Math major and advanced courses FAQ

For information about placement exam and calculus, please see our other FAQ

If you have questions that are not addressed here, e-mail the DUS.

Introductory and advanced courses

Requirements of the major

Intensive major, B.S. / M.S. degree

Senior requirement

Other questions

What courses should I take after integral calculus, if I’m considering a math major?

There are two main entry sequences into the major.  The first is Math 230+231, a two-term course with an integrated treatment of linear algebra and vector calculus. This is a demanding but rewarding course for students with a very strong interest and background. The second is Math 120+225+250, covering multivariable calculus, linear algebra with proofs, and vector calculus (generalizing calculus to n-dimensions, with proofs).  It is possible to replace Math 225 with Math 222 (linear algebra with applications), but it is not recommended for students who wish to continue with proof-based courses, such as Math 250. 

Can I skip Math 120, if I took multivariable calculus in high school?

If you are considering a math or a combined math major, you should speak with the math DUS. If they agree that you are ready to take classes beyond multivariable calculus, they can give you permission to substitute a higher level course for Math 120 in requirements of the major (note that this course will then not count towards the required ten courses).

If you are considering another major, you must speak with the DUS of that major to ask whether something similar may be possible. 

If you are interested in taking proof-based math courses, you may also consider taking Math 230+231, as an alternative to calculus and linear algebra. Most students benefit from taking this sequence, even if they have already seen multivariable calculus.

Note that completing the sequence Math 230 + 231 satisfies the multivariable calculus prerequisite for math and joint math majors (and it counts as two credits toward level courses level 200+). 

Can I skip Math 230+231?

Math 230+231 is a very sophisticated, proof-based course. It is extremely rare that an incoming student cannot benefit from taking it. If you believe that you have all the skills and knowledge that is taught in Math 230+231, please speak with the mathematics DUS.

Can I skip other required courses?

As a rule, the answer is “no”. Courses required for the major must be completed. In rare cases where a student already has knowledge of the material and the skills taught in a particular required course, DUS may grant an option to substitute a higher level course in the same area. Please be sure to discuss this with the DUS ahead of time.

What is the difference between Math 120 and Math 250?

Math 120 is “multivariable calculus” and Math 250 is “vector calculus”. What is the difference? Math 120 focuses on situations where “multi” really means 2 or 3 – that means it leans heavily on geometric intuition, and is strongly grounded in geometric applications in engineering and the sciences. Math 250 generalizes this to the setting of n dimensions, or variables, where n can be 3, 10, or 450,000. In order to do this, linear algebra must be brought in as a tool to manage the computations and to clarify what is conceptually going on – that’s why Math 222 or 225 is a prerequisite to Math 250. The theorems of Green, Gauss and Stokes, the beautiful integral equalities that are the capstone of Math 120, are generalized in Math 250 to a single master theorem (still called Stokes’ theorem) which applies in any dimension. Don’t think that 450,000 dimensions means the subject is not practical: any large system, such as the economy or the weather, can easily involve that many variables.

What is the difference between Math 222 and Math 225?

Both courses cover linear algebra, but Math 222 focuses more on computational techniques and applications, while Math 225 emphasizes mathematical proofs and a more conceptual approach. Math 225 is recommended for students who wish to take further proof-based mathematics courses (in particular, all math majors).

What is the difference between Math 230 and Math 250?

Math 230+231 is a two-term course with an integrated treatment of linear algebra and vector calculus. This is a demanding but rewarding course for students with a very strong interest and background. Math 250 is the third semester of the sequence 120-225-250 (or 120-222-250), and it covers just the vector calculus.

If I enroll in Math 230 and find that it is not the right class for me, can I switch into another course?

If it is before Midterm, you can switch from Math 230 into Math 120. You must speak with instructors of both courses to ensure a smooth transition, find out what work you will need to make up in Math 120 etc.  Please see the calculus FAQ for further information. If you took multivariable calculus in high school, you may also be able to switch into Math 222 or 225. If your intended / potential major requires Math 120, you will first need to speak with the DUS of that major to see if it is possible to satisfy the requirement in another way (for example by substituting a higher level course).

Can I simultaneously count courses from both intro sequences toward the major?

The short answer is “no”, because the sequences are considered to be parallel. If you complete Math 230 + 231, you cannot count Math 222, 225, or 250 toward the major. If you complete Math 120 + 222/5 + 250, you cannot also count 230 or 231 toward the major.

This becomes more complicated if you decide to switch from the middle of one sequence to the other; for example, if you complete 230 but decide not to continue with 231. In this case, please see the DUS, and we will help you figure out a way to satisfy the introductory sequence, by combining courses from the two sequences. (A typical scenario would be to substitute Math 230 for Math 120 (note that this effectively changes 230 to a level 100 course, not counting toward the required 10) and then complete Math 222/5 and Math 250.)

Can I take Math 301 or 300 without Math 231 or 250?

This is not recommended, but if your previous background is sufficiently strong you may try to obtain permission from the instructor.

Can I take Math 310 without Math 301?


Can I take Math 310 without Math 250/231?

This is not a good idea unless your background is quite strong.

I don’t want to be a math major but I want to know what mathematics is about in some deeper way. What should I take?

Not necessarily more calculus. There are several of courses that either do not require or do not emphasize calculus, and offer a window into mathematical thinking, for example: • Math 244, Discrete Math: (Math 115 recommended) the structure of finite sets, graphs, trees, and enumeration. • Math 270, Set Theory: (Math 120 is a prerequisite) The foundational underpinnings of mathematics, through the study of infinite sets.

Is there a good math course that fulfills the QR requirements even if I haven’t taken any calculus?

Try Math 107 or Math 108.

Requirements of the major 

Where can I find the details of math major requirements?

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

A roadmap for the math major can be found on the major roadmaps site:

For a double major, how much overlap can there be in terms of courses?

At most two courses can be counted simultaneously toward both majors. However, you may count the attributes from a math course toward the math major, even if you are counting the course itself toward the other major  (you just cannot count the course toward the required 10 math courses level 200+, if you already have two overlapping courses there). 

Extra note: Math 120 is a pre-requisite for math, and pre-requisites do not count toward the overlap. So if your second major requires Math 120, you would be able to count it as a pre-requisite in Math as well, and still overlap two level 200+ courses between the two majors. 

Can a course taken Cr/D/F count toward the math major?


Can I take a graduate course - and what number should I use, if it’s cross-listed?

If you have the pre-requisites for a graduate course, you may certainly enroll. You should consider starting with courses that are cross-listed as undergraduate (with a 300 number) and graduate (with a 500 number). The cross-listed courses tend to be more accessible for undergraduates, and they carry attributes (which pure graduate courses typically do not (see below). 

Generally speaking, when taking a cross-listed course, undergraduates should use the undergraduate number, unless they are planning to apply the graduate version toward the intensive major or B.S. / M.S. degree requirements. 

Can I take a graduate course for Cr/D/F?

No. (This has nothing to do with the math major, it’s just not possible.)

Can a graduate math course count toward the undergraduate degree?

Yes. 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 attributes, either category or core area. The one and only exception is Math 544, which counts toward Geometry / Topology core area.

Undergraduate courses that are cross-listed as graduate do carry attributes.

Can a course be simultaneously counted towards two different categories?


Can a course be simultaneously counted towards a category and toward a core area?


Can a course from another department be substituted as a general elective for a math course in the requirements?

Any course that has a Math number counts towards the requirement (whether you register for it with the math number or not).

• 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 in the math department.

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 one of these courses do not carry core area or category designations, with the exception of PHIL 267 and 427 (logic). 

If you have a question about a course that is not on the list, please e-mail the DUS.

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

  • AMTH: 437, 561
  • CPSC 267, 365, 366, 427, 440, 468, 562, 662
  • ECON 135 (as an alternative to Math 241, we will not count both), same for ECON 136
  • ECON 351
  • PHIL 267, 427
  • S&DS 351, 364, 410, 631

Currently not approved:

  • CPSC: 201*, 202, 467*
  • ECON 530, 531
  • EENG 200, 202
  • ENAS: 194
  • OPRS: 235
  • PHIL: 268
  • PHYS 460
  • S&DS: 230, 238,

Special cases: 

  • AMTH 364 from Spring 2019 counts for pure math, and for math+cs majors
  • CPSC 640 from Spring 2019 counts for pure math, and for math+cs major
  • S&DS 669 from Spring 2019 counts for pure math, and for math+cs major

*Extra note: CPSC 201 and 467 are counted for everyone who took them before or during Fall 2018.

*Another extra note: As of Spring 2019, the DUS of CPSC allowed S&DS 365 to replace the requirement of taking one of CPSC 440, 462, 465, 468, 469. If you wish to explore this option, please be sure to check with the current CPSC DUS first. 

What can be counted as the physical science course for the B.S. requirement?

If a course has a Math number, it cannot be counted towards this requirement (since the requirement is meant to enhance the mathematics major with science courses that are outside of the B.A. portion of the program). 

Below are courses that are typically approved to satisfy this requirement. If you wish to find out about a course that is not on the list, please write to the DUS.

  • ASTR 418, 420, 430
  • CHEM: 328, 333, 470
  • PHYS: 342, 344, 401, 402, 410, 420, 428, 430, 440, 441

​Currently NOT approved

  • ASTR 465
  • PHYS 343
  • All courses numbered below level 300

Can independent study (Math 470) be counted toward requirements of the major?

Independent study cannot be counted toward requirements of the B.S. or B.A. major.  A sufficiently advanced independent study (taken for credit) can, in some cases and with DUS permission, be substituted for a graduate course required for the intensive major or for the M.S. portion of the B.S. / M.S. combined program.

Do I have to take Math 301? 350? 310?

The gateways to the core areas of mathematics are provided by these courses: Real Analysis (301), Algebra (350) and Complex Analysis (310). They are beautiful subjects and every math major is strongly encouraged to take them and continue upwards with the sequences that they begin. All math majors are required to take courses in 2 out of 3 of the core areas. Intensive majors must take all three.

Can transfer students count math courses taken outside Yale (which are accepted for transfer credit) toward the math major?

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.

Intensive major, B.S. / M.S. degree

For the intensive major, do the two graduate courses also count toward the required ten? 

Yes. In other words, the total is still 10 math courses level 200+, same as the regular major, but two of the ten have to be graduate courses.

Do cross-listed courses count as graduate, for purpose of the intensive major? 

Course cross-listed as both undergraduate and graduate can be counted toward the graduate portion of the requirement. For example, if you take Math 380 = Math 500, it will count as a graduate course.

Where can I find general information about combined B.S. / M.S. degrees?

Where can I find the math B.S./M.S. degree requirements?

Where can I find detailed information about the qualifying exam required for the M.S. degree? 

One of the requirements of the M.S. degree is passing a written qualifying examination in algebra, analysis, or topology. Examinations in all three subjects are offered toward the end of the Fall semester. 

You will need to choose one (and only one) of the three subjects, and sign up for the examination. If you do not pass, you may try one more time, in the same subject, the next time the examination is offered (typically, this would be the following Fall semester, though some subjects may occasionally be offered in the Spring as well). 

Syllabus for each of the exam is posted at . 

For dates of the examinations, and to see copies of past papers, please see the Math Registrar, in DL 438.  

For the B.S. / M.S. combined degree, how many courses can be counted toward both?

At most two courses can be counted simultaneously toward the B.S. and the M.S. portions of the requirements. Extra note: if you are also doing a double major, you are only allowed one set of overlaps. For example, if you are double majoring and math and physics, and also doing the B.S. / M.S. in math, you can either (a) overlap one or two courses between math and phyics, or (b) overlap one or two courses between B.S. and M.S. in math, but not both. 

What do I need to do to apply for the B.S. / M.S. combined degree?

Proposals are due at the Dean’s office by the last day of classes of your fifth term at Yale. The proposal is meant to show that you are close to finishing the B.S. requirements, and to provide a tentative plan for completing the M.S. requirements. As of October 2018, there is also a form to fill out, available online at:

The relevant past, current and future courses are to be listed on the form (rather than being listed within the proposal).

For the B.S. / M.S. combined degree, does it matter whether I have taken a particular course with the undergraduate or graduate number?

You have to enroll with the undergraduate number, until you are accepted into the combined program. After that, you will have to petition to have the relevant courses converted to the graduate version. The petition is called  ”Simultaneous Degree Program Course Conversion Request” and it is available on the Registrar’s site .

Senior requirement

Are all sections of 480 the same? How do I decide which to take?

Every year, one section of the senior seminar, 480, is dedicated to topics of interest to Econ/Math majors. The others are usually on a more pure-math subject, and the precise plan is worked out between the instructor and the participants in the beginning of the semester. Contact the instructor for details, or check the department web page. 

Note that all seniors are welcome to choose any section that they like; the section dedicated to Econ+Math topics is open to pure math majors, and likewise Econ+Math majors are free to select one of the other sections if they wish. 

NEW: For the academic year 2019-20, the topics will be:

  • Fall 2019, taught by Professor Van Vu: probabilistic combinatorics. 
    Our main source of material is  the book “The probabilistic method” by Alon and Spencer. 
    The main content of the course is: probabilistic methods to prove existence of delicate objects, randomized algorithms, and random discrete structures (such as random graphs and random matrices).
    Beside the book above, we will also add several research papers and monographs. 
  • Spring 2020, section taught by Professor Van Vu: Applications of harmonic analysis.
    This section will focus on the applications of harmonic analysis in number theory and combinatorics. 
  • Spring 2020, section taught by Dr. Ofir Lindenbaum (this will be the designated section of special interest to Economics + Mathematics majors).
    This seminar will span themes that are of interest to both economists and mathematicians. The themes center around social networks. Here, we will cover the underlying theory of networks and game theory and examine a variety of applications. 
    Presentations are mainly based on the textbook: 
    “Networks, Crowds, and Markets: Reasoning About a Highly Connected World” (2010, Cambridge University Press) by D. Easley and J. Kleinberg, which is available online for free. We will supplement it by other books and articles as needed.
    List of chapters:
    1. Graph Theory and Social Networks
    2. Game Theory
    3. Markets and Strategic Interaction in Networks 
    4. Information Networks and the World Wide Web
    5. Network Dynamics: Population Models
    6. Network Dynamics: Structural Models
    7. Institutions and Aggregate Behavior

Do Math 475 (senior essay) and Math 480 (senior seminar) count as math electives?

Yes, though you may only count one of those. 

Should I choose Math 480 or Math 475?

Both courses will fulfill the senior requirement.

Most students choose Math 480, which runs as a combination of a reading project and guided research experience, with presentations to other students in the seminar. It requires no prior preparation, and is accessible to any senior majoring in mathematics.

To enroll in Math 475, the student must find a faculty adviser to sponsor the project. 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 them 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 experience prior to senior year. Some options include a summer REU, the Yale math directed reading program run by graduate students, or working on a 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.

How does Math 475 work?

1. You need to find a 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 475 once, for the semester when you wish to complete the essay).

2. A month before the end of term you need to e-mail the DUS in order to schedule your final presentation, to take place at the end of term (we usually schedule them for last week of classes and reading week). You will also need to submit a 20 - 25 page summary of your work. 

3. The presentation is given to a committee of two mathematics faculty, who are chosen by the DUS. The presentation itself is 30 minutes long, followed by questions and conversation with the committee. The committee’s evaluation will contribute to your grade for the course.  

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. 

If I plan to spend all year working on my senior essay, when should I enroll in Math 475?

You cannot enroll in Math 475 twice. You should enroll during the semester that you are planning to complete your essay and your oral presentation.

How does senior project work for computer science + mathematics, and mathematics + physics majors?

1. Computer science + mathematics majors typically enroll in CPSC 490, and mathematics + physics majors enroll in PHYS 471 or 472, in order to complete their senior project. For joint majors, the project must be on a topic acceptable to both departments; in particular, it must have sufficient mathematical content to satisfy the mathematics portion of the senior requirement.

2. The project proposal must contain an explicit description of the mathematical component, and it must be approved by both departments early in the semester. 

3. At the end of the semester, you will need to give an oral presentation to a committee of two mathematics faculty chosen by the DUS. The presentation must focus on the mathematical aspects of your senior project. It will be 15 minutes long, followed by 10 minutes of questions and conversation with the committee. A passing grade from the committee will satisfy the mathematics portion of the senior requirement.  

In Spring 2019, the presentations will be on Monday, April 27. 

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. 

Other questions

How does advising work in math?

When you declare a math major, the DUS (of both departments, for joint majors) automatically become your official advisers. We encourage you to declare early (it is not binding) so that we know you are interested in the major, can assist you with your progress, contact you with relevant information (job opportunities, summer programs, new courses, etc.)

Before each semester begins, adviser lottery is run for all newly declared majors. Thorugh the lottery, an additional adviser is assigned to you - an experienced faculty member who will be available to you until graduation. In particular, they will meet with you at the beginning of term to talk about courses and to sign your schedule.

This additional-adviser-system was put in place so that each adviser would have a smaller group of advisees, which gives more opportunity for individual conversations about classes, summer programs, applying for graduate school, or anything else you wish to discuss. 

Note that the advisers do not necessarily have full knowledge of every detail of math major requirements, and are not meant to - with such questions, students are still meant to see the DUS.

Our office hours are posted on the math DUS site. As noted above, you should still see us with technical questions about requirements of the major, and you are welcome to see us with other questions as well, any time that you wish - or if you cannot reach your adviser, or if you are interested in math courses but haven’t declared math as a major, or declared recently and have no adviser assigned through the lottery yet, etc. We are here to assist you, don’t hesitate to come see us :)

Does math have a peer mentoring program?

The math department has established an informal peer mentoring system, where junior and senior mathematics majors provide advice and information about the major. They can answer questions about what it’s like to major in mathematics, about our classes, job and research opportunities, summer programs, and so on.

More information about the program and the current mentors can be found at .

Is there an unofficial math mailing list?

We do 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
and you can use it to subscribe or unsubscribe any time you wish.

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

Can I do research with math department faculty?

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 stipends for independent work during the summer. Contact the DUS, or check the website for more information.

Does Yale have a summer research program?

Our summer research program is called SUMRY, and you can find its website at . Applications for the summer 2020 program are open until February 15.

Can I take graduate courses?

Yes, if you have the appropriate background. You should obtain the approval of the instructor and of the Director of Graduate Studies, and make sure you have agreed ahead of time on what you will be required to do and how you will be graded. This is not necessary for those graduate courses that are cross-listed with undergraduate courses (315, 380, 381, 320, 325).

Is there an undergraduate math organization?

The Yale Undergraduate Math Society 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 for more information.

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 are welcome to public events sponsored by Dimensions. To subscribe to our panlist and stay updated on events, please email

What jobs are available in the Math department?

There are four regular positions that we have available:

1. Undergraduate learning assistants (ULA’s). Currently, we have ULA’s in Math 110 / 111, 230 /  231, and 350. In Math 110 / 111, ULA’s run weekly workshops for groups of students, with content prepared by the instructor. In Math 230 / 231, they run weekly study group sessions. In Math 350, each ULA runs a weekly proof writing workshop with prepared content, and a weekly study group session. The position is for a maximum of 10 hours a week. 

2. Peer tutors. These positions are available in the larger courses numbered between 112 and 370. 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. 

Our main hiring process for both of the above positions typically takes place around 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. 

3. Graders. These positions are available in nearly all math courses. Application is usually available on SEO before the start of each semester. These positions are for a maximum of 10 hours a week. For more information, send a message to John Hall at

4. Private tutors. Students who need additional assistance with a course can request a private tutor, who meets with them once or twice a week for the rest of the semester, at a time that they arrange with each other.

The application for calculus private tutoring positions is posted on SEO before the start of every semester. For more information, send a message to John Hall at . There is no set number of hours for these positions, it depends on how many students request a tutor, and how many students a particular tutor wants to work with. 

Private tutors for courses level 200 and above are hired through the CTL. You can find more information about the position, and an application form, at .