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**Applied Mathematics Major: FAQ**

Welcome to Applied Math at Yale! This FAQ is designed to serve as a one-stop-shop for students interested in the undergraduate Applied Math major: from prospective Applied Math majors all the way to seniors completing their final requirements. If you are a graduate student, please instead consult the section on the graduate program in Applied Math.

If you have a question about the Applied Math major, chances are it is answered here. Please read the FAQ fully before checking with the DUS for information.

If you have further questions, contact the Director of Undergraduate Studies (DUS), John Wettlaufer. If you have information you’d like added to the FAQ, contact the DSAC.

The table of contents below is clickable so you can jump straight to the part you’re looking for:

What is the Applied Math mailing list, and how do I join?

I am a first-year interested in Applied Math. What should I do to learn more about the major?

I am a sophomore thinking about majoring in Applied Math. What should I do to prepare for the major?

Who is the DUS, and what does he do?

How does one arrange a meeting with the DUS?

How should I get my schedule signed?

Requirements of the Applied Math major

What courses do I need to take to receive an Applied Math degree?

What is the Applied Math spreadsheet?

What is the Applied Math checklist?

Does your concentration appear on your transcript or diploma?

What are the requirements for concentration courses?

Can I take any of my major courses Credit/D/Fail?

How can I earn distinction in the Applied Math major?

Should I take S&DS 238 or S&DS 241?

Do non-mathematical courses in quantitative departments count toward the Applied Math major?

Should I take CPSC 202 or MATH 244?

If I’m interested in algorithms, should I take CPSC 365 or 366?

What’s the new data science major?

What’s the new data science certificate?

Will my schedule satisfy the requirements of a double major in Applied Math and another major?

Is there a way to receive a B.S. in Applied Mathematics while only fulfilling the B.A. requirements?

What is the senior requirement for the Applied Math major?

What are the mathematical requirements for the senior thesis?

How should I find a thesis advisor?

When should I do my senior project?

What are the deliverables and requirements for AMTH 491?

The Departmental Student Advisory Committee (DSAC)

What is the peer mentoring program, and how can I take advantage of peer mentoring opportunities?

**Prospective Students**

**What is the Applied Math mailing list, and how do I join?**

If you are an Applied Math major or are thinking of becoming one (you can always unsubscribe if you pick another major), you should be on our mailing list. You can sign up here. We will use this list to let you know about opportunities for jobs and internships, and other important information for the major.

**I am a first-year interested in Applied Math. What should I do to learn more about the major?**

**Familiarize yourself with the requirements of the major.** The outline of the general major requirements is available in the YCPS (prerequisites, core, breadth, concentration, senior project), but the most comprehensive listing of courses and concentrations for the major is available on the Applied Math spreadsheet. Learn more about these courses to find out what interests you, and read reviews from students who have taken these courses in the past on OCE or CourseTable.

**Read through this FAQ** fully to familiarize yourself with the various options and requirements of the major.

**Create a copy of the ****Applied Math checklist** for yourself to see how you would balance the major’s requirements over four years at Yale. Fill out all the requirements, even those you haven’t taken yet, to start planning and decide whether the major appeals to you. Share it with the DUS if/when you get serious about the major and want to meet with him.

**Take advantage of shopping period** to attend the first one or two lectures of courses you might take in future years, even if you don’t plan to take them now. Don’t bother with adding it to your worksheet or acquiring books — just show up to see how you like it. During the first week of shopping period, that’s completely okay and expected!

**Join the Applied Math email list**, using this link. You can always unsubscribe later if you decide to major in something else. If you are exploring other majors, sign up for their email lists, too.

**Meet other Applied Math majors** and learn more about the major from your peers, at events put on by the DSAC. These events will be announced on the email list — see above.

**Attend a peer mentoring session.** Any student interested in the Applied Math major can attend; you don’t need to be declared. These are helpful ways to learn more about the major in a low-pressure environment, and help resolve issues or concerns that you have. These will be publicized on the email list, as well as the Applied Math website.

**Email a peer mentor with similar interests.** Don’t be afraid; this is what the peer mentors are there for, and they’d love to talk to you! They can set up a casual, informative meal at a time that suits both of you, and can talk about anything from course choices to concentrations to internship advice.

**Take prerequisite courses, **especially if they’re prerequisites to other majors you might be interested in. Multivariable calculus, linear algebra, and computer programming are prerequisites for Applied Math, but also for most STEM majors at Yale, so even if you are unsure about majoring in Applied Math, taking these courses is still a good idea. In particular, Multivariable Calculus at the level of MATH 120 or ENAS 151 is a prerequisite to 18 different majors at Yale, so if you plan to major in a STEM field, start with that now. Applied Mathematics courses are challenging, and it will be harder to complete the major if you try to compress the requirements into only your sophomore, junior, and senior years, so start now. If it turns out you don’t like Applied Math, your first year is also a good time to find that out and avoid falling behind in a different major.

**If you are trying to narrow down your choice of majors,** try to map out a schedule that counts to both majors. The Applied Math checklist might be helpful here. As discussed in the double majors portion of this FAQ, only two courses can count to both majors in a double major — this is a Yale College regulation. But if you are deciding between S&DS and Applied Math, for example, you could try taking many courses that count to both so it is easier to switch later. Indeed, you will find that you could almost entirely fill up the Applied Math major with courses that count to the S&DS major, too. Ordinarily, switching to the Applied Math major in your junior year would be very difficult, but as an S&DS junior taking mathematically-oriented courses, you might be right on track. Start planning this out in your first year to keep your options open should you decide to switch majors later on.

**I am a sophomore thinking about majoring in Applied Math. What should I do to prepare for the major?**

First of all, do everything suggested for first-years, above.

The Applied Math major requires 3 prerequisites, plus 11 more courses (for the B.A.) or 14 more courses (for the B.S.), and these courses are challenging, so it’s important to spread them out over your four years at Yale. To make sure you are on-track to complete the major, **start taking at least two classes that count to the major each semester**.

If you are thinking about another major as well, try to take classes that count to both Applied Math and that major (even if you’re not planning to double-major), so that if you ultimately switch to the other major, you have not fallen behind in that major.

Think about your preferred concentration, and **fill out the ****Applied Math checklist** with your planned courses over the next three years. Even if you don’t follow the plan closely or at all, going through the exercise of planning a schedule that meets all the Applied Math requirements will help you gain a more thorough understanding of the major.

Finally, schedule a meeting with the DUS to talk through your academic plans. Come prepared to clearly articulate what your plans are so far, where you’re still unsure, and what questions you have that the DUS can answer.

**What does it mean to officially declare my major? As a first-year or sophomore, should I declare Applied Mathematics as my major?**

If you think you will probably major in Applied Math, then yes, you might as well declare. All Yale students need to declare a major by the beginning of their junior year and then fulfill the requirements of that major by the end of their senior year to graduate. But unlike in other programs such as Global Affairs, History, or Political Science, declaring Applied Math as your major does not afford you any special privileges like pre-registration for seminars. And unlike at some other universities, you don’t transfer between different schools depending on your undergraduate major at Yale, meaning there isn’t a lot of importance attached to your major declaration. There is also no special process to declare your major; you just choose it in SIS and can change it whenever you want. Keep in mind, though, that to stay on track in the Applied Math major you need to start taking prerequisite courses right away (perhaps prerequisites that also count toward the requirements of other majors), even if you haven’t yet declared.

**Meetings and the DUS**

**Who is the DUS, and what do they do?**

The DUS is the Director of Undergraduate Studies, and is the main point of contact for all undergraduates interested in or majoring in Applied Mathematics. The DUS is always a professor who uses math extensively in their studies and is familiar with the mathematical course offerings at Yale. The DUS is responsible for advising undergraduates in the major and approving course schedules, as well as approving the structure of the major itself. The DUS serves as the main academic advisor for students in the Applied Math major outside of their residential college dean.

Currently, the DUS of the Applied Math major is the A. M. Bateman Professor of Geology and Geophysics and Professor of Mathematics and of Physics, John Wettlaufer.

**How does one arrange a meeting with the DUS?**

If you are a first-year and need a sophomore advisor because you will likely major in Applied Math, send him an email. john.wettlaufer@yale.edu

If you are a major wishing to meet with the DUS for academic advising, set up a meeting using his scheduler. Meetings are held in the DUS’ office, KGL 109, unless otherwise indicated. Make sure to share your Applied Math checklist with him before meeting.

Meetings with the DUS are yours to drive. Come in prepared with the questions you want to have answered, and a clear set of other topics for which you want to receive advice.

**How should I get my schedule signed?**

To save time for students and faculty, the Applied Math program offers electronic signature for course schedules at the beginning of each term. To take advantage of this option, seal your schedule, save it as a PDF, and email it to the DUS **at least 24 hours** before your schedule is due. He will electronically sign it and send it back to you. After you print the schedule with his signature, **be sure to sign the schedule yourself in the “Student’s Signature” section** before turning it in to your residential college dean.

If you wish to discuss your courses with the DUS, you may make an appointment with him and bring your sealed schedule to him for in-person signature. Some students may choose to meet with the DUS at the beginning of shopping period with a preliminary plan, then email their schedule for electronic signature at the end of shopping period when their plans are finalized.

You may wish to update your Applied Math checklist after sealing your schedule.

**Requirements of the Applied Math major**

**What courses do I need to take to receive an Applied Math degree?**

The most complete and up-to-date description is available in the YCPS, but here is a summary:

**3 prerequisites:**multivariable calculus, linear algebra, and programming**4 core courses:**data analysis, probability theory, discrete math, and differential equations**3 breadth courses:**pick courses from three different breadth categories on the Applied Math sheet**3 concentration courses:**three*mathematical*courses in the same subject area, at least two of which are numbered 300 or higher; again reference the Applied Math sheet**1 semester-long senior thesis:**a project in which you use math to solve a research question

For the B.S. you need everything above, and you also need:

**Analysis**(MATH 300, 301, or 305)**1 more breadth course****Any other course**numbered 300 or higher in a quantitative field

Keep track of the courses you’ve taken so far and those you plan to take in the future using the Applied Math checklist.

**What is the Applied Math spreadsheet?**

The Applied Math sheet is a comprehensive listing of all courses that count to the Applied Math major. If you are unsure whether a course counts, check there first. The sheet also lists distributional designations — i.e., the concentrations associated with a particular course — and the names of previous Applied Math majors who took the courses. If you are curious about an Applied Math course, previous students are often your best resource, so reach out to friends or Applied Math peer mentors who may have taken the course in the past.

The sheet is maintained by the DSAC. Contact them if you want to suggest any changes.

**What is the Applied Math checklist?**

The Applied Math checklist is designed to help majors and prospective majors plan out their Applied Math courseload over their four years at Yale. To use the checklist, make a copy of the template for yourself, and fill it out with the courses you’ve taken so far and plan to take in the future. If you are not yet sure whether you want to major in Applied Math, you can keep your copy private for your own planning purposes and only share with the DUS when you are ready. Read carefully the instructions written at the top of the checklist itself, and make sure to share it before meeting with the DUS. Keeping the checklist in Google Sheets means that you can update it whenever you want as your plans evolve over time, and the DUS will always have access to the latest version. (Remember that you also need to fulfill Yale College distributional requirements, which are not tracked in the checklist.)

**Does your concentration appear on your transcript or diploma?**

No. Yale does not acknowledge your concentration in any official way. This allows the major to be more flexible in allowing concentrations that may not be traditional fields of study at Yale.

**What are the requirements for concentration courses?**

All concentration courses must be mathematical. That is, the problem sets, projects, and exams must all involve substantial mathematical work. At least two of the courses must be advanced, which typically means they have a number 300 or higher.

Many students choose a concentration that is already another major/department at Yale; for example, computer science, S&DS, or physics. But please do not feel limited to these options: recent majors have concentrated in machine learning, mathematical biology, and other more niche fields. As long as there are three mathematical courses to take in the field (at least two of which are advanced), you can consider concentrating in it. But all concentrations, even standard ones like S&DS, must be approved by the DUS, and must have their constituent courses approved as well.

**Can I take any of my major courses Credit/D/Fail?**

Yes, you can take one Applied Math course Credit/D/Fail, as long as the course is not the senior project. (Prerequisite courses do not count toward this limit, but think carefully about whether you want to major in Applied Math if you need to use a Cr/D on a prerequisite.) Keep in mind that courses taken Credit/D/Fail are counted as non-A grades for the purpose of distinction in the major, and you may not want to take a core Applied Math course Cr/D if you’re interested in applying to graduate school, but courses taken Cr/D won’t affect your GPA.

**How can I earn distinction in the Applied Math major?**

Earn a grade of A or A– in at least 9/11 of the non-prerequisite courses in the Applied Math B.A., or at least 11/14 of the non-prerequisite courses in the B.S. One of those A’s or A–’s must come from AMTH 490 or AMTH 491, with the rest coming from core, concentration, and/or breadth courses. Grades of Cr in classes taken Cr/D/F count as non-A grades. Grades earned in prerequisite courses (multivariable calculus, linear algebra, and programming), and grades of P or W, are ignored in the calculation. Please consult this page of the YCPS for more information.

**Courses in the major**

**Should I take S&DS 238 or S&DS 241?**

Most Applied Math majors take S&DS 241. It is a prerequisite for more courses, and is especially helpful for S&DS 242, which is itself a prerequisite for many courses. However, there are also good reasons to take S&DS 238. Please consult the S&DS FAQ for more information, as the S&DS department has written up extensive reasoning for why you may prefer one over the other, and they are experts in the S&DS course pathways.

Also note: S&DS 241 is a purely theory-based course, while S&DS 238 mixes theory with programming in R. But the Applied Math major already requires you to take S&DS 230 (or 361), which will spend an entire semester teaching you to program in R. So it may be easier/cleaner for you to just learn R once (in 230/361), and learn probability theory separately (in 241).

**Do non-mathematical courses in quantitative departments count toward the Applied Math major? **

No, they don’t. As a general rule, keep in mind that the mathematical content of a course is much more important than the departmental designation for determining if a class counts toward the Applied Math major. If the course does not meaningfully apply mathematics, it cannot count toward Applied Math. Some courses in this category, which do ** not **count to the major, include:

- CPSC 223 (Data Structures and Programming Techniques)
- S&DS 240 (Introduction to Probability)
- S&DS 314 (Introduction to Causal Inference)
- S&DS 315 (Measuring Impact and Opinion Change)
- S&DS 355 (Introductory Machine Learning)
- S&DS 363 (Multivariate Statistics for Social Sciences)

**Should I take CPSC 202 or MATH 244?**

It depends on your interest in discrete mathematics and how you wish to apply your knowledge of discrete math to other fields. If you are less interested in proof-based and theoretical/abstract math, CPSC 202 may be a better choice. If those concepts are a main area of interest for you, consider taking on the challenge of MATH 244.

CPSC 202 is primarily designed for computer science students who need an introduction to concepts in discrete mathematics (propositional and predicate logic, inductive proof, number theory, graph theory, Big-O, relations) and methods of formal proof, especially to prepare them for classes like the CPSC 365 Algorithms course — which counts toward the Applied Math major as a breadth or concentration credit for interested students. Although it is listed in the computer science department, CPSC 202 does not require students to write any computer code on problem sets or exams, and no computer science knowledge is necessary to take the course. It is instead focused on mathematical concepts that have applications to computer science.

MATH 244 is designed for students coming in with a background in proof, and covers more advanced material at a faster pace than CPSC 202. MATH 244 is the prerequisite to the Intensive Algorithms CPSC 366 course, so some computer science students with strong math backgrounds opt for MATH 244 followed by CPSC 366.

**If I’m interested in algorithms, should I take CPSC 365 or 366?**

Neither course is required for the major, but taking one of them will count toward a breadth requirement or the CS concentration requirement. (Please note: you cannot take both CPSC 365 and 366 and count both to Applied Math. In fact, you cannot even take both courses for Yale College credit.)

CPSC 365 and 366 meet at the same time, to facilitate switching for students who decide the course they enrolled in is not at the proper level. CPSC 365 is a much bigger course than CPSC 366, and is the mainstream offering for computer science students seeking to fulfill their algorithms requirement. It generally targets students who built their discrete math background in CPSC 202.

CPSC 366 is deliberately kept to a small class size for the most advanced students, and generally targets students with a math background at the level of MATH 244. Both courses suggest CPSC 223 as a prerequisite so students are familiar with basic data structures and sorting algorithms before taking algorithms, but the goal is to use the data structures already developed in 223, rather than to implement them in code.

CPSC 365 does not require you to write any computer code, but many problems require pseudocode, at a level that should be accessible to Applied Math students who have satisfied the Applied Math programming prerequisite and taken CPSC 202.

**Other Majors**

**What’s the new data science major?**

As of 2017, there is now a major in Statistics & Data Science, replacing the old major in Statistics. This change was accompanied by faculty and course offerings in areas of statistics that focused on computing. Many of the S&DS major requirements overlap with Applied Math, but as with all majors in Yale College, double majors may only count two non-prereq courses toward two different majors. (For example, if you are a double major in Applied Math and S&DS, you might choose to double-count S&DS 230 and 241 to both majors, but would need separate courses to fulfill all other non-prereq requirements.)

**What’s the new data science certificate?**

As of 2019, there is now a certificate in Data Science. Unlike with a double major, you may not count *any* classes taken for your major to the data science certificate, and so you must take five courses on top of your major in order to receive the certificate.

This may pose problems for Applied Math majors interested in the certificate. For example, if you’ve already taken S&DS 241 and S&DS 242 for Applied Math, you would need to take an advanced probability course like Stochastic Processes or Information Theory to satisfy the probability requirement for the certificate, which most other people pursuing the certificate would fulfill by simply taking S&DS 238 or 241. In fact, you may have already completed all the requirements for the certificate just by majoring in Applied Math, and would essentially need to redo all the requirements, but at a more advanced level, to earn the certificate.

Plan early if you want to major in Applied Math while also receiving the certificate. If you don’t want to take five additional courses, an S&DS, data science, or machine learning concentration within the Applied Math major might be a good option instead.

**If I am a double major and my Applied Math concentration is in the same field as my double major, what should I do?**

If you are in this situation, then you may need any other possible third course in the concentration to count to your other major. In this case, you may complete the Applied Math concentration requirement with just two courses from your other major, as long as both courses are advanced. These two courses will then count as the maximum allowed overlap between the two majors. We allow this because you presumably have taken many other courses in this concentration and have sufficient grounding in the material already. In place of the last concentration course, you may take one additional breadth course.

**Will my schedule satisfy the requirements of a double major in Applied Math and another major?**

Make sure to set up conversations with the DUSes of both majors to be sure. In advance of your meetings, create a list of all courses you are counting toward the Applied Math major, and all courses you are counting toward the other major. Your Applied Math checklist might be helpful in drawing up this list. There can only be two courses on both lists (prerequisites do not count toward this limit). If you are taking advantage of the allowance to count just two credits toward your concentration (see above), recall that both courses must be advanced.

**Is there a way to receive a B.S. in Applied Mathematics while only fulfilling the B.A. requirements?**

Yes. If you fulfill the B.A. requirements of the Applied Math major and the B.S. requirements of another major, you will receive a B.S. in both, under the presumption that your training in the other major has given you sufficient scientific background to merit a B.S.

**Senior Requirements**

**What is the senior requirement for the Applied Math major?**

All seniors must complete a semester-long research project in either AMTH 490 or AMTH 491, colloquially referred to as “the thesis.”

AMTH 491 is offered every semester. Students work on mathematical research under the supervision of a faculty member and produce a written report at the end.

AMTH 490 is offered during some semesters. It contains all the elements of AMTH 491, plus a weekly meeting in which students meet with other students in the major and with the DUS to discuss their projects.

Start early to find a faculty member willing to supervise you for your research. Past Applied Math theses are available here for your reference.

**What are the mathematical requirements for the senior thesis?**

The research you do must be mathematical. The area of application does not have to be. For example, if you would like to undertake a mathematically rigorous analysis of evidence from the history department, you may do so — with the very important caveat that **your supervisor must be an applied mathematician** (meaning that s/he uses math to carry out research, not that s/he must be appointed in the math department). If you choose to conduct mathematical research in the history department, then you would need to choose *both* a history professor *and* a professor with mathematical training to supervise your project and ensure that during the semester you will grow as an applied mathematician.

**How should I find a thesis advisor?**

There are two ways that students usually find projects and advisors.

The first is to have an idea for a research project, and then get in touch with a faculty member who is knowledgeable about the area of the project. You should read some relevant articles/papers before emailing the faculty member about your idea. That faculty member will usually be able to help a student refine their ideas for a project and to choose goals that can be achieved within one semester.

Other students get in touch with professors they have met through classes,

and ask the professors if they have any suggestions for projects. Sometimes they do.

Whether you have a project in mind or only a very specific area, you can talk to past professors, friends in the major, peer mentors, the DUS, and anyone else you can think of to get an idea for which professors have ongoing research projects, or even labs.

A general rule of thumb is that the closer the professor’s main body of research is to your project, the better your project will turn out. This is for three important reasons: 1) the professor will have expertise in the area and be able to provide you useful help, 2) the professor will be invested in your work because it is relevant to what the professor is spending time on his/herself, and 3) the professor will be better able to scope a project for you, and figure out what work is feasible for someone at your level and will take about a semester to complete.

The danger of working with a professor less familiar with what you want to do is that s/he may have less interest in or ability to help you, and you may end up with a project that hits a dead end six weeks in, or that turns out to be far too complicated for a semester’s worth of work. Going to an interesting professor first and asking for a project the professor already has an interest in can often help mitigate these risks.

The Yale Society for Physics Students (SPS) has some advice for how to contact professors which you may find helpful.

**When should I do my senior thesis?**

Most students complete their thesis requirement in either the fall or the spring semester of their senior year, although motivated students can complete their thesis the spring of their junior year if they wish. (Of course, if there is more to do on your project, you may continue doing research for credit through AMTH 482.)

Students applying to graduate school in the fall are encouraged to do their thesis in the fall, since this allows their thesis advisor to write a letter of recommendation in support of their candidacy.

Any student wishing to do a thesis in the fall should ideally begin contacting potential advisors in the spring break of the previous semester, and at the latest over the preceding summer.

Any student wishing to do a thesis in the spring semester should email or meet in-person with potential advisors in the fall, finalizing a project idea (at the latest) over winter break.

**What are the deliverables and requirements for AMTH 491?**

By the end of shopping period, your advisor must send an email to the DUS, with a cc to you, containing a 3 – 4 sentence project description and the advisor’s agreement to supervise you for the project. You should probably write a draft of this description and send it to your advisor for review, both to be sure you are on the same page regarding the project, and to make the advisor’s life easier.

By midterm, your advisor must send an email to the DUS, again with a cc to you, with a status report to confirm that you are making progress on the project and that it hasn’t gone substantially off-course in any way.

By the last day of finals, you must submit your final project to your advisor. Your advisor will review the project and determine your grade. Your advisor will then forward your paper to the DUS and discuss the project and grade with the DUS. The DUS is the instructor of record for the AMTH 491 course and will officially record the grade, which is almost always the grade recommended by your advisor.

If the primary department in which your advisor is appointed requires that its undergraduates present their senior theses, then you must also present yours at their presentation session. If the department has no such requirement, you do not need to do so.

**The Departmental Student Advisory Committee (DSAC)**

**What is the DSAC?**

The DSAC was formed in Spring 2019 to consolidate input and feedback from students to help the DUS make continuous improvements to the major, and to develop resources for students in the major, like the Applied Math sheet, the peer mentoring program, and even this FAQ. Per the name, the DSAC is *advisory*: it does not approve or reject course schedules, make unilateral changes to the major requirements, etc.

As a student in the Applied Math major, the DSAC should be your first point of contact for feedback about how to improve the major or the resources within it. That’s what it’s here for!

**Who is on the DSAC?**

The current members of the DSAC are:

- Nash Keyes ‘21 (they/them) — G&G
- Adam Madievsky ‘21 — S&DS
- Keshav Raghavan ‘21 — Physics

**How can I join the DSAC?**

Email the DUS or any of the members of the DSAC. We’re always happy to have more people work on making Applied Math the best program it can be.

**What is the peer mentoring program, and how can I take advantage of peer mentoring opportunities?**

The peer mentoring program was launched in spring 2019 to facilitate more connection among Applied Math majors and to provide a resource for younger students in the major seeking advice. The peer mentoring program does *not* pair specific mentors with specific mentees; instead, any student in the major is welcome to reach out to any mentor at any time. Mentorship can range from quick emails to meals in the dining hall.

The current peer mentors, and their concentrations, are:

- Nash Keyes ‘21 - G&G
- Adam Madievsky ‘21 - S&DS
- Keshav Raghavan ‘21 - Physics, Data Science

Please, don’t hesitate to reach out to any of the peer mentors for advice, whether you just have a quick question about a course or aspect of the major or want to sit down for a longer meeting!