll meet with your academic mentor regularly to discuss your work. Your mentor can provide advice and guidance on academic issues and, where appropriate, personal concerns.

Other academic support: at LSE, we offer lots of opportunities to extend your learning outside the classroom.

LSE LIFE is a great place to get advice and practise the skills you’ll need during your studies and beyond.

Through LSE LIFE, you can:

• attend workshops on developing leadership skills, finding the right study/work/life balance and preparing for the world of work
• develop your reading, academic writing and critical-thinking skills
• gain experience of working in study groups and develop your cross-cultural communication and teamwork skills.

Disability and Mental Health Service: we want all LSE students to achieve their full potential. Students can access free, confidential advice through our Disability and Mental Health Service . This is the first point of contact for students.

Your timetable

• The standard teaching day runs from 9am to 6pm, Monday to Friday. Undergraduate teaching is not normally scheduled for Wednesdays after 12 noon to allow for sports, volunteering and other extra-curricular activities.
• The lecture and seminar timetable is published in mid-August and the full academic timetable (with information on classes) is published by mid-September via the LSE timetables web pages .
• All personal undergraduate timetables are published in LSE for You (LFY) . For personal timetables to appear, you must be registered at LSE, be signed up for courses in LFY and ensured that there are no unauthorised clashes in your course selections. We try our best to minimise changes once personal timetables have been published. However, you’ll be notified about any changes by email.

Formative coursework

All taught courses include formative coursework, which is not assessed. This helps prepare you for summative assessment. We use a range of formative assessment methods, such as essays, case studies, reports, quizzes and mock exams.

Feedback is an essential part of the learning experience at the School. You’ll receive feedback on any formative coursework within three weeks, provided it’s submitted on time.

Summative assessment

This assessment counts towards your final course mark and degree award.

Summative assessment includes exams at the end of each year (May or early June). Some courses also include assessments in January.

You’ll receive feedback on any summative coursework as part of the assessment for individual courses (except for final submitted dissertations). Feedback will normally be provided before the examination period.

Assessment on individual courses can change from year to year. See details of the current formative coursework and summative assessment for each course in the relevant  course guide .

Find out more about LSE’s teaching and assessment methods .

Graduate destinations

Career support.

Recent graduates have gone on to work in the areas of corporate finance, accountancy, management, banking, and in data analysis related to those businesses. Many have pursued graduate study in areas related to mathematics, economics, or both.

Further information on graduate destinations for this programme

Median salary of our undergraduate students 15 months after graduating:

Top 3 sectors our students work in:.

From CV workshops through to careers fairs, LSE offers lots of information and support to help you make that all-important step from education into work.

Many of the UK’s top employers give careers presentations at the School during the year and there are numerous workshops covering topics such as job hunting, managing interviews, writing a cover letter and using LinkedIn.

See LSE Careers for further details.

Discover Uni

Every undergraduate programme of more than one year duration will have Discover Uni data. The data allows you to compare information about individual programmes at different higher education institutions.

Programmes offered by different institutions with similar names can vary quite significantly. We recommend researching the programmes you're interested in and taking into account the programme structure, teaching and assessment methods, and support services available.

Find out more

Explore lse, student life.

Student support

Accommodation

Meet, visit and discover LSE

It is widely recognized that students can prepare in many fields for highly rewarding careers in only two to three years of concentrated study. Such fields include management, criminal justice, computer information technology, care and development of young children, fire and emergency services, radiologic technology, respiratory care, and nursing. Associate degree programs are offered in all of these areas at LSU Eunice, and graduates of these programs are actively sought by employers throughout the state and nation. In addition, students may complete and certificates of technical studies in specific technical fields. LSU Eunice also offers the Associate of Arts Louisiana degree, the Associate of Science Louisiana Transfer degree, and the Associate of General Studies degree.

LSU Eunice Degree Requirements

Students must meet the curricular requirements for a degree as outlined in one issue of the LSU Eunice Catalog. Students are responsible for knowing degree requirements. They may elect any issue of the LSU Eunice Catalog in force during their residence at this or any other accredited institution of higher learning, provided their residence is continuous. The catalog chosen is to be used for determining curricular requirements only. Students whose enrollment here or elsewhere is interrupted (either voluntarily or by compulsion) for at least two consecutive regular semesters may not elect a catalog issued earlier than the one in force at the time of re-entry. The act of transferring from one institution to another is not regarded in itself as an interruption of enrollment; the interval between enrollments is the controlling factor. Students changing from one curriculum to another may not elect to follow a catalog in force earlier than the date on which the student’s change was made. Under no circumstances may a catalog more than 5 years old be used.

Where programs include curricular requirements set by external agencies such as accrediting associations, changes in these requirements may be made without prior notice, and students may be required to conform to the changes when they become effective. Should LSU Eunice find it necessary to discontinue an academic program, every reasonable effort will be made to enable students already admitted to the program to complete degree requirements on schedule.

General Degree and Certificate Requirements

• Students must achieve an overall grade-point average (GPA) of 2.0 (C average) or better on all college work attempted, plus a minimum grade-point average of 2.0 on all work taken at Louisiana State University Eunice.
• Students must earn 25 percent of the credits required for the associate degree at LSU Eunice. All students must be enrolled at LSU Eunice during the semester in which degree requirements are fulfilled.
• Students must take a minimum of 15 semester hours within the academic division granting the associate degree.
• Students shall receive no degree credit for developmental courses i.e. MATH 0001   , MATH 0015   , MATH 0021   , UNIV 0008   , ENGL 0001   , or ENGL 0101   .
• Students desiring to receive more than one associate degree must complete a minimum of 15 semester hours at LSU Eunice in addition to fulfilling the requirements for the first degree. The 15 hours taken for the second degree must be approved by the division head of the division granting the degree.
• Students earning associate degrees must complete ENGL 1001    and ENGL 1002   . Students should refer to the particular associate degree program for specific mathematics requirements.
• Humanities: Communication Studies, English, Foreign Language, History, Philosophy
• Fine Arts: Art, Music, Theater
• Social Sciences: Anthropology, Economics, Geography, Political Science, Psychology, Sociology, Mass Communication
• Natural Sciences: Agriculture, Agronomy, Animal Science, Astronomy, Biology, Botany, Chemistry, Dairy Science, Environmental Studies, Horticulture, Microbiology, Nutrition, Physical Science, Physics, Poultry Science, Zoology

In addition to the above discipline areas, students may take elective courses in business, criminal justice, nursing, fire science, education, agriculture, etc.

MAJOR CORE Requirements:

A waiver of no more than two major core requirements (six semester hours of substitutions) can be granted in an associate degree curriculum. No waiver can be granted without being recommended with written justification by the faculty advisor and approved by the Division Head.

• Students should consult with the appropriate division head concerning transfer credit evaluation. Transfer credit from regionally accredited institutions will be accepted on the same basis as if it were earned in the LSU System. Credit earned at institutions which are not regionally accredited must be validated through appropriate departmental examinations. Non-traditional credit earned outside the LSU System must conform to advanced-standing policies stated in this catalog or be validated through appropriate departmental examinations.
• Credits which are over 10 years old may be applied toward degree or diploma requirements only with the approval of the student’s division head.
• Graduates desiring to complete an additional certificate program must complete a minimum of 9 semester hours at LSU Eunice in addition to fulfilling the requirements for the first certificate or degree.
• A waiver of no more than one course requirement (three semester hours) may be made in a certificate program. No substitutions may be made for the English and mathematics requirements specified in Number 6 above. When the courses in question are from the humanities, social sciences, or natural sciences, another course from the same general area must be substituted.

LSUE Honors

Louisiana State University Eunice recognizes those students who complete degree/certificate requirements with high academic achievements. Students who complete degree/diploma/certificate requirements with a cumulative grade point average of 3.50=3.79 will graduate with honors. Students who complete degree/diploma/certificate requirements with a cumulative grade point average of 3.80-4.00 will graduate with high honors.

General Education Requirements

Information regarding the general education requirements for LSU Eunice degrees and certificates can be found here: General Education Requirements   .

Degree Program Definitions

Louisiana Transfer Associate (AA/LT or AS/LT) An Associate of Arts or Associate of Science degree that follows a prescribed curriculum (providing both structure and flexibility) and assures transfer of the 60 hours in the degree plus credit for completion of the required general education block at any public university. Example: Associate of Arts Louisiana Transfer    

Associate (A) An academic degree program with a significant general education core, designed to prepare students for immediate employment or career entry, but which also may serve as prepatory education for transfer to a related baccalaureate program. The use of this particular degree designation should be limited to cases wherein other associate degree designations (A.A.S., A.A., or A.S.) have been determined to be inappropriate. All coursework must meet SACSCOC requirements. Non-designated associate degrees are limited to community colleges and two-year transfer institutions. Example: Associate of General Studies    

Associate of Science (A.S.) An academic degree program with a significant general education core, designed primarily to serve as prepatory education for transfer to a related baccalaureate program. All coursework must meet SACSCOC requirements. A.S. degrees are usually offered by community colleges and two-year transfer institutions. Example: Associate of Science in Criminal Justice    

Associate of Applied Science (A.A.S.) An applied/academic degree program, with a limited general education core component, primarily designed to prepare students for immediate employment or career entry. A.A.S. degrees can be formed by combining a T.D. with 15 hours of required general education or can be a distinct curriculum unrelated to any preexisting program of technical studies. All general education coursework must meet SACSCOC requirements. If coursework required of the degree is intended for transfer to a four-year institution, this coursework must meet appropriate SACSCOC requirements. Example: Associate of Applied Science in Computer Information Technology    

Certificate of Technical Studies (C.T.S.) An applied, technical program (usually 16-33 hours) to provide a student with a broad technical competency. C.T.S. programs are strictly limited to technical and community colleges. The C.T.S. is not designed for transfer to an associate or baccalaureate degree program; the C.A.S. is more appropriate for such transferability.

Example: Administrative Technology Specialist Certificate of Technical Studies    

Programs by Degree Type

Division of health sciences and business technology.

Associate of Science

• •  Nursing, ASN
• •  Radiologic Technology, AS
• •  Respiratory Care, AS

Associate of Applied Science

• •  Computer Information Technology, AAS
• •  Management, AAS

Certificate of Applied Science

• •  Diagnostic Medical Sonography (Abdomen & OB / GYN) Certificate of Applied Science

Certificate of Technical Studies

• •  Accounting Technology: Account Clerk Certificate of Technical Studies
• •  Administrative Technology Specialist Certificate of Technical Studies
• •  Human Resources Management Certificate of Technical Studies
• •  Medical Coding and Billing Certificate of Technical Studies

Division of Liberal Arts

Associate of Arts Louisiana Transfer

• •  Business, AA / LT
• •  Criminal Justice AA / LT
• •  Fine Arts, AA / LT
• •  Humanities, AA / LT
• •  Mass Communication, AA / LT
• •  Social Sciences, AA / LT

Associate of General Studies

• •  Associate of General Studies
• •  Care and Development of Young Children, AS
• •  Criminal Justice, AS
• •  Fire and Emergency Services, AAS
• •  Fire Service Technology Certificate of Technical Studies

Division of Science and Mathematics

Associate of Science Louisiana Transfer

• •  Natural Sciences (Biological Sciences), AS / LT
• •  Natural Sciences (Physical Sciences), AS / LT
• •  Chemical Technician CTS

Apr. 17, 2024

Rice, lone star college celebrate agreement helping transfer students complete rice degrees without losing credits.

The Take Flight STEM Pathway , a partnership between Rice University, Lone Star College (LSC) and San Jacinto College (SJC), is building on its efforts to expand education access and increase the number of students who complete STEM degrees.

Rice and LSC celebrated the renewal of a memorandum of understanding and the signing of an articulation agreement to allow transfer students in LSC’s Take Flight Program to receive Rice credit for core science, technology, engineering and mathematics courses completed at LSC. The transfer of course credits is key to transfer students’ timely progress to degree completion.

“We are here to further the relationship between two institutions as Houston begins to grow,” said Dwight Smith, LSC vice chancellor for academic and workforce success, whose daughter is a Rice graduate. “We’re so fortunate to come to an agreement and develop it with Rice because you’ve already provided wonderful experiences for our students and we look forward to working with you in the years to come.”

“One of the shared values that makes this Take Flight program and partnership so fruitful is Lone Star College and Rice University’s shared commitment to student success — and that means every student’s success,” said Amy Dittmar, Rice’s Howard R. Hughes provost and executive vice president for academic affairs.

“What we’ve achieved together is, above all, the product of our two institutions’ shared values and commitment to educational excellence and to expanding access to educational opportunity for students from across the greater Houston area, particularly for students from underrepresented or underresourced communities,” said Matthew Taylor, Rice senior associate provost for strategic and educational initiatives.

Katharine Caruso, LSC associate vice chancellor for the Honors College and international education, referred to the Take Flight Program as a testament to “good neighbors and to access and excellence.” She thanked the Rice faculty, many of whom attended the celebration, for their work with LSC students.

“You have no idea how many messages we get from our students about the wonderful, transformative experiences they are taking part in with you,” said Caruso.

LSC Board of Trustee and alumnus Mike Sullivan also attended.

Take Flight is a cohort cocurricular pathway developed and offered in partnership with Rice for LSC and SJC Honors College students interested in STEM careers. The program has two tracks: one for first-year students and one for second-year students. Both groups have access to specialized curricular and cocurricular STEM opportunities collaboratively offered by Rice and LSC STEM faculty and mentors. For the first-year track, programming focuses on career exploration, while second-year students receive STEM-specific advising on selective transfer application writing and transfer preparedness.

Take Flight students also have access to specialized application support for funded, summer research experiences for undergraduates, which are offered by Rice and other sites around the country. The Provost’s Office and Rice faculty members have provided nearly $300,000 in research stipends for Take Flight students since the program’s inception.

Three Take Flight students who participated in full-time summer research experiences spoke during the celebratory signing. After her first year as an Honors College student at LSC and a participant in Take Flight, Alexis Lopez conducted research at Cornell University on using computer vision to study plant health. The experience led her to be the first author of a published paper she presented at conferences around the country, including the Institute of Electrical and Electronics Engineers. She was recently announced as a Barry Goldwater Scholarship recipient.

Jocel Angelo Reyes spent his summer interning in a nanotechnology lab with Matteo Pasquali, director of Rice’s Carbon Hub, professor of chemistry and materials science and nanoengineering and the A.J. Hartsook Professor of Chemical and Biomolecular Engineering.

Carlos Carreon completed an internship on gasoline fractional distillation, followed by a computational research internship with Princeton University in the Czech Republic, illustrating the quality and versatility of his honors coursework at LSC and the impact of the STEM programming and advising he received as a Take Flight student.

All three said they are happy to serve as representatives of the program that gave them the opportunity to apply the research skills they learned as LSC honors students.

“The Honors College created these foundational research skills,” said Lopez.

The internship “invigorated my passion for research,” said Reyes. “Without these programs, I don’t know how much of that would be possible.”

The research experiences also helped build interpersonal skills, said Carreon. “I got to practice my ability as a listener.”

Established in September 2022 by Rice, LSC and SJC, Take Flight began to address the barriers that often prevent first-generation, low-income and historically excluded students from attaining a four-year degree in STEM.

• Open access
• Published: 19 April 2024

Causes and outcomes of at-risk underperforming pharmacy students: implications for policy and practice

• Alice Campbell 1 ,
• Tina Hinton 1 , 2 ,
• Narelle C. da Costa 1 ,
• Sian E. O’Brian 1 ,
• Danielle R. Liang 1 &
• Nial J. Wheate 1  

BMC Medical Education volume  24 , Article number:  421 ( 2024 ) Cite this article

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This study aimed to understand the key determinants for poor academic performance of students completing a Bachelor of Pharmacy (BPharm), Bachelor of Pharmacy and Management (BPharmMgmt), or Master of Pharmacy (MPharm) degree.

Data were collected on pharmacy students who had not met academic progression requirements between 2008 and 2018 at The University of Sydney, Australia. This included: age at the start of pharmacy degree; gender; whether they transferred from another university; whether they were a domestic or international student; Australian Tertiary Admissions Rank upon entry, previous studies in biology, chemistry, or mathematics; show cause triggers (units of study failed); number of show causes; students’ written show cause responses; weighted average mark at last show cause or graduation; whether they graduated and were a registered pharmacist; and, the number of years they spent studying the degree. Descriptive studies were used to analyse student characteristics using SPSS software, and student self-reported reasons for poor performance were analysed reflexively using thematic analysis procedures using NVivo.

This study included 164 pharmacy students enrolled in a BPharm (79.3%, n  = 130), BPharmMgmt (1.2%, n  = 2), or MPharm (19.5%, n  = 32). Of the students, 54% ( n  = 88) were men, 81% ( n  = 133) were domestic students, 15% ( n  = 24) transferred from another degree program, and 38% ( n  = 62) graduated from the course. Show cause students were less likely to graduate if they transferred from another degree program ( P  = 0.0002) or failed more than three units of study (UoS; P  < 0.0001). The most commonly failed UoS were related to organic or pharmaceutical chemistry, and the top student self-reported reasons for poor performance was stress/anxiety, physical health, and depression.

Pharmacy schools should aim to address student foundational knowledge in chemistry, identify at-risk students early using pre-subject testing, and provide better services to address student mental health.

Peer Review reports

Introduction

A student’s academic performance in higher education is typically defined by their achievement of learning outcomes and demonstration of their ability to apply the concepts taught. Measurement of these attributes can include assessments, quizzes, role plays, field work, practical placements, workshops, tutorials, laboratories, and examinations. In most higher education programs, a minimum standard of academic achievement is required in order to progress through the course, to ensure the student has gained adequate knowledge and skills, and that they have achieved the specified learning outcomes. In this regard, poor academic performance can be defined by instances where a student fails to meet the expected minimum academic standard. Usually this comprises a minimum overall score in a subject and/or passing a specific barrier assessment, which is ultimately linked to their retention or attrition.

Understanding the key determinants of student success, failure, retention, and attrition has become increasingly important for higher education institutions, and has been the subject of extensive research over the past few decades. Early studies on student attrition focused primarily on student characteristics [ 1 ], before attention shifted to interactions between the student and their institutions. Prominent researchers, including Spady [ 2 , 3 ], Tinto [ 4 , 5 ], and Bean [ 6 ] proposed models to explain the interplay between academic and social integration leading to underperformance, and eventually, attrition. More recently, interest has increased in examining student engagement [ 7 , 8 , 9 ], where the student and institutions have a joint responsibility for academic success. To be successful, a student needs to participate, and higher education institutions need to provide an appropriate learning environment, opportunities, and support [ 10 ].

Studies on the key determinants of student underperformance reveal an array of contributing factors. Recent systematic reviews on underperformance and dropout rates show that key determinants fall into categories relating to the institution, personal life, demographics, and social integration [ 11 , 12 ]. Within higher education institutions, studies have found that an academic’s professional knowledge and pedagogical skills, along with the institution’s learning resources, course structure, and environment, are key factors that influence academic performance and non-completion [ 13 , 14 , 15 , 16 , 17 ]. Teaching methods that higher institutions adopt have also been evaluated, with student-centered approaches that encourage active learning resulting in better performance when compared with a traditional teacher-centered approach [ 15 , 16 ].

In terms of individual factors, studies have found a lack of effort, distraction, poor time management, and no longer being interested in the course as having a negative impact on academic performance [ 14 , 15 , 18 , 19 ]. Active learning (e.g. self-quizzes, completing problem sets, and explaining concepts) has been found to yield better academic outcomes when compared with passive learning (e.g. reading lecture slides or class notes, watching lecture videos, and reading textbooks) [ 20 , 21 ]. In the same study, how early a student studied in relation to their exam did not affect their outcome, whereas students who were more distracted during the time they allocated for study, performed worst [ 20 , 22 ]. Education-related stress, poor mental health, exam anxiety, and sleep quality are also factors found to cause poor performance [ 23 , 24 , 25 , 26 , 27 ]. Other studies have shown that part-time students and those who have previously failed subjects are at risk of further poor performance and attrition [ 17 , 28 , 29 ]. Social factors including cyberbullying [ 30 ], homesickness for international students [ 31 ], and excessive socialising [ 16 ] also have a negative effect on academic performance.

Working status was found to negatively impact academic performance [ 27 ], where poor academic outcomes were correlated with a longer time spent at work [ 16 , 28 , 32 ]. Many studies have associated the lower socioeconomic status of students and their family, or financial strain with poor academic performance [ 27 , 28 , 29 ]; whereas, other studies have shown that students in families where one parent has attended higher education tend to achieve higher grades [ 31 ]. Some studies have found men and minority students are more at risk of poor performance [ 31 , 33 ]. Part-time students are much more likely cite work and family responsibilities as reasons for stopping their studies [ 17 ]. Research on students whose first language is not that of the higher education institution is mixed, with some confirming it to be a key attributor to underperformance [ 34 , 35 , 36 ], along with students with a migrant background or who are first-generation university attendees (commonly referred to as first-in-family) [ 31 , 37 , 38 ]. In contrast, other studies have found that academic performance of international students was similar, or better, than domestic students [ 39 , 40 ].

A government panel in Australia reported that the leading drivers for non-completion in higher education are both institution-related (learning environment, an academic’s ability to teach, student to staff ratios, student engagement, and support services) and student-related (health, finance, and personal responsibilities) [ 41 ]. A survey conducted by the Australian Bureau of Statistics (ABS) identified the top three reasons for attrition for students studying a bachelors degree to be: loss of interest, employment/financial reasons, and personal reasons (health, family, or other personal reasons). For postgraduate courses, reasons for attrition were highest in the order of personal reasons, employment/financial, followed by loss of interest [ 42 ].

Where a student has underperformed, they may be offered remediation assessments; to re-enroll and attempt the entire subject again, which may result in a delay in degree completion; or in some cases, be excluded from reenrolling into the same course for a period of time [ 43 , 44 ].

Consequences of poor performance vary across higher education institutions and may depend on the reasoning provided, extent of underperformance, and number of failed subjects. Key stake holders impacted by poor performance and attrition from higher education can include the students and their families, the higher education institution they are enrolled in, their community workforce, and government. Non-completion directly impacts the funding and reputation of an institution [ 17 , 45 , 46 ]. In Australia, where the cost of higher education for domestic students is subsidised by the federal government, non-completion incurs a direct cost to both the student and the tax-payer. The cost to the student includes lost time, psychological health, student debt, and forgone income [ 9 ]. From the perspective of workforce planning, a delay or non-completion of study reduces the number of employees entering into the workforce, and can lead to workforce shortages and place a burden on those currently in the field.

There are many studies that have examined the key determinants for student success or underperformance and attrition in health; however, most have focused on nursing or medical education [ 13 , 15 , 47 , 48 , 49 , 50 ]. Consequently there are limited studies that have examined the rate and reasons for attrition within pharmacy degrees. Being a degree known to be difficult in technical content, and which requires students to achieve a high level of competence, it is important to investigate reasons for attrition and potential opportunities for improvement in student teaching and engagement.

In this study we analysed 10 years of demographic data and responses to why academic progression requirements had not been met in a cohort of students enrolled in a Bachelor of Pharmacy (BPharm), Bachelor of Pharmacy and Management (BPharmMgmt), or Master of Pharmacy (MPharm) degree at The University of Sydney. Our aim was to understand the key determinants for poor performance within this group of students and identify opportunities for policy and practice to reduce underperformance in the future.

Approval for this study was granted by the Human Research Ethics Committee of The University of Sydney (2022/815).

Data collection

The inclusion criteria for this study were students enrolled in a BPharm, BPharmMgmt, or MPharm degree between the period of 2008 and 2018 (inclusive), who were required to provide a minimum of one show cause at any stage of their study. Data collected on each student included: age at the start of pharmacy degree; gender; whether they transferred from another university; whether they were a domestic or international student; Australian Tertiary Admissions Rank (ATAR) upon entry, which is a percentile score that ranks Australian students finishing secondary school in relation to their academic achievement [ 51 ]; previous studies in biology, chemistry, or mathematics; show cause triggers (units of study failed); number of show causes; students’ written show cause responses; weighted average mark (WAM) at last show cause or graduation (WAM is an average grade score indicating a student’s overall academic performance over the course of their degree and is similar to a grade point average) [ 52 ]; whether they graduated; and, the number of years they spent studying the degree. Whether those students who had graduated were currently registered as a pharmacist in Australia was retrieved using the Australian Health Practitioner Regulation Agency online registry list [accessed in 2023].

Data analysis

Researchers Da Costa, O’Brien, and Liang collected, screened, and de-identified the data, and researchers Campbell, Hinton, and Wheate analysed the data. Descriptive statistics, including mean ± SD, median, and frequencies (count and percentage) were calculated using Microsoft Excel. Mann-Whitney U tests were undertaken in GraphPad Prism 9.0 (GraphPad Software, Boston, MA, USA) to ascertain any differences between ATAR scores. Chi Square analyses were undertaken in GraphPad Prism 9.0 to compare categorical data including differences between men and women, domestic and international students, transferring and non-transferring students, and graduating and non-graduating students.

Written show cause responses were transcribed by Campbell and uploaded into NVivo (1.5.1) software (QSR International, Massachussets USA). The show cause responses were analysed reflexively using inductive thematic analysis procedures [ 53 ].This involved manually reviewing each show cause response to identify emerging themes relating to the reasons stated by the student for their poor performance. From the themes identified, a total of 43 codes were generated based on the ideas, trends, and content. Coding was conducted in a theory-driven manner, seeking to code information referencing the specific themes arising from the show cause response [ 53 ]. Themes were guided by the frequency of mention, and reported in the results if there was more than a single mention. The frequency of the subthemes was analysed to demonstrate the prevalence of stated factors that the student believed led to their poor performance.

Show cause process

Pharmacy students who do not meet the progression requirements of their degree enter one of three stages of academic intervention (Fig.  1 ). Triggers for a student not meeting the requirements for progression include: awarded a fail grade in over 50% of total units of study (subjects; UoS) taken in a semester or teaching period; an average grade (WAM) less than 50 across all UoS in a semester or teaching period; failing one, or more, barrier or compulsory UoS which includes CHEM1611, CHEM1612, PHAR2822, and any 3000 or 4000 level UoS for BPharm/BPharmMgmt; and any single UoS for MPharm; any practical component (e.g. field work or clinical work), failing the same UoS twice, having unsatisfactory attendance, or exceeding the maximum time limit allowed for the degree to be completed.

Students who fail to meet progression requirements for the first time are placed on Stage 1 of the at-risk register at which point they receive a letter from the Faculty of Medicine and Health, and are advised to complete a ‘Stay on Track’ survey and information session. At the discretion of the Associate Dean of Education, some students at Stage 1 may be required to consult an academic adviser. If a student is enrolled in a degree with a duration of less than two years full-time (e.g. MPharm), they are advised that should they fail to meet progression requirements in the following semester, they would be asked to ‘show good cause’ in order to be allowed to re-enrol in the same program; that is, they would be excluded from the degree for two years unless they could give reasons for why they should be allowed to remain studying. They are also recommended to speak to an academic advisor.

Stage 2 is triggered for a student in a 4 or 5 year undergraduate degree program (e.g. BPharm and BPharmMgmt) if they fail to meet progression requirements after being placed on Stage 1 in the previous semester, at which point the faculty sends a letter, advising the student to complete the ‘Staying on Track’ survey if they had not yet done so, and to consult an academic adviser. Stage 3 is triggered if a student fails to meet progression requirements a third time, or fails the same compulsory or barrier UoS, or any practical component twice. Students on Stage 3 are required to ‘show good cause’ and provide reasonable evidence to be allowed to re-enrol into the degree program.

The three at-risk stages of academic intervention for students who fail to meet course progression requirements. Show cause is required at Stage 2 (MPharm) or Stage 3 (BPharm/BPharmMgmt) in order to re-enrol

Demographics

In total, 164 pharmacy students received at least one show cause notification between the period of 2008 to 2018 (inclusive) and were enrolled in a BPharm (79.3%, n  = 130), BPharmMgmt (1.2%, n  = 2), or MPharm (19.5%, n  = 32) degree (Table  1 ). Of the students, 54% ( n  = 88) were men, and 81% ( n  = 133) were domestic students.

Students who transferred from another degree program made up 15% ( n  = 24) of the sample, and were a median two years older than those who did not transfer (median age 21, range 19–43 years). All students who transferred from another degree, were enrolled in the BPharm. Ninety-two percent of transfer students ( n  = 22) were domestic and 71% ( n  = 17) were women.

The age of students at the start of their degree was positively skewed, with a median age of 19 years for BPharm and BPharmMgmt (range 17–43 years). For MPharm, the median age at commencement was 24 (range 20–24) years. The median age of domestic students at the start of their BPharm or BPharmMgmt degree was 19 (range 17–43) years compared with international students at 22 (range 18–33) years. For MPharm, the median age for domestic students at commencement was 24 (range 20–54) years while for international students it was 24.5 (range 22–38) years.

Performance on entry and exit of the degree

The ATAR scores of the students in either the BPharm or BPharmMgmt were not normally distributed ( n  = 78, mean ATAR 88.8 ± 4.8) (Supplementary Figure S1 ). The average ATAR required for entry into BPharm and BPharm/Mgmt at the University of Sydney is around 90. Of the 24 students who transferred from another degree program, the ATAR score was available for four students, with an average of 78.8 ± 9.8, including two outliers who had ATAR scores of 67.80 and 74.15. The average ATAR on entry to the degree of the students who graduated was 89.4 ± 3.4, which was similar to those who did not graduate, 88.5 ± 5.4. A Mann-Whitney U test showed this difference was not statistically significant (W = 702.5, p  = 0.937).

The proportion of students who graduated after receiving at least one show cause was 37.8% ( n  = 62), of which 77.4% ( n  = 48) were registered as pharmacists at the time of data collection (Fig.  2 ). One student did not graduate their BPharm; however, they did return and complete the MPharm degree and was registered as a pharmacist at the time of data collection. The median time taken to graduation was 7 (range 1–9) years for students enrolled in the BPharm and 3 (range 2.5-8) years for those enrolled in the MPharm. During the study period, 188 students were enrolled in the BPharmMgmt degree but only two (1.1%) were required to show cause due to poor performance. Neither of those two students graduated.

A WAM score was available for all but three of the 164 students. The overall average WAM either at last show cause, if the student had not graduated, or at degree completion was 52.1 ± 12.0. For students who graduated (38.5%, n  = 62), the average WAM was 62.2 ± 5.1, while for those who did not graduate (61.5%, n  = 99), the average WAM was 45.7 ± 10.5.

When the proportion of students who graduated was compared across the ATAR bands (Table S1 ), it was evident that show cause students who entered their degree with an ATAR between 85 and 89.99 were more likely to graduate (44%) when compared with those who entered their degree with lower (27%) and higher (25–35%) ATAR scores.

Units failed

Across the cohort, show cause students received between 1 and 8 show cause notifications (Fig.  1 ). When the proportion of students who graduated was compared across the number of show causes received for those who received 1–5 show causes, the rate of graduation ranged from 36 to 50%, while none of the students who received six or more show causes graduated.

Percentage of students who graduated (black) and did not graduate (grey) by number of show causes received

Number of failed UoS

The median number of UoS failed across the three degree programs was 8 (BPharm, range 2–33), 9 (BPharmMgmt, range 5–13), and 5 (MPharm, range 2–12), respectively. In total, 8.5% ( n  = 14) students were required to show cause because they failed 2 or 3 UoS, 19.5% ( n  = 32) students failed 4 or 5 UoS and 72% ( n  = 118) students failed more than 6 UoS. Of the 14 students who failed 2 or 3 UoS, 86% were studying the MPharm degree and the remaining were BPharm students. Students who failed 4 or 5 UoS, were studying a BPharm (66%), BPharmMgmt (3%), or MPharm (31%) degree. The majority of students who failed more than 6 units were studying BPharm (91%), followed by MPharm (8%), and BPharmMgmt (1%). Students who failed 2 or 3 UoS were significantly more likely to graduate when compared with those who failed 4 or 5 UoS, or more than 6 UoS \( (X_2^2=21.86, \text{P}<0.0001)\) (Supplementary Figure S2 ).

Type of failed UoS

The most failed UoS that triggered a show cause across students in the BPharm and BPharmMgmt degrees were a mix of pharmaceutical sciences, chemistry and biology, across the first and second years of the degree programs (Table  2 ). The top five UoS failed were Basic Pharmaceutical Sciences (8.8%, 116/1314 fails; unit code: PHAR1812), Chemistry 1B (Pharmacy) (6.9%, 91/1314 fails; unit code: CHEM1612), Drug Discovery and Design 1 (6.7%, 88/1465 fails; unit code: PHAR2811), Molecular Biology and Genetics (6.5%, 86/1314 fails; unit Code: MBLG1001), and Chemistry 1A (6.2%, 81/1314 fails; unit code: CHEM1611).

For students studying the MPharm, the majority of UoS failed were for pharmaceutical sciences in first year and one specific pharmacy practice unit (PHAR5717) in the second year. The top three UoS failed for MPharm were Pharmaceutical Chemistry 1A (12.6% 19/151 fails; unit code: PHAR5513), Pharmaceutical Science (7.9%, 12/151 fails; unit code: PHAR5515), and Pharmaceutical Chemistry 1B (7.9%, 12/151 fails; unit code: PHAR5516) (Table  3 ).

Gender, transfer and international students

There was no significant difference between the number of men and women who graduated after receiving at least one show cause \( (X_1^2=0.056, \text{P}=0.813)\) . There was also no significant difference in the number of UoS failed \( (X_2^2=2.249, \text{P}\hspace{0.17em}=\hspace{0.17em}0.325)\) or number of show causes received \( (X_6^2=2.829, \text{P}=0.830)\) between men and women.

Students who transferred from another degree program were significantly less likely to graduate \( (X_1^2=13.53, \text{P}\hspace{0.17em}=\hspace{0.17em}0.0002)\) . The likelihood of graduating was not statistically significant different between domestic and international students who received a show cause \( (X_1^2=0.88, \text{P}<0.348)\) (Supplementary Figure S3 ).

Student responses to show causes

There were 293 show causes in total, of which only 141 show cause response letters were available. Reasons given by students for their poor performance could be classified under four major themes: personal life matters, institutional aspects, social integration, and interest in the course (Fig.  3 ). Personal life matters could be further sub-divided into health, study familiarity, responsibilities, and other personal life matters.

The majority of show cause responses attributed poor performance to personal life reasons (87%, 396 responses), followed by institution-related (8.8%, 40 responses), lack of interest in the degree (2.2%, 10 responses), and social integration (2%, 9 responses). The five most mentioned personal life reasons that led to poor performance were stress and anxiety ( n  = 63, 45%), physical health ( n  = 51, 36%), and depression ( n  = 39 28%). This was followed by family health, mentioned 37 times (26%), and reasons relating to employment or financial health, mentioned 33 times (23%). Reasons that related to the institution totalled 40, interest of the course totalled 10, and social reasons totalled 9. Personal life health-related reasons accounted for 41% of show cause responses. These included a combination of physical, mental, and unspecified health issues.

All show cause responses provided by students could be categorised into four major themes. Personal life was subcategorised into health, study skills, responsibilities, and other personal life

Some students identified a lack of study-related skills and study familiarity as a source of underperformance. Reasons included: carelessness in exams, poor study habits, language barrier, being an international student or mature age student, misjudging the course difficulty, overloading, burning out after high school, and being unaware of opportunities to apply for special consideration. Another set of reasons provided for underperformance included: needing to meet responsibilities and commitments for family, friendships, and romantic relationships. A variety of other personal life reasons were provided, which included: employment, finance, transition to independent living or a new country, living environment, distance to travel to the university, needing to relocate, and being physically unable to attend classes.

Student show cause responses that attributed poor performance to inefficiencies within the institution included UoS changes, error or poor timing of exams, dissatisfaction with the course and staff, and unhelpful support. Some students found the UoS content too difficult. Social reasons that lead to poor performance included: bullying, stigma from peers once failing, and homesickness (for those studying abroad). Another reason provided was no longer being interested or committed to the course.

This study investigated the key determinants of underperformance by pharmacy students at an Australian higher education institution. Our findings indicate that across the students enrolled in BPharm, BPharmMgmt, and MPharm degrees, those who had failed more UoS overall, were less likely to graduate. The types of UoS failed were weighted towards chemistry-based subjects, and the most frequent student-reported reasons for poor performance were related to personal health.

Our study also found that students who transferred from another higher education institution were less likely to graduate compared with students who had not transferred. Some studies in the US have found that students who transfer to bachelors programs from similar institutions or community colleges, which are US institutions that only offer two year undergraduate associate degrees that lead to a specific skilled job or can be used to transfer into a bachelor course [ 54 ], experience ‘transfer shock’ where grade point average (GPA) declines at the post transfer institution, which can eventually result in attrition [ 55 , 56 ]. In contrast, other studies have found no significant effects from transfers, and an overall lack of consensus on this as a universal experience [ 57 , 58 ]. A study that examined transferring engineering students found that students who transferred from similar degrees were more likely to graduate when compared with students who transferred from less comprehensive degrees [ 56 ]. A literature review that examined transferring student performance found factors that negatively influenced persistence and course completion included: a lack of social integration, limited transferrable credits, lower GPAs, lack of funding, distance from institution, academic rigour, and personal work/life balance [ 57 ].

Our analysis also found that students failing more than three UoS were more likely to not graduate when compared with those who failed fewer UoS. This finding parallels many studies that show students with poor academic outcomes are more likely to not complete their degree [ 59 , 60 ]. A recent study on student attrition, found that students who failed one subject were more likely to fail more subjects, and also had a four-fold higher likelihood of not graduating [ 27 ]. The Grattan Institute presents similar statistics, where students who consistently fail to meet academic progression requirements eventually decide to leave or are excluded from re-enrolling by the university [ 61 ].

The high occurrence of underperformance in relation to chemistry is consistent with other studies [ 62 , 63 ]. Pancyk et al. found that chemistry marks were correlated with attrition while biology marks predicted likelihood of delayed graduation for Master of Science (in Pharmacy) students. Another study found that the prior attainment of a Bachelor of Science degree to be a predictor of performance in a Doctor of Pharmacy program [ 64 ]. In countries, such as the US, where a specialised pre-admissions pharmacy test (Pharmacy College Admissions Test; PCAT) is used for entrance into a pharmacy program, the PCAT score correlated with student academic performance in the pharmacy course [ 65 ]. There are five areas examined by the PCAT, including: writing, biological processes, chemical processes, critical reading, and quantitative reasoning [ 66 ]. There is also evidence that better outcomes attained in pre-pharmacy biology and mathematics GPA [ 67 , 68 ], or having completed a four-year bachelor course, contributes to student performance in American pharmacy colleges [ 64 , 69 , 70 ]. Another study found prior academic achievement in secondary school, or pre-university study, can predict performance in an UK MPharm course; however, not the likelihood of graduation [ 71 ]. Other studies have found that pre-tests, for certain UoS, like biochemistry and pharmaceutical calculations conducted before starting a subject are correlated with overall subject performance, which makes these tests a good predictor for at-risk students [ 67 , 68 ].

The most common reasons reported by students for their underperformance in the present study were stress and anxiety, personal health, and depression. This is consistent with current literature [ 17 , 23 , 24 , 25 , 26 , 27 ], and the 2022 Australian Student Experience Survey [ 72 ], which reported that health or stress, followed by work/life balance were the leading causes for students attrition. A specific study in pharmacy students found that exam anxiety had a negative impact on student performance in pharmacy practical exams [ 26 ]. Psychological distress among students completing a higher education degree in Norway showed negative impacts on their self-perceived academic ability, and course progression [ 73 ]. Another study investigating students’ self-reported explanations for their poor academic performance found mental health as a contributing factor, and vice versa, where poor performance intensified mental distress [ 27 ]. Although the Australian Bureau of Statistics also reported personal health reasons as a major contributor for non-completion in bachelor programs between 2018 and 2019, the leading reason was that students were no longer interested in their chosen degree. In the same report, non-completion of masters degrees was driven by family, health, or other personal reasons [ 42 ]. Student mental health is a significant driver of attrition and is common across both private and public higher institutions in Australia [ 41 ]. The mental health burden on students is recognised at The University of Sydney and so significant mental health support is offered. All students are able to access free counselling and psychological support sessions, there is a 24/7 mental health support telephone line, and additional self-help resources (like mindfulness and relaxation) are provided through the university’s website. Mental health first health training is also included in the curricula for all pharmacy degree programs at the university.

Successful completion of a pharmacy degree requires not only academic ability, but a certain level of pre-knowledge, in particular, biology and chemistry, to decrease failure rates in these subjects, avoid delays in degree completion, and possible attrition. Institutions should aim to address these barriers by introducing pre-requisite subjects or mandate compulsory bridging courses if a prior level of knowledge attainment in these subject areas is not provided. Alternatively, pre-tests for certain UoS can be conducted prior to the course commencement to identify at-risk students, and additional academic support services can be offered.

With student poor mental health found as the most common self-reported reason for poor performance in this study, often exacerbated by academic performance pressures, institutions should implement policies for early detection and support for students going through challenging times. Such policies could include more frequent reminders for students to self-assess their mental health, and information on where to seek support services. This could take form in programs being introduced prior to lectures, access to support portals made more prominent on online learning platforms, or self-check surveys to be taken at a frequency deemed appropriate.

Limitations

The present study had a number of limitation. Not all student’s ATAR scores (or equivalent) were available. The method of collecting whether a student was registered as a pharmacist was based on them not having changed their last name which may be the case for some students who changed their name after graduation (e.g. upon marriage). Students who may be registered as a pharmacist in countries other than Australia could not be determined. Not all student show cause reasons were available because of the change from physical to electronic filing over the period studied. The limited number of students who received five or more show causes also meant the study was not powered to establish a cut-off whereby after receiving a certain number of show causes, the chance of graduating is highly unlikely.

Conclusions

This study investigated the key determinants for poor academic performance in a cohort of pharmacy students enrolled in a BPharm, BPharmMgmt, and MPharm degree. The key factors that influenced whether a show cause student completed their studies included whether they transferred from another institution, and failed more than three UoS. The UoS with the highest fail rates were chemistry based, and the most frequent student self-reported reason for poor performance was personal stress and anxiety. The results indicate that pharmacy schools should aim to address student foundation knowledge in chemistry, identify at-risk students early using pre-subject testing, and provide better access and knowledge of available services to address student mental burden. Future studies should investigate whether students who have completed chemistry and biology pre-requisites perform better in their pharmacy degree.

Data availability

The data that support the findings of this study are available on request from the corresponding author, N.J.W.

Aljohani O. A comprehensive review of the major studies and theoretical models of student retention in higher education. High Educ Stud. 2016;6:1–18.

Article   Google Scholar  

Spady WG. Dropouts from higher education: an interdisciplinary review and synthesis. Interchange 1984. 1970;1(1):64–85.

Spady WG. Dropouts from higher education: toward an empirical model. Interchange. 1971;2(3):38–62.

Tinto V. Dropout from higher education: a theoretical synthesis of recent research. Rev Educ Res. 1975;45(1):89–125.

Tinto V. Leaving college: rethinking the causes and cures of student attrition. 2nd ed. Chicago: University of Chicago Press; 1993.

Google Scholar  

Bean JP. Dropouts and turnover: the synthesis and test of a causal model of student attrition. Res High Educ. 1980;12(2):155–87.

Tight M. Student retention and engagement in higher education. J Furth High Educ. 2020;44(5):689–704.

Carini RM, Kuh GD, Klein SP. Student engagement and student learning: testing the linkages. Res High Educ. 2006;47(1):1–32.

Thomas L, Kift S, Shah M. Student retention and success in higher education. Cham: Springer International Publishing; 2021. pp. 1–16.

Book   Google Scholar  

Coates H. The value of student engagement for higher education quality assurance. Qual High Educ. 2005;11(1):25–36.

Al-Tameemi RAN, Johnson C, Gitay R, Abdel-Salam A-SG, Hazaa KA, BenSaid A, et al. Determinants of poor academic performance among undergraduate students—A systematic literature review. Int J Educ Res. 2023;4:100232.

Lorenzo-Quiles O, Galdón-López S, Lendínez-Turón A. Factors contributing to university dropout: a review. Front Educ Res. 2023;8.

Wilkinson TJ, McKenzie JM, Ali AN, Rudland J, Carter FA, Bell CJ. Identifying medical students at risk of underperformance from significant stressors. BMC Med Educ. 2016;16:43.

Le HTTN, La HTT, Le TP, Nguyen TTT, Nguyen NT, Tran TP. Factors affecting academic performance of first-year university students: a case of a Vietnamese university. Int J Educ Prac. 2020;8(2):221–32.

Sharma P, Singh P, Kalhan S, Garg S. Analysis of factors affecting academic performance of MBBS students in pathology. Ann Int Med Dent Res. 2017;2.

Mascolo M, Castillo J. The origins of underperformance in higher education in America: proximal systems of influence. Pedgog Hum Sci. 2015;5(1):1–40.

Norton AC, I. and, Mackey W. Dropping out: the benefits and costs of trying university. The Grattan Institute, 2018. p. 1–65.

van Rooij E, Jansen EPWA, Van de Grift W. First-year university students’ academic success: the importance of academic adjustment. Eu J Psychol Educ. 2017;33:1–19.

Arshad M, Zaidi SM, Mahmood D. Self-esteem and academic performance among university students. J Educ Pract. 2015;6:2015.

Walck-Shannon EM, Rowell SF, Frey RF. To what extent do study habits relate to performance? CBE - Life Sci Educ. 2021;20(1):ar6.

Roick J, Ringeisen T. Students’ math performance in higher education: examining the role of self-regulated learning and self-efficacy. Learn Individ Differ. 2018;65:148–58.

Nonis SA, Hudson GI. Performance of college students: impact of study time and study habits. J Educ Bus. 2010;85(4):229–38.

Jevons C, Lindsay S. The middle years slump: addressing student-reported barriers to academic progress. High Educ Res Dev. 2018;37(6):1156–70.

Pascoe MC, Hetrick SE, Parker AG. The impact of stress on students in secondary school and higher education. Int J Adolesc Youth. 2020;25(1):104–12.

May RW, Bauer KN, Seibert GS, Jaurequi ME, Fincham FD. School burnout is related to sleep quality and perseverative cognition regulation at bedtime in young adults. Learn Individ Differ. 2020;78:101821.

Hadi MA, Ali M, Haseeb A, Mohamed MMA, Elrggal ME, Cheema E. Impact of test anxiety on pharmacy students’ performance in Objective Structured Clinical examination: a cross-sectional survey. Int J Pharm Pract. 2018;26(2):191–4.

Ajjawi R, Dracup M, Zacharias N, Bennett S, Boud D. Persisting students’ explanations of and emotional responses to academic failure. High Educ Res Dev. 2020;39(2):185–99.

Rodríguez-Hernández CF, Cascallar E, Kyndt E. Socio-economic status and academic performance in higher education: a systematic review. Educ Res Rev. 2019;29:100305.

Tomul E, Polat G. The effects of socioeconomic characteristics of ctudents on their academic achievement in higher education. Am J Educ Res. 2013;1:449–55.

Peled Y. Cyberbullying and its influence on academic, social, and emotional development of undergraduate students. Heliyon. 2019;5(3):e01393.

Sun J, Hagedorn L, Zhang Y. Homesickness at college: its impact on academic performance and retention. J Coll Stud Dev. 2016;57:943–57.

Triventi M. Does working during higher education affect students’ academic progression? Econ Educ Rev. 2014;41:1–13.

Voyer D, Voyer SD. Gender differences in scholastic achievement: a meta-analysis. Psychol Bull. 2014;140(4):1174–204.

Dafouz E, Camacho-Miñano MM. Exploring the impact of English-medium instruction on university student academic achievement: the case of accounting. Engl Specif Purp. 2016;44:57–67.

Civan A, Coskun A. The effect of the medium of instruction language on the academic success of university students. Educ Sci: Theory Prac. 2016;16:1981–2004.

Sawir E. Language difficulties of international students in Australia: the effects of prior learning experience. Int Educ J. 2005;6:567–80.

Mishra S. Social networks, social capital, social support and academic success in higher education: a systematic review with a special focus on ‘underrepresented’ students. Educ Res Rev. 2020;29:100307.

López MJ, Santelices MV, Carmen Maura T. Academic performance and adjustment of first-generation students to higher education: a systematic review. Cogent Educ. 2023;10(1).

Zheng RX, Everett B, Glew P, Salamonson Y. Unravelling the differences in attrition and academic performance of international and domestic nursing students with English as an additional language. Nurse Educ Today. 2014;34(12):1455–9.

Rienties B, Beausaert S, Grohnert T, Niemantsverdriet S, Kommers P. Understanding academic performance of international students: the role of ethnicity, academic and social integration. High Educ. 2012;63(6):685–700.

Final Report -. Improving retention, completion and success in higher education. Higher Education Standards Panel; Australian Government Department of Education; 2017.

Qualifications. and Work, 2018-19. Australian Bureau of Statistics; 2020.

Academic Progression. The University of Sydney [updated 31 March 2023; cited 2023 September ]. Available from: https://www.sydney.edu.au/students/academic-progression.html .

Failed. withheld and invalid units: Monash University; [updated 2023; cited 2023 September]. Available from: https://www.monash.edu/students/admin/enrolments/change/failed-withheld-invalid-units .

OCED. Education at a Glance 2023. Organisation for Economic Co-operation and Development Publishing 2023 [Available from: https://www.oecd-ilibrary.org/content/publication/e13bef63-en .

Yorke M, Longden B. Retention and student success in higher education. McGraw-Hill Education (UK); 2004.

Faisal R, Shinwari L, Hussain S. Academic performance of male in comparison with female undergraduate medical students in pharmacology examinations. J Pak Med Assoc. 2017;67:204–8.

van Moppes NM, Willems S, Nasori M, Bont J, Akkermans R, van Dijk N et al. Ethnic minority GP trainees at risk for underperformance assessments: a quantitative cohort study. Br J Gen Pract Open. 2023;7(1).

Liu XL, Wang T, Bressington D, Nic Giolla Easpaig B, Wikander L, Tan JB. Factors influencing retention among regional, rural and remote undergraduate nursing students in Australia: a systematic review of current research evidence. Int J Environ Res Public Health. 2023;20(5).

Caponnetto V, Dante A, Masotta V, La Cerra C, Petrucci C, Alfes CM, et al. Examining nursing student academic outcomes: a forty-year systematic review and meta-analysis. Nurse Educ Today. 2021;100:104823.

Australian Tertiary Admission Rank. Universities Admission Centre; [cited 2023 November ]. Available from: https://www.uac.edu.au/future-applicants/atar .

Weighted Average Mark (WAM). The University of Sydney; 2023 [cited 2023 November]. Available from: https://www.sydney.edu.au/students/weighted-average-mark.html .

Braun V, Clarke V. Using thematic analysis in psychology. Qual Res Psychol. 2006;3(2):77–101.

Community College. Education USA; [cited 2023 November ]. Available from: https://educationusa.state.gov/ .

Ivins T, Copenhaver K, Koclanes A. Adult transitional theory and transfer shock in higher education: practices from the literature. Ref Serv Rev. 2017;45(2):244–57.

Smith NL, Grohs JR, Van Aken EM. Comparison of transfer shock and graduation rates across engineering transfer student populations. J Eng Educ. 2022;111(1):65–81.

Aulck L, West J. Attrition and performance of community college transfers. PLoS ONE. 2017;12:e0174683.

Diaz PE. Effects of transfer on academic performance of community college students at the four-year institution community. Coll J Res Prac. 1992;16(3):279–91.

Li I, Carroll D. Factors influencing university student satisfaction, dropout and academic performance: an Australian higher education equity perspective. Perth: National Centre for Student Equity in Higher Education, Curtin University;; 2017. p. 56.

Sosu EM, Pheunpha P. Trajectory of university dropout: investigating the cumulative effect of academic vulnerability and proximity to family support. Front Educ. 2019;4.

Cherastidtham I, Norton A, Mackey W. University attrition: what helps and what hinders university completion? Grattan Institute; 2018.

Panczyk M, Rebandel H, Belowska J, Zarzeka A, Gotlib J. Risk of attrition from master of science in pharmacy degree program: 15-year predictive evaluation. Ind J Pharm Educ Res. 2016;50(1):70–9.

Houglum JE, Aparasu RR, Delfinis TM. Predictors of academic success and failure in a pharmacy professional program. Am J Pharm Educ. 2005;69(1–5):283–9.

McCall KL, Allen DD, Fike DS. Predictors of academic success in a doctor of pharmacy program. Am J Pharm Educ. 2006;70(5):106.

Meagher DG, Pan T, Perez CD. Predicting performance in the first-year of pharmacy school. Am J Pharm Educ. 2011;75(5):81.

Pharmacy College Admission Test American Association of Colleges of Pharmacy. [updated 2023; cited 2023 October]. Available from: https://www.aacp.org/resource/pharmacy-college-admission-test .

Vinall R, Khansari P, McDowell J, Ried LD, Kreys E. Impact of completion of a pre-pharmacy biochemistry course and competency levels in pre-pharmacy courses on pharmacy student performance. Pharm 2019;7(3).

Aronson BD, Eddy E, Long B, Welch OK, Grundey J, Hinson JL. Identifying low pharmaceutical calculation performers using an algebra-based pretest. Am J Pharm Educ. 2022;86(1):8473.

Chisholm MA, Cobb HH, DiPiro JT, Lauthenschlager GJ. Development and validation of a model that predicts the academic ranking of first-year pharmacy students. Am J Pharm Educ. 1999;63(4):388–93.

Chisholm MA, Cobb HH, Kotzan JA. Significant factors for predicting academic success of first-year pharmacy students. Am J Pharm Educ. 1995;59(4):364–70.

Bush J. Entry characteristics and academic performance of students in a master of pharmacy degree program in the United Kingdom. Am J Pharm Educ. 2012;76(7).

2022 Student Experience Survery. National Report. 2023.

Grøtan K, Sund ER, Bjerkeset O. Mental health, academic self-efficacy and study progress among college students - the SHoT Study, Norway. Front Psychol. 2019;10:45.

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Campbell, A., Hinton, T., da Costa, N.C. et al. Causes and outcomes of at-risk underperforming pharmacy students: implications for policy and practice. BMC Med Educ 24 , 421 (2024). https://doi.org/10.1186/s12909-024-05327-z

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DOI : https://doi.org/10.1186/s12909-024-05327-z

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