Math Major FAQs

If you have not seen multivariable calculus before and need it for your major (e.g. all the combined Math majors), or for other courses you plan to take (e.g. in Economics or Physics), then you should consider taking Math 1200 as soon as you can. 

For the pure math major, you have a choice to complete either Math 1200 or 3020. Most students either complete Math 1200 in their first year (before Math 2250 and 2550), or complete Math 2250 and 2550 first and then take 3020 in their second or third year. 

Yale does not allow transfer credit for courses taken during high school, even if they were taken at a local college. That does not mean you have to repeat material you already know, however. The details depend on why you need Math 1200: 

1. If you need it as a pre-requisite for another Yale course, it should not be an issue: instructors typically accept a high school course in place of Math 1200. If you’re not able to reach the instructor, contact their program’s DUS. 
    
2. If you need it for the pure math major: You can complete the multivariable requirement with Math 3020. This option is available to all students, whether or not they have already completed a course similar to Math 1200. 
    
3. If you need it for a combined math major:  You can send your transcript (unofficial is fine) to math.dus@yale.edu , and request permission to substitute Math 3020 for Math 1200 in requirements of the relevant major (Math + CPSC / Econ / Phil / Phys). Please be sure to specify which major you are interested in. 
   
   If you would like to consider other options for substitutions (i.e. another class in the same area, such as Math 2460 or an analysis course), you can request an evaluation of the course that you have completed. For this evaluation, we would need a copy of your transcript, syllabus for the course, detailed list of topics covered, and a copy of the final exam or a sample final exam. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu .  
    
4. If you need it for another major, please contact the major’s DUS to see what options there may be, as they are in charge of all requirements and exceptions for their major. 

No (but if you passed ENAS 1510 before deciding on the math major, you can complete the multivariable calculus requirement with Math 3020). 

Yale does not allow transfer credit for courses taken during high school, even if they were taken at a local college. Beyond that, the answer and its details depend on why you need linear algebra: 

1. If you need it as a pre-requisite for another Yale course, it should not be an issue: instructors typically accept a high school course, if it is equivalent to the pre-requisite. If you’re not able to reach the instructor, contact their program’s DUS. 
    
2. If you need it for Math + Phil or Math + Phys: These majors recommend taking Math 2250 or 2260, but do not require any linear algebra, so you will not need to get permission to substitute. 
    
3. If you need it for another major, please contact the major’s DUS to see what options there may be. 
    
4. If you need it for the Pure math, Math + Econ or Math + CPSC: These three majors require Math 2250 or 2260, so substitution can only be considered if your course was fully proof-based (e.g. you learned proof techniques such as induction, and most problems on homeworks and exams explicitly asked “prove [something]”). In all three majors, students who completed linear algebra in high school typically still enroll in Math 2250 or 2260. 
   
   If your course was proof-based you can request an evaluation of it. For this evaluation, you will need to reach out to math.dus@yale.edu during the summer before your first semester at Yale. We will need a copy of your transcript, syllabus for the course, detailed list of topics covered, a copy of one or two assignments, and a copy of the final exam or a sample final exam. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu .    
   
   If the course is reasonably equivalent to Math 2250, then you may be granted permission to substitute Math 3400. We will also help you find the best starting course (likely Math 255 or 256 – or higher, if you have taken real analysis as well). Please note that this permission has to be granted by the Math DUS - obtaining permission from the Math 255 instructor to enroll will not take care of requirements of the math major. 
   
   If you know proof-based linear algebra but have not taken officially taken a course in it, or if your course is not evaluated as equivalent to Math 225, you can try placing out of Math 225 by taking an exam during the summer before your first semester at Yale.  Details are listed in a question just below. 
   
    

First, please note that the test does not award course credit or fulfill any requirements at Yale. It can only grant permission to substitute a higher level course in the same area for Math 225, in requirements of the math and joint math majors. 

The test is available to incoming first-year students who learned the material of a fully proof-based linear algebra course (such as Math 225) prior to enrolling at Yale, but the course was not evaluated as equivalent to Math 225. (See above for how to have a course evaluated.)

The test is only open to students who have had some formal training in proofs and linear algebra, including regular feedback about their work from experienced mathematicians. 

If you wish to take the test, you must first e-mail us the materials from the course you completed, at math.dus@yale.edu. This needs to be done by August 15, during the summer before you first enroll at Yale. (The exam is not available to continuing students.) 

We will offer the test in person, at the end of August, just before classes start (usually that Monday or Tuesday). We will set the time according to everyone’s availability: you will hear from us after August 15 about scheduling, if your name is on our list. 

Students who pass will receive permission to substitute a higher level course in the same area for Math 225, in requirements of the math or combined math major (Math + CPSC, Econ, Phil, Phys)  

If you need linear algebra for another major, please check in with their DUS - our process only works for math majors, we have no say in requirements of other majors (though we would be happy to assist, if the DUS wishes). 

As a rule, the answer is “no”. Courses required for the major must be completed. In rare cases where an incoming student has learned in high school the material and skills taught in a particular required course, the DUS may grant an option to substitute a higher level course in the same area. Please be sure to discuss this with the DUS prior to your first semester at Yale. 

To evaluate the course you have completed, we will need a copy of your transcript, syllabus for the course, detailed list of topics covered, a copy of one or two assignments, and a copy of the final exam or a sample final exam. If the instructor wishes to keep the test confidential, it can be sent directly to math.dus@yale.edu .

All three courses cover linear algebra. Math 2220 focuses more on computational techniques and applications, while 2250 and 2260 emphasize mathematical proofs and a more conceptual approach.

Math 2250 (linear algebra) or 2260 (intensive linear algebra) is recommended for students who wish to take further proof-based mathematics courses. Students majoring in mathematics, Math + CPSC or Math + Econ are required to complete either Math 2250 or Math 2260. 

 In more detail: For math majors, and students who wish or need to continue with proof-based math courses, the theory and proof writing skills learned in Math 2250 or 2260 provide essential preparation for further study. That is why the math major does not accept Math 2220. 

Outside of the major: generally speaking, proofs are useful in many fields. They help one to become a better problem solver, evaluate different approaches to a question, consider options along the way, keep track of important details, check solutions for correctness, and present them in a way that is accessible to others. These skills are very helpful, in math and outside of it. 

For that reason, many students find it beneficial to take Math 2250 or 2260, even if they do not continue with further math courses. If you try the course and enjoy it, the skills you learn will not be wasted. 

If you enjoy applications more, and want to get lots of practice solving concrete problems, rather then focus on theory, then Math 2220 is a better choice. It provides great preparation on the practical side of linear algebra, and it is preferred by the majority of students in engineering, social sciences, and many other fields. 

Moving from Math 2260 to Math 2250 is permitted until Midterm. Moving from Math 2260 or 2250 to Math 222 is permitted until the end of the third week of classes (this has an earlier deadline because the courses are quite different, and it is too difficult to catch up later on). You can read more about how moving works in our Calculus FAQ. 

Our requirements are listed in the Yale College Programs of Study:

• Math
• Math and Computer science
• Math and Economics
• Math and Philosophy
• Math and Physics

For detailed notes about choosing which courses to start with, and a path through the introductory sequences, please visit our first-year student resources site. 

At most two courses can be counted simultaneously toward both majors.

Extra note: Pre-requisites do not count toward the overlap. If your second major has Math 120 as a pre-requisite, for example, you can still use Math 120 to fulfill the multivariable calculus requirement in math, even if you have two other overlapping courses.

The rules get more complicated if you also want to earn a B.S./M.S. degree in one of your two majors. In this case, you are either allowed to overlap 1-2 courses between the two majors, or 1-2 courses between your B.S. and M.S. in the same major, but not both. That is to say, one set of overlaps must be empty (even if the other only has one course in it). 

No. This is not permitted, and no exceptions will be granted for any reason. 

To get the most out of math graduate classes, we recommend that students should first take at least three or four regular level 3000 courses.

For most students, the most accessible graduate courses to start with are those cross-listed with both an undergraduate (level 3000) number and a graduate (level 5000) number (for example, Modern algebra is listed as Math 3800 and Math 5000), as well as those listed only at the 5000 level. Graduate courses level 5000-5999 can be used toward requirements of the major.

Courses level 6000+ are topics courses, and we strongly recommend that students only consider taking them after they have passed at least two level 5000 graduate courses. You must also consult with the instructor before enrolling, particularly in regard to pre-requisites - at this level, pre-requisites are not necessarily obvious from the course description. 

Courses level 6000 and above may not be counted toward requirements of the major in mathematics, or math + economics / computer science / philosophy / physics. The only exception is the two-course graduate course requirement of the intensive mathematics major, and the M.S. portion of the requirements of the mathematics B.S./M.S. degree. 

Generally speaking, when taking a cross-listed course, undergraduates should use the undergraduate number, if they wish to count the course toward the undergraduate requirements. 

If you need a cross-listed course (such as MATH 3800 = MATH 5000) toward the graduate course reuqirement of the intensive degree, or toward the M.S. degree, then you must register for it with the graduate number. 

If you are currently enrolled with the undergraduate number, and need the graduate one, then you need to switch to the graduate course before the last day of classes. You can do so with the Yale college course change form.  

No change to the course number is possible after the last day of classes, so it is critical that you do this in time. 

No. (This is a university-wide rule: Cr/D/F is only available for Yale College courses.)

Graduate courses level 5000-5999 can be used toward requirements of the major.

Courses level 6000+ are topics courses, and we strongly recommend that students only consider taking them after they have passed at least two level 5000 graduate courses. You must also consult with the instructor before enrolling, particularly in regard to pre-requisites - at this level, pre-requisites are not necessarily obvious from the course description. 

Courses level 6000 and above may not be counted toward requirements of the major in mathematics, or math + economics / computer science / philosophy / physics. The only exception is the two-course graduate course requirement of the intensive mathematics major, and the M.S. portion of the requirements of the mathematics B.S./M.S. degree. 

For cross-listed courses (e.g. Math 3800  = Math 5000), you should use the undergraduate number, if you wish to apply the course toward undergraduate requirements. 

If you need it toward graduate requirements, for the intensive major or the M.S. degree, you must use the graduate number when you register. See the M.S. degree section for more details. 

Note 1: If you are in the B.S. / M.S. program, there is a maximum overlap (see the B.S./M.S. degree section for details).

Note 2: As a rule, graduate courses do not carry the math distribution attribute. The one and only exception is Math 5440. 

The math-distribution requirement courses can be counted toward other undergraduate requirements at the same time. For instance, Math 3020 can be applied toward the multivariable requirement and count as math-distribution at the same time. 

No other overlaps are permitted between requirements. 

Any course that has a Math number counts towards the requirements. If you wish to count it toward math, we recommend enrolling with the math number (e.g. Math 2410, as opposed to S&DS 2410). If you register with another number and later change your mind, and need to count the course toward math, please write to math.dus@yale.edu and we will help you sort it out.

About courses that do not carry a math number:

• Math majors can substitute up to two courses from another department, provided that the math DUS approves the selection.

• Joint math majors may not substitute courses from another department for the mathematics portion of their major requirements. The idea behind allowing substitutions is to allow pure math majors to explore applications of mathematics by taking up to two math-intensive courses in other departments, while still taking a minimum of eight math courses.  For joint majors, the mathematics requirement is smaller, and cross-discipline exploration is already built into the program. That being so, the mathematics portion of the requirement must be satisfied with courses that have a math number. No exceptions will be granted. 

Below is a list of courses that the DUS will normally approve for substitution towards the math (not joint math) major, and a list of courses that we do not currently approve.  Please note that these courses do not carry any attributes, in particular, they do not count toward math-distribution. 

If you have a question about a course that is not on the list, please e-mail the DUS, and we will evaluate it for this purpose. Please note that the evaluation is not instant; but we can usually do it within a couple of business days. 

As a general rule, graduate courses from other departments cannot be counted.

Extra note: These lists are regularly revised, but some of the courses may not be offered anymore. We need to keep each discontinued course on the list for four years, so that it remains available to everyone who may have completed it during their time at Yale. 

Typically approved, for pure math (not joint math) majors:

• CPSC 3650 = Econ 3365 (algorithms)
• CPSC 3660 = ECON 3366 = AMTH 3660 (intensive algorithms)
• CPSC 4610 (statistics and learning theory for cs)
• CPSC 4620 (spectral graph theory, this is not a regular course, but it’s offered about every 3-6 years)
• CPSC 4680 (computational complexity)
• CPSC 4860 (probabilistic machine learning)
• ECON 2135 (formerly 135, intro to probability cannot be counted in parallel with Math 241 or 242)
• ECON 2136 (formerly 136, econometrics cannot be counted in parallel with Math 241 or 242)
• ECON 3351  (formerly 351, mathematical econ: game theory)
• LING 2249 ( formerly 224, math of language)
• PHIL 2267 (formerly 267, mathematical logic)
• PHIL 4427 (formerly 427 computability and logic)
• S&DS 3640 = AMTH 3640 = EENG 454 (information theory)
• S&DS 4100 (statistical inference)
• S&DS 4310 = ECON 4431 = AMTH 4310 (optimization and computation)
• S&DS 4320 (advanced optimization techniques)

Currently not approved:

• AMTH 3610 = S&DS 3610
• AMTH 2350, 3640, 4280, 5530
• APHY 4700
• CPSC: 2010, 2020, 4400*, 4470, 4550, 4670, 4690, 4810
• ECON 3350 (formerly 350), 3361 (formerly 361), 5530, 5531
• ECE 2000, 2020
• ENAS: 1940
• PHYS 5060 (formerly 460)
• S&DS: 2300, 2380, 2400, 2650, 3170, 3630, 3650, 4110

*CPSC 4400 counts for students who completed it in the academic year 2024-25 or earlier (as CPSC 440). 

If you are registered for the course with another department’s number (e.g. S&DS 2410), and you wish to count the course toward the math major, you should submit a Yale college course change form and switch to the math number (e.g. Math 2410). The form can be submitted any time before the last day of classes in the semester that you are registered for the course. 

If you have already completed the course, write to math.dus@yale.edu for assistance. 

If you are already registered for the course under its math number, and it’s not showing up, write to math.dus@yale.edu for help. 

If a course has a Math number, it cannot be counted towards this requirement (the requirement is meant to enhance the mathematics major with science courses that are outside of the B.A. portion of the program). The same applies to courses that do not have a math number, but are essentially mathematics courses.

Note that the courses on this list are not introductory, as the degree is meant to certify that students reached an advanced level in their physical science education. This is to say that if you wish to complete the B.S. degree, you should plan ahead for the science courses, as you will first need to complete their pre-requisites first. (Courses without physical science pre-requisites typically do notcount toward this requirement.)

Below are courses that are typically approved to satisfy this requirement. If you wish for us to evaluate a course that is not on either list, please write to the DUS.

As a general rule, graduate courses cannot be counted. 

• ASTR 3200, 4180, 4300
• CHEM: 3330, 4700
• PHYS: 3420, 3440, 4010 or 4100 (but not both), 4020 or 4300 (but not both), 4500 (formerly 420), 4400, 4410

​Currently NOT approved

• APHY 4700
• ASTR 4000, 4650
• CHEM: 3280, 3320
• EPS 319, 421, 456
• PHYS 3410, 3430, 3450, 3560, 4120*, 4280, 4390, 4480, 5060 (formerly 460)
• All courses numbered strictly below 3000
• All courses that are not physical science (e.g. we cannot count courses in life sciences, engineering, computer science, etc.) 

*Phys 4120 counts in semesters when it is a full credit course (not half credit).

Next year’s schedule will be posted prior to April registration. Until then, it will not be possible for us to give a definite answer as to which courses will be offered. 

The list of undergraduate courses usually does not change that much from year to year, but there are several courses we typically offer only ever other year, such as Math 3530, 3540, 3730, 4210, 4300, 4350, 4400, 4470. If they are offered in the current year, it is unlikely (though possible) that they will be offered again the following year. 

Graduate courses (that are not cross-listed as undergraduate) vary from year to year. Our intention is to offer Math 5260, 5360, and 5440 every year. Topic courses (= all courses level 6000+) change every year. Note that courses level 6000+ cannot be applied toward the major in mathematics, or math + economics / computer science / philosophy / physics. The only exception is the two-course graduate course requirement of the intensive mathematics major, and the M.S. portion of the requirements of the mathematics B.S./M.S. degree. 

Math 4700 is independent study, intended for learning a full course worth of math topics that are not regularly offered. It is pass / fail, and cannot be counted toward the major, but it does receive graduation credit. (Please note the “not regularly offered” condition: it means that there cannot be a significant overlap with any course that we typically offer.)

To sign up, you will need to find a math faculty adviser who will supervise the study. It is recommended that you start looking during the previous semester, so that everything is ready to start at the beginning of term. 

You and your supervisor should agree on a tentatively list of topics that will be covered, and how the class will work. Typically, this includes a weekly meeting, the student either writes or presents about what they have been learning and / or solutions to selected problems. The course usually ends with a project. The student is required to write a short paper (10 - 15 pages). 

At least three days before pre-regitration ends the previous semester, you must submit your initial proposal for the project to math.dus@yale.edu . If you wish to make adjustments after that, the final version is due at least three days before the end of add / drop period.  Please be sure to discuss the proposal with your project adviser, as their approval will be essential—and to list your adviser’s name on the proposal. 

The proposal should be 1-2 pages long, approved by your adviser, and contain the following:

• Your name, and your adviser’s name
• Tentative list of topics that will be covered
• Main book(s) or other sources that will be used
• Timeline for the project
• Brief note about plan for the course (such as weekly meetings with homework / presentations, etc.)  
  Note that writing a paper at the end is required (but you can choose the topic later on). 

If you have any questions, please don’t hesitate to contact the Math DUS at math.dus@yale.edu .

Independent study cannot be counted toward undergraduate requirements of the B.S. or B.A. major.  

A sufficiently advanced independent study (taken for credit) might receive permission to be substituted for a graduate course required the M.S. portion of the B.S. / M.S. combined program. This must be approved by the DUS prior to the beginning of the independent study. 

In this case, the student would register under the graduate number, Math 970. By Yale rules, this is only possible after being accepted into the M.S. program, and no exceptions can be made. 

Technical note: Yale does not allow transfer credit for courses taken during high school (even college courses). You can only transfer college courses that you completed after graduating from high school. 

Yale has a limit of two transfer courses from other universities (except for transfer students, for whom the rules differ). 

Courses may be transferred for graduation credit, for university requirements such as QR, and / or for major credit. Your College Dean would be the best person to assist with transfer procedures. 

For counting a transfer course toward the math major, the course has to be reasonably equivalent to an existing Yale course, as far as topics taught and level of rigor. 

For the final approval, after the course is completed, the DUS will need the syllabus, detailed list of topics taught in the course, and copies of the exams. (The blank test is enough, if the graded exams are not returned.) 

Students are strongly advised to consult the DUS before enrolling in the course, with all materials available (including a list of topics, and a sample final exam). That way, the DUS can provide an estimate as to whether the course is likely to count or not. 

Generally speaking, the higher the Yale course number, the more strict the evaluation. In particular, it is rare that we would accept a level 300 core class from another university, outside of official Yale study abroad programs such as the Budapest semesters is mathematics or the Exeter programme. 

This depends on the situation. Typically, we require at least half the courses toward the major to be taken at Yale, but the DUS must decide individually in each case.

To see which of your courses may count, please contact the DUS at math.dus@yale.edu . We will need a copy of your transcript (unofficial is fine), the syllabus and detailed list of topics for each course, as well as the final exam. (If exams were not returned, and the instructor wishes to keep the test confidential, a copy can be sent directly to math.dus@yale.edu .)

A brief summary of the pure math options could be like this:

Math 4750, senior essay. It is a semester-long project done independently, with a math faculty adviser. At the end, students write an essay, and give a 30-minute presentation. The essay must contain some original work; some students incorporate original research, but this is not required. An insightful expositions into existing results also works, so long as the essay provides something new (e.g. some applications of the topics, or thoughtfully constructed examples). 

Math 4800 is the pure math senior seminar. In the seminar, students explore topics in an area chosen by the instructor, they read papers, present within the seminar, and attend presentations of the other students. The number of presentations, and whether they are individual or group projects, depend on the instructor and on enrollment. Pre-requisites likewise depend on the instructor; for some sections, Math 2250 + 2550 are sufficient, some require level 3000 course work. Topics of the senior seminar are typically announced below in March, for the upcoming year. 

Math 4810 description is very similar to Math 4800, except the topics are math + economics. Pre-requisites are Math 2250 + 2550. It is offered every Spring. 

Math 4820 is a new math education section, with 2250 + 2550 as pre-requisites. The main focus will be on developing presentation and teaching skills. Students will also read pedagogy papers, discuss classroom case studies, there will be sessions on active learning, inclusive teaching, public speaking, etc.  Enrollment is limited to 12 students, with deadline for applications in early April. 

Pure math major allows all of the above options to count toward the senior requirement. The course will count toward the required number of math courses level 200+. Math majors may only enroll in these courses for the purpose of fulfilling the senior requirement. 

Math + Economics major allows Math 4800 or Math 4810, or an Econ theory seminar.

Students are only permitted to enroll in Math 4800 or 4810 if they are using it for the purpose of fulfilling the senior requirement. 

Math + Economics majors can also complete their senior requirement with an Econ theory seminar - these will carry the designation “YC ECON: Theory Seminar” on YCS. 

Technical note 1: The major requires seven economics and five mathematics courses. If the senior requirement is completed with Math 4800 or Math 4810, this will also count as one of the five math courses. If the senior requirement is completed with an Econ theory seminar, this will also count as one of the seven Economics courses. 

Math + Philosophy major allows Math 4800, Math 4810, Math 4820 or a senior seminar in Philosophy approved for the student by the Philosophy DUS prior to the start of term.

For description of the options, see the first question in this section. 

All of the options develop skills that are valued by graduate schools, and that can be useful outside of Academia as well. The best choice to make is whichever one you find most interesting.

Math 4800 and 4810 run as a combination of a reading project and guided exploration experience, with presentations to other students in the seminar. Either is a great option for students who prefer a structured program where a mentor and reading projects to work on are already identified. It requires no research experience, and is accessible to any senior majoring in mathematics. 

Math 4750 requires more independent work. To enroll, the student must find a faculty adviser to sponsor the project. It is recommended to start looking for an adviser at least a semester in advance. Typically, the student will be expected to have an idea of a project they wish to work on, or an area of interest that is aligned with the adviser’s field of study, and allows the adviser to help the student identify a suitable problem to work on.

It is recommended that students who wish to complete the senior essay should get a bit of research or independent study experience prior to senior year. Some options include a summer REU, our own summer program SUMRY, applying for the Lewis summer research award, the Yale math directed reading program run by graduate students every semester, independent study through Math 4700, or working on an unofficial project with a faculty member. These will help you get the experience and research project ideas you will need to successfully complete a senior essay.

Math 4820 is focused on mathematics education at the college level, and includes a lot of practice with teaching. It is a good option for students who are interested in education and would like to develop or sharpen their teaching skills. 

Math 4800 Fall 2025 topics, Prof. Igor Frenkel

Pre-requisites: At least two level 3000 courses are required. 

The topics of the seminar will be chosen from the following two subjects, depending on the interests of the class: “Groups in Mathematics” or “Number Theory.”

The instructor will give a brief review of history, general facts, and various applications of the theory to different areas of Mathematics. Students will be able to choose a topic related to their interests and knowledge and prepare 1–3 lectures (depending on the size of the class) under the instructor’s guidance, including relevant literature. Below are a few examples of topics:

Groups in Mathematics
Since their introduction in the XIXth century, groups have played an increasingly important role in all areas of Mathematics: algebra, geometry, analysis. Group theory provides a unified picture of seemingly isolated concepts of Mathematics. It also has fundamental significance in Physics.

1. Reflection groups and regular solids
2. Hyperbolic geometry in dimensions 2 and 3 and their symmetry groups
3. Space-time and Lorentz group
4. Harmonic oscillator and Heisenberg group
5. Quaternions and octonions and their symmetry groups
6. Codes and lattices and their symmetry groups
7. Fourier series and their analogues on 2 and 3 dimensional spheres
8. Problems of linear algebra and representations of quivers
9. Haar measure, dynamics and geometry
10. Quantum groups and knot invariants
11. Combinatorics of trees and Thompson groups

Number Theory
Number theory is one of the oldest areas of Mathematics. It is still an important field of modern research, with connections to other areas of Mathematics and Physics. In the senior seminar, we will study some famous achievements in analytic, algebraic and geometric number theory.

1. Modular group
2. Modular functions
3. Theta-functions
4. Riemann zeta-function
5. Eisenstein series
6. P-adic numbers, adeles
7. Tate’s approach to zeta-functions
8. Roots of unity, abelian extensions
9. Elliptic curves over complex and rational numbers
10. Fermat’s theorem and  theory of ideals
11. Fermat’s theorem and elliptic curves

Plus, any other topic within the chosen general themes that students would like to propose. (Since essentially all results in pure mathematics and mathematical physics are related to certain types of groups or appear in number theory, in one way or another, students  are welcome to suggest their favorite topics).

These are samples of possible topics, and we’ll certainly not be able to cover all of them, but just a few, and not necessarily from this list. Each topic can be developed into a sequence of lectures by several students.

Math 4820 Fall 2025 topics, Miki

Pre-requisites: Math 2250 + 2550

Math 482 focuses on math education - see description above. Enrollment is limited to 12 students. Application link is available on the Canvas course site starting in mid-March, due April 19. 

Math 4800 Spring 2026 topics, Prof. Ro Wang

Pre-requisites: Math 2250 + 2550. Some experience with level 3000 courses is recommended but not required. 

Topic: Classical and modern dynamics

Description: we will focus on topics from the classical (classical mechanics) and modern (symbolic and hyperbolic dynamics) theories of dynamical systems. In plain English, we want to mathematically study how likely and how frequently does a (natural) phenomenon happens in a system. Students will choose a topic and prepare 1–3 lectures (depending on the size of the class).

Math 4810 Spring 2026, Prof. Dirk Bergemann (Economics) and Prof. Pei-Chu Su (Math)

Pre-requisites: Math 2250 + 2550

Optimal transport is a powerful mathematical theory at the interface between optimization and probability theory with far reaching applications. It defines a natural tool to study probability distributions in the many situations where they appear: data science, partial differential equations, statistics and economics. In this course we will read and present  the classical theory of optimal transport, efficient algorithms to compute it and economic applications such as matching, optimal pricing, auctions and others.

1. You will need a project to work on, keeping in mind that the final essay must contain some original work. This could be a new result, an extension of an old result, an application of an old result to some new mathematics, or a new proof of something known. An insightful exposition of existing results also works, provided that you explore some aspects of the topic on your own, and add some elements to what is already available (thoughtfully constructed examples, for instance). 
    
2. You need to find a math faculty adviser who will sponsor the essay. It is recommended that you start looking during the previous semester, so that everything is ready to start at the beginning of term (some students even start their project a semester early, though you can only enroll in Math 4750 once, for the semester when you wish to complete the essay). You may also have a secondary adviser in another field, if relevant. 

3. At least three days before pre-regitration ends the previous semester, you must submit your initial proposal for the project to math.dus@yale.edu . If you wish to make adjustments after that, the final version is due at least three days before the end of add / drop period.  Please be sure to discuss the proposal with your project adviser, as their approval will be essential—and to list your adviser’s name on the proposal. 

   The proposal should be 1-2 pages long, approved by your adviser, and contain the following:

   1. Your name, and your adviser’s name
   2. Background reading and topics that you plan to learn
   3. Topics you plan to investigate for the project 
   4. Books, papers, and / or other sources you anticipate using
   5. Intended timeline for the project
       
4. During the semester, you will be working on your project, and meeting with your adviser for an hour every week. During each meeting, you will need to present to the adviser the work that you have done the previous week. (Presenting your work is one of the skills that Math 475 helps to (further) develop, and it helps the adviser to guide your project, suggest resources to look at, etc.) 

5. By the last day of classes, you will need to submit your essay, with length of 20-25 double space pages, to your adviser, with cc to the Math Registrar. The essay will be shared with the committee (and must be shared with them at least a week before your presentation takes place). 

   (If your essay is turning out to be longer than 25 pages, you could move some parts to an appendix, for example background information that does not contain your own work, or detailed notes from calculations. The total length, counting this appendix, should not exceed 50 pages.) 

6. Two weeks before the end of term, you should work with your math adviser to schedule your final presentation, to take place at the end of term (typically during reading or finals week). The presentation is given to a committee of two mathematics faculty, one of whom is your project adviser.  The other committee member is selected by your adviser and the DUS’es. The presentation itself is 30 minutes long, followed by up to 30 minutes of questions and conversation with the committee. 

7. The grade for Math 4750 is based on 

   1. Your work during the semester (as reported by your adviser)
   2. your paper submission at the end
   3. your presentation and Q&A with the committee.  

   For the talk, you can use any format you wish: you can give a blackboard talk, or use slides (beamer, powerpoint, etc.), or a combination of these. Recently, most presentations have used slides to some extent, because the time is relatively short, and the audience doesn’t have to take detailed notes. But your format is up to you.  

Tips for using slides

• The typical purpose of slides is to supplement your presentation. They do not have to deliver the entire detailed content (nor would the audience be able to read it that fast). 
• The recommended slide rate is about 1 per minute. 
• Present only one idea per slide.
• Keep the slide relatively sparse, with main phrases / bullet points only, so your audience has a chance to absorb it real time while listening to your presentation. (Slides full of text are impossible for the audience to read, and so they are rarely helpful.) 
• As noted above, it’s good to try your presentation on someone who doesn’t know your project, and see if they are able to follow the ideas and absorb the slides with your current content and rate of going through them. 

You cannot enroll in Math 4750 twice. You should enroll during the semester that you are planning to complete your essay and your oral presentation (otherwise you will need to apply for a temporary incomplete, and finish your work the following semester). 

Here are descriptions of a few sample projects, posted with permission from the students: 

• Sonali Durham ‘20: Nesting rules for political redistricting: methods for sampling matchings and tripling.
• Sanelma Heinonen ‘20: Discrete convexity with applications to maximizing user satisfaction in bike sharing systems.
• Noah Kravitz ‘20: Lonely runner conjecture, and Noah’s advice for writing a research-based senior essay.
• Claire Thompson ‘19: Binary irreducible quadratic-residue codes and the Good code problem.

Computer science + mathematics majors can enroll either in MATH 4750 or in CPSC 4900. Mathematics + physics majors must enroll in PHYS 471 or 472. For joint majors, the project must be on a topic acceptable to both departments.

For students in the joint major, the additional requirement for their chosen course is that the project proposal must include a specific description of how the projects uses topics from both majors, and it must be approved by DUS’es in both departments early in the semester.  The deadline in CPSC 490 is typically on the third Thursday of classes. For students in Phys 4710 or 4720, we set the same deadline for receiving the proposal in math. You can send the proposal to math.dus@yale.edu .

As for Fall 2024, students are no longer required to give an oral presentation to the Math department on the mathematical aspect of their project. 

No. Senior essay must be independent, you cannot do a joint project with others. Your essay may fit into a bigger project that other people are working on, but you must perform and write up work that you have done yourself.

Nomination for distinction in any major requires 1. Grade of A or A- on the senior requirement, and 2. Grades of A / A- in three quarters of courses within the major. 

For distinction in Mathematics, students are also required to complete at least one course in each of the three core areas. 

For distinction in Econ + Math, students must also write the optional essay in Economics, with a grade of A or A-. 

Note that the percentage-of-A’s calculation is based on all courses you have taken in the major, as well as all courses that routinely count toward the major. In other words, if you have taken more than the necessary number of courses, we are required to count them all, rather than selecting the ones with best grades.

Here are some of the common situations with degree audit:

1. For some of the requirements, it only recognizes undergraduate course numbers. 

Solution: If your graduate course is level 5000-5990, then it may be applied toward the undergraduate degree. You will need to e-mail math.dus@yale.edu and we can add it on degree audit for you. Courses level 6000+ may not be applied toward the major, except for the graduate course requirement of the intensive degree and the graduate portion of the B.S./M.S. degree. 

2. Degree audit will sometimes list in-progress courses for requirements that are already completed. (E.g. if you have already completed the algebra core area with Math 3500, and then you enroll in Math 3700, degree audit might list the core area as “in progress” with Math 3700, instead of listing it as “done” with Math 3500.)

Solution: According to the Registrar, there isn’t any way to make degree audit prioritize completed courses. If you’d like confirmation as to the requirements your existing courses satisfy, e-mail math.dus@yale.edu , we’d be happy to check for you. 

3. Degree audit only recognizes math numbers, so if you enroll (say) in S&DS 2410, it may not get applied to your math requirements. 

Solution: If you wish to count a course toward math, it’s best to enroll in it using the math number. If you enroll under another number, you can use the add/drop form before the last day of classes, to switch to the math number. If you’ve already completed the course, e-mail math.dus@yale.edu and we will help you sort it out. 

General note: These peculiarities may be a bit confusing. If you have questions about what degree audit says, or encounter some issue with it that isn’t mentioned above, e-mail math.dus@yale.edu to ask about it. 

The default system in STEM is that the DUS advises all the majors. In our case, that is typically well over 300 math (including joint-math) majors. 

To make sure that all math majors have a chance for meaningful conversations with their advisers, we assign individual faculty advisers to everyone. The main benefit is that each adviser has only 15-20 students, as opposed to 300. 

Most of our advisers are dedicated to a single major (e.g. pure math, or Econ + Math). 

Extra note: The DUS will continue to be available to everyone. Our office hours are posted on the math DUS site. You should still see us with technical questions about requirements of the major, for transfer credit or other types of exceptions, and for anything else that you wish or need, for example if you have trouble reaching your designated adviser for any reason.  We are here to assist you, don’t hesitate to come see us :)

Timing: Adviser lottery is usually run before the start of each semester; that is, late December / early January, and early August. Assignments are given to all students who are newly on the math major list at that time.

Extra note: First year advising is done through the colleges, and we do not assign faculty advisers until just before the second year. In the meantime, you are very welcome to consult the DUS about the mathematics major - we will be happy to assist. 

Yes, we have an unofficial mailing list, created for students who are interested in getting messages from the math DUS (about events, job openings within and outside of the department, summer programs, news from the department, and other similar information). All students are welcome to sign up, whether or not they are majoring (or thinking about majoring) in math. The link is 
https://subscribe.yale.edu/browse?search=math+dus , 
and you can use it to subscribe or unsubscribe any time you wish. Be sure to use the “Yale NetID login” (guest e-mails are not permitted for this list). 

Official math major information is sent to all current majors, independently of the DUS newslist. The newslist was partly created for reaching students who are interested in news from us but are majoring in something else or have not declared a major yet. Partly because we try to keep the official list for essential information only, and avoid sending to everyone unofficial messages that many math majors might not be interested in receiving. The unofficial list is there so you can sign up to receive them if you like :)

(Extra note: Only undergraduate students will receive messages that are sent to the DUS newslist.)

Undergraduate research and independent study opportunities do exist, depending on your interest and that of available faculty. During the summer the department organizes REU opportunities for interested students, and runs its own summer research program called SUMRY. The department also awards the John Alan Lewis prize each spring, which provides a stipend for independent work during the summer. 

During the academic year, our graduate students organize a directed reading program, where students can explore topics and work on projects with a graduate student mentor. Applications to the DRP are typically due at the beginning of each semester. 

We also offer Math 4700, independent study, which allows for one opportunity to do a more extensive directed reading project with a faculty member. More information about Math 4700 is available above, under “How does Math 4700 work?” 

Students can also approach a faculty member to ask about mentoring an informal research project during the academic year. This tends to be more independent work, on a project that’s proposed by the student, and students usually select it after they have some research experience from a more structured program such as a summer REU or the Yale DRP. If you have a project in mind, with or without prior research experience, don’t hesitate to ask! 

Our summer research program is called SUMRY and you can learn more about it on the program website. We also award the John Alan Lewis prize each spring, which provides a stipend for independent work during the summer. 

The Yale Undergraduate Math Society (YUMS) hosts a number of events for undergraduate students, including colloquia, study sessions, game nights, and panels about the math major and summer opportunities.  Check out https://yums.sites.yale.edu for more information. You can also take a look at their recent seminar recordings, and visit our contact information site to sign up for their weekly newsletter. 

Dimensions seeks to inspire, celebrate and empower women in mathematics at Yale. To help facilitate a community of Yale women in math, Dimensions offers a mentorship program, pairing graduate students, upper and lower class people based off interests, as well as workshops, speaker events and organized meetings with professors. We hope to create an encouraging space for women and other gendered minorities to pursue their interests in the under represented fields of mathematics.  All students are welcome to join Dimensions as well as attend all events sponsored by Dimensions. Please visit us at our website or our Istagram page. 

There are four regular positions that we have available:

1. Undergraduate learning assistants (ULA’s). Currently, we have ULA’s in Math 1030-1080, 1100 / 1110, 2250, 2260, 2550, 2700, 3050, 3500, 3700. The position is for up to ten hours per week, and we expect students will work approximately 8 hours per week. ULA’s typically run sessions with prepared content, as well as walk-in study groups. They may also help with grading quizzes or exams to some extent, or perform other duties. As of Fall 2025, the pay is $18.50 per hour. 

2. Peer tutors. These positions are available in the larger courses numbered between 1120 and 2440. Peer tutors hold four walk-in office hours a week, in blocks of two hours at a time. The position is for maximum of 6 hours a week (this includes time for prepararation, any extra time spent in the sessions, and time for a small administrative component that takes about 15 minutes a week). As of Fall 2025, the pay is $20.50 / hr. 

Our applications for peer tutors and ULA positions are typically due before Spring break, for the following academic year. When the application opens, we send an e-mail to “Math DUS news” - if you would like to sign up for the list, the link is listed in the “unofficial mailing list” question earlier in this FAQ. 

We rarely have open positions in the middle of the year (that is, for the Spring term only); if it happens, a note will be sent to the DUS newslist. 

The application process has two rounds. After the written applications are collected, interview invitations are sent to selected candidates. 

Tutors who are hired will go through training sessions just before the beginning of the Fall semester (one session is with the department, for ULA’s there is a second training session with the CTL). 

A few rules to mention:

(a) Yale does not permit first-year students to work as peer tutors or ULA’s (but you can apply during the Spring of your first year, for Fall positions). 

(b) Only students who have already completed at least one math course at Yale are eligible to apply. That is, you may apply in March only if you have completed a Yale math class the previous Fall or earlier. 

(c) The CTL does not typically permit students to hold two simultaneous ULA / peer tutor / grader positions. In particular, if you get a job with us as a peer tutor or ULA, you will not be eligible to also work as a grader. 

(d) The following coursework is required, by the time the job is to start:

• Tutoring Math 1100/1110 requires completion of Math 1150 or higher.
• Tutoring Math 1120 or 1150 requires completion of Math 1200. 
• Tutoring Math 1160 or 1210 requires completion of those specific courses (as they have specialized curriculum that is not taught in other math classes). Typically we would also ask for completion of a higher level course in the same area (e.g. to tutor for Math 1160, we ask for completion of Math 1200 or 1210).   
• Tutoring Math 1180 requires completion of Math 1200 and linear algebra (Math 2220/2250/2260), or Math 1180 and at least one higher level math course. 
• Whenever feasible, tutoring for courses numbered 1200 and above requires completion of at least one course beyond the one being tutored, preferably in the same area. For example, with Math 2250, preference is given to students who have completed Math 3400 or 3500. For tutoring Math 2550, we prefer at least one level 3000 analysis course. For tutoring Math 3500, we ask for Math 3700. (These are needed by the time the job starts; e.g. if you are enrolled in Math 3700 when applications open in the Spring, you can apply for the Math 3500 position to start in the Fall.) 

3. Graders. These positions are available in nearly all undergraduate math courses.

Applications for the Fall typically open toward the end of the preceding Spring term. Applications for Spring tend to be due in December. A notice will be sent to the DUS newslist when grading application opens. 

Grading positions are for up to 5 hours per week over 15 weeks (i.e. 75 hours total per semester), which translates to approximately 6.5 - 7.5 hours per problem set. As of  Fall 2025, the pay is $16.50 / hr. 

For more information, please reach out to Meghan Anderson at first.last@yale.edu . 

Rules:

• Every student in their second year or above is eligible to applly for grading any math course that they have completed (at Yale or elsewhere).  
• We are not able to hire students to grade if they are already working as peer tutors or ULA’s.  (Offers for peer tutor and ULA positions are always sent out first, during the two main hiring times in late Fall and Spring.)