Published on *Department of Mathematics* (https://math.yale.edu)

For information about placement exam [1] and calculus, please see our other FAQ [2].

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

**Introductory and advanced courses**

- What courses should I take after integral calculus, if I’m considering a math major?
- Can I skip Math 120, if I took multivariable calculus during high school?
- Can I skip Math 222 / 225, if I took linear algebra during high school?
- Can I skip Math 230+231?
- Can I skip other required courses?
- What is the difference between Math 120 and Math 250?
- What is the difference between Math 222 and Math 225?
- What is the difference between Math 230 and Math 250?
- If I enroll in Math 230 and find that it is not the right class for me, can I switch into another course?
- Can I simultaneously count courses from both intro sequences toward the major?
- Can I take Math 301 or 300 without Math 231 or 250?
- Can I take Math 310 without Math 301?
- Can I take Math 310 without Math 250/231?
- 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?
- Is there a good math course that fulfills the QR requirements even if I haven’t taken any calculus?

**Requirements of the major**

- Where can I find the details of math major requirements?
- For a double major, how much overlap can there be in terms of courses?
- 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?
- Can I take a graduate course for Cr/D/F?
- Can a graduate math course count toward the undergraduate degree?
- 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?
- What can be counted as the physical science course for the B.S. requirement?
- Can independent study (Math 470) be counted toward requirements of the major?
- Do I have to take Math 301? 350? 310?
- Can transfer students count math courses taken outside Yale (which are accepted for transfer credit) toward the math major?

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

- For the intensive major, do the two graduate courses also count toward the required ten?
- Do cross-listed courses count as graduate, for purposes of the intensive major?
- 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?
- For the B.S./M.S. combined degree, does it matter whether I have take a particular course with the undergraduate or graduate number?
- What (and when) do I need to do to apply for the B.S./M.S. combined degree?
- For the B.S./M.S. combined degree, does it matter whether I have taken a particular course with the undergraduate or graduate number?

**Senior requirement**

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

June 14: topics for Fall 2020 and Spring 2021 sections have been added to this question. - Should I choose Math 480 or Math 475?
- Do Math 475 (senior essay) and Math 480 (senior seminar) count as math electives?
- How does Math 475 work? [updated for presentations during Spring 2020]
- If I plan to spend all year working on my senior essay, when should I enroll in Math 475?
- Is any information available about past Math 475 projects?
- How does senior project work for computer science + mathematics, and mathematics + physics majors? [updated for presentations during Spring 2020]
- Are joint senior projects / theses allowed?
- How does calculation for distinction in the major work?

**Other questions**

- How does advising work in math? [NEW as of July 24, 2020.]
- Does math have a peer mentoring program?
- Is there an unofficial math mailing list?
- Can I do research with math department faculty?
- Does Yale have a summer research program?
- Can I take graduate courses?
- Is there an undergraduate math organization?
- What jobs are available in the Math department?

**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 this substitution 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? **

Please note that Yale does not grant credit for courses taken during high school, even if they were taken at a university. This does not mean that you have to repeat these classes, only that you cannot get transfer credit for them.

For Math 120, these are some of the options:

If you are considering a math or a combined math major, or if you plan to take proof-based math courses later on, then a good option may be taking Math 230+231. This is a year-long vector calculus and linear algebra sequence, and most students benefit from taking it even if they have already seen multivariable calculus. The sequence fulfills any multivariable calculus and linear algebra requirements and pre-requisites, upon completion of both semesters.

Another option is to enroll directly in an upper level course, such as linear algebra (Math 222 or 225, the latter being recommended for math majors and students who wish to continue with further proof-based math courses).

Please note that many majors at Yale, including mathematics, require multivariable calculus. Before you skip the course, please speek with the DUS of your intended major to see if arragements can be made about the major requirements. In math, for example, we can give you permission to substitute a higher level course (note that this course will then not count towards the required ten courses level 200+).

**Can I skip Math 222 / 225, if I took linear algebra during high school? **

Most math and joint-math majors who have seen a regular linear algebra course would benefit from taking Math 230+231, or Math 225. If you have had a full proof-based course on linear algebra, we would encourage you to consult with the Math DUS. Upon a brief evaluation of the course you have taken, we can grant permission for you to substitute a higher level course for Math 225 in requirements of the major, and you can enroll directly in Math 250.

Students who intend to major in another field that requires Math 222 are encouraged to speak with the DUS of their intended major, to see if arrangements can be made to substitute a higher level course for it.

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 during the summer.

**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. Please note that Math 250 requires both Math 120 and Math 225 (or 222, though this is not recommended).

**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 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.

**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? **

Yes.

**Can I take Math 310 without Math 250/231? **

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

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:

- Math: [3]
- Math and Computer science [4]:
- Math and Economics: [5]
- Math and Philosophy: [6]
- Math and Physics: [7]

A roadmap for the math major [8] 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?**

No.

**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, because Cr/D/F is only available for Yale College courses.)

**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 category.

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

**Can a course be simultaneously counted towards two different categories? **

No.

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

Yes.

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 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, 136 (neither of these counts for students who completed Math 241)
- ECON 351
- PHIL 267, 427
- S&DS 351, 364, 410, 631

**Currently not approved: **

- AMTH 553
- 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 count 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).

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 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.

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: 333, 470
- PHYS: 342, 344, 401, 402, 410, 412, 420, 430, 440, 441

Currently NOT approved

- ASTR 465
- BENG 475, 476 (it’s not physical science)
- CHEM: 328 (see note below), 332
- PHYS 343, 356, 428
- All courses numbered strictly below 300

Note: Chem 328 counts for everyone who completed it before Spring 2020.

**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.

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?**

http://catalog.yale.edu/ycps/subjects-of-instruction/mathematics/ [3]

**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 https://math.yale.edu/grad-programs/syllabi-qualifying-examinations [10] .

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 (and when) do I need to do to apply for the B.S. / M.S. combined degree? **

You must submit your application to the Dean’s office during your fifth term at Yale, no later than the last day of classes. **The Dean’s office is strict about this deadline, and if you miss it, you will not be able to apply later. **

Note that the proposal must include endorsement by the math department. That being so, you must have everything ready and set up a meeting with us to take place at least a week in advance of the deadline. In Fall 2020, that means before November recess.

The application can be found on the Dean’s office website [11]. Once you fill it out, e-mail it to Miki and we will set up a meeting to talk about it.

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 https://registrar.yale.edu/forms-petitions [12] .

**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.

Topics for the academic year 2020-21 will be posted here during summer 2020.

- Fall 2019, taught by Professor Igor Frenkel. Topic: Groups in mathematics and physics.
- Spring 2020, section 1, taught by Dr. Ofir Lindenbaum (this section may be of special interest to math+econ majors). Topic: Theory of networks and game theory.
- Spring 2020, section 2, taught by Professor Yifeng Liu. Topic: Introduction to mathematical cryptography.

Groups in Mathematics and Physics.

Since their introduction in the XIXth century, groups play increasingly important role in all areas of Mathematics: Algebra, Geometry, Analysis. They also have fundamental significance in Physics. I plan to give a brief review of history, general facts about groups and various applications of the theory to different areas of Mathematics and Physics. 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 my supervision. I will provide the students with the literature as well as with my personal guidance during preparation of their lectures. Below are a few examples of topics:

1) Regular solids and subgroups of SO(3),

2) Symmetric functions and permutation groups,

3) Representations of SU(2) and the notion of spin,

4) Representations of SU(3) and classification of elementary particles,

5) Hyperbolic geometry in dimensions 2 and 3 and their symmetry groups,

6) Space-time and Lorentz group,

7) Harmonic oscillator and Heisenberg group,

8) Quaternions and octaneons and their symmetry groups,

9) Codes and lattices and their symmetry groups,

10) Continuous fractions and modular group,

11) Fourier series and their analogues on 2 and 3 dimensional spheres,

12) Problems of linear algebra and representations of quivers,

13) Any other topic that students would like to propose.

This is a sample 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.

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.

**Course format**

This is a research seminar and students are expected to attend every session. Do not schedule job interviews or trips that conflict with the appointed times of the seminar. Only absences due to illness may be excused with a Dean’s excuse. There will be a few introductory lectures and the remainder of the seminar will be student presentations.

**Evaluation**

The evaluation will be based on the quality of classroom presentations and written work. Each student will make 1 or 2 presentations and post comments on other presentations. The comments should be posted on the discussion board in Canvas by the end of each class day. Each presentation will comprise 50% of the grade and comments comprise 50% of the grade.

**Course materials**

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.

Available for free online at http://www.cs.cornell.edu/home/kleinber/networks-book/ (Links to an external site.) [13]. We will supplement it by other books and articles as needed.

Additional resources:

- “Social and Economic Networks” (2008, Princeton University Press) by M. Jackson
- “Connections” (2007, Princeton University Press) by S. Goyal
- “Games on networks” by M. Jackson and Y. Zenou. In: P. Young and S. Zamir (Eds.), Handbook of Game Theory Vol. 4, Amsterdam: Elsevier Publisher, pp. 91-157
- “Learning in Social Networks” by B. Golub and E. Sadler. The Oxford Handbook of the Economics of Networks, (Yann Bramoullé, Andrea Galeotti, and Brian Rogers, eds.), 2016

The topic will be: Introduction to Mathematical Cryptography.

I will mainly use the book

**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.

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 double-spaced summary of your work by the last day of classes, to your project adviser, with cc to the Math Registrar.

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.

4. The grade for Math 475 is based on (a) Your work during the semester (as reported by your adviser), (b) your paper submission at the end, (c) 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.

Extra note: the projectors in LOM are ancient, and you may need an adapter to make it work with your laptop. Be sure to test your setup at least a day ahead of time (on presentation day, there will be talks back to back, so you will not be able to get into the room in advance).

**SPRING AND FALL 2020 ADJUSTMENTS (online version)**

In the current circumstances, all presentations will be online. The default instructions are below, but you and your committee can adjust as needed. In particular, you can have the presentation earlier (but not later), and it can take place live on zoom rather than being recorded, if that is what you prefer and your remote learning circumstances allow it. Please be sure to get in touch with your committee to arrange the details.

TIMELINE

**1. Your 20-25 project summary will be due on the last day of classes**.

**2. ****By the last day of classes, you will need to write to your committee and schedule the live Q&A session** with them, to take place during reading week or the first three days of finals week.

**3. A minimum of three days in advance of your scheduled Q&A session, you will need to submit ****a 30 minute recorded presentation** via the Math 475 Canvas site.

Please use your last name as the first part of the file name, so that your committee members can easily spot which file is yours.

Three days in advance of the Q&A is a firm deadline, because your committee needs time to view the submission. I would very much encourage you not to leave its recording until the last minute, because you may encounter any number of difficulties, and it could prevent you from completing your presentation this semester.

Once on the site, click on the “Media library” tab, then on the “Media presentations” folder, and then use the “Create” drop-down menu on top to “upload media”.

The folder is set so that you can upload, and see your own submission, but you will not see anyone else’s submission.

The recording can be done in any number of ways, for example:

a) Writing on a tablet and recording screen and voice (there are several programs that allow for this, including zoom).

b) Recording voice with a presentation done in powerpoint or using pdf (with scanned or typed notes).

c) A whiteboard presentation recorded through a computer camera.

The advantage of recording the presentation is that it allows for more flexibility, as far as when and how you want to do it, and it avoids live technical issues (of which we, ourselves, have encountered many, while trying to put all of our classes online). In particular, you can record offline, without the need strong internet connection.

If you run into technical complications, the Poorvu center or ITS are the best people to ask (or you can write to Miki, and I’ll try to help if I can).

**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.

**Is any information available about past Math 475 projects?**

Here are descriptions of a few sample projects, posted with permission from the students: (This part is being prepared and the links will be available soon.)

- Sonali Durham ‘20: Nesting rules for political redistricting: methods for sampling matchings and tripling [15].
- Sanelma Heinonen ‘20: Discrete convexity with applications to maximizing user satisfaction in bike sharing systems [16].
- Noah Kravitz ‘20: Lonely runner conjecture [17], and Noah’s advice [18] for writing a research-based senior essay.
- Claire Thompson ‘19: Binary irreducible quadratic-residue codes and the Good code problem [19].

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

0. Be sure to e-mail Miki Havlickova at the beginning of the semester that you will be completing your thesis. (This is to get on my list of students who need to give an oral presentation in math at the end of term.)

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 on the mathematical aspects of your project, to a committee of two mathematics faculty chosen by the DUS. The presentation 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.

The presentation has a prescribed format: you will have five minutes to introduce the physics / computer science background of your project, and then **you must spend ten minutes explicitly discussing the mathematics you have learned and used during your project**. The committee will evaluate the matematics portion.

Extra note: the projectors in LOM are ancient, and you may need an adapter to make it work with your laptop. Be sure to test your setup at least a day ahead of time (on presentation day, there will be talks back to back, so you will not be able to get into the room in advance).

*In Fall 2020, the presentations will be on Monday, December 7. *

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.

**SPRING AND FALL 2020 ADJUSTMENTS (online version)**

In the current circumstances, all presentations will be online. This is how it will work:

1. By the last day of classes, you will need to submit a 15 minute recorded presentation, via a Canvas site called “Math DUS: senior presentations” (invites will be sent to everyone who told Miki that they are finishing their senior requirement this semester).

Please use your last name as the first part of the file name, so that your committee members can easily spot which file is yours.

The last day of classes is a firm deadline, because your committee needs time to view the submission. I would very much encourage you not to leave its recording until the last minute, because you may encounter any number of difficulties, and it could prevent you from completing your presentation this semester.

Once on the site, click on the “Media library” tab, then on the “Media presentations” folder, and then use the “Create” drop-down menu on top to “upload media”.

The folder is set so that you can upload, and see your own submission, but you will not see anyone else’s submission. . The recording can be done in any number of ways, for example:

a) Writing on a tablet and recording screen and voice (there are several programs that allow for this, including zoom).

b) Recording voice with a presentation done in powerpoint or using pdf (with scanned or typed notes).

c) A whiteboard presentation recorded through a computer camera.

2. We will schedule a 15-minute live questions session with your committe for the presentation day listed above (typically Monday of reading week).

The reason for recording the presentation is that it allows for more flexibility, as far as when and how you want to do it, and it avoids live technical issues (of which we, ourselves, have encountered many, while trying to put all of our classes online). In particular, you can record offline, without the need strong internet connection.

If you run into technical complications, the Poorvu center or ITS are the best people to ask (or you can write to Miki, and I’ll try to help if I can).

If you run into other complications with completing the project, recording the presentations, scheduling a Q&A session, or anything else, please write to Miki and Yifeng. We understand that the current situation is challenging, and we will do everything we can to help you finish your senior requirement this term.

** Are joint senior projects / theses allowed?**

No.

** How does calculation for distinction in the major work? **

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

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 - that is, 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.

**Other questions**

**How does advising work in math?**

We’re phasing in a new system (again) (sorry) (but it’s a really nice one!) (I think).

**Very old system:** The DUS would advise all 200 math and joint-math majors.

**Old system: **Math and joint-math majors were assigned a faculty adviser, through a lottery. We changed to this system so that students would have more opportunities for personal conversations with their adviser (as the advising groups were 15-20 students, rather than 200).

**New system: **We will take away the random aspect, and designate faculty in this way:

- Professor Moncrief is already the designated adviser for Math + Phys.
- We will likewise designate particular faculty members to be the advisers for joint majors (probably two to Math + CPSC, two to Math + Econ, one to Math + Philosophy, based on the sizes of the majors).
- We will designate two advisers each to pure math majors in each class year (that is, two faculty for class of 2024, two to class of 2025, etc.)

We think this will allow the advisers to concentrate on one major (rather than keeping track of five), it will be clear which students should see whom without lottery and even before they declare the major, the new system will be a bit more stable as far as faculty going on leave, etc.

**How to phase between these systems: **We will try to keep as many existing adviser assignments as we can, by keeping several advisers in the old system (so their advisees can continue with the same adviser). New advisers, those returning from leave, and a couple of existing advisers will switch to the new system (so each joint major will have one designated adviser, and so will math majors in class of 2023 and 2024). A few students will have to be reassigned to a new adviser (this can’t be helped, unfortunately).

**Extra note:**

The DUS will continue to be available to everyone. Our office hours are posted on the math DUS site [20]. 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 :)

**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

https://math.yale.edu/math-peer-mentor-program [21] .

**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

https://subscribe.yale.edu/browse?search=math+dus [22] ,

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

During the academic year, the graduate students organize a directed reading program [23], where students can explore topics and work on projects with a graduate student mentor.

**Does Yale have a summer research program?**

Our summer research program is called SUMRY, and you can find its website at https://sumry.yale.edu/ [24] . Applications for the summer 2020 program are open until February 15.

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** (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 [25] for more information. You can also take a look at their recent seminar recordings [26].

**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 Dimensionsatyale@gmail.com [27].

**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 workshop, 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 (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).

Our main **hiring process for peer tutors ULA’s **typically takes place 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.

Tutors who are hired will go through two **training sessions** just before the beginning of the Fall semester (one session is with the department, one is with the CTL).

As of the academic year 2019-2020, the pay for ULA and peer tutor positions is $18.50 / hr.

**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 next year’s positions).

(b) Only students who have already completed at least one math course numbered 120 or above are eligible to apply. (In particular, students currently enrolled in Math 120 are not eligible.)

(c) Where possible, we require that tutors complete (by the time the job starts) at least one course above the one they are tutoring. For example, tutoring Math 120 requires completion of Math 222 or 225. Tutors for Math 222/225 will have completed Math 250. The ULA position in Math 230 requires completion of Math 231; the ULA position in Math 350 requires completion of Math 370.

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 Ian Adelstein at first.last@yale.edu [28] .

Rules: Every student in their second year or above is eligible to grade any math course that they have completed.

Applications for Fall 2020 math grading position closed on August 14.

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 first.last@yale.edu [28] . 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

https://poorvucenter.yale.edu/tutoring/quantitative-reasoning-science/small-group-and-1-1-tutoring [29] .

**Links:**

[1] https://math.yale.edu/undergraduate/placement-exam

[2] https://math.yale.edu/calculus-and-placement-exam-faq

[3] http://catalog.yale.edu/ycps/subjects-of-instruction/mathematics/

[4] http://catalog.yale.edu/ycps/subjects-of-instruction/computer-science-mathematics/

[5] http://catalog.yale.edu/ycps/subjects-of-instruction/economics-mathematics/

[6] http://catalog.yale.edu/ycps/subjects-of-instruction/mathematics-philosophy/

[7] http://catalog.yale.edu/ycps/subjects-of-instruction/mathematics-physics/

[8] https://registrar.yale.edu/students/major-roadmaps

[9] http://catalog.yale.edu/ycps/academic-regulations/special-arrangements/#Simultaneous_Bach_and_Masters

[10] https://math.yale.edu/grad-programs/syllabi-qualifying-examinations

[11] https://yalecollege.yale.edu/deans-office/deans-office-forms

[12] https://registrar.yale.edu/forms-petitions

[13] http://www.cs.cornell.edu/home/kleinber/networks-book/

[14] http://www.math.brown.edu/~jhs/MathCryptoHome.html

[15] https://gauss.math.yale.edu/~cav7/dept-pdfs/sonali_durham.pdf

[16] https://gauss.math.yale.edu/~cav7/dept-pdfs/sanelma_heinonen.pdf

[17] https://gauss.math.yale.edu/~cav7/dept-pdfs/noah_kravitz.pdf

[18] https://gauss.math.yale.edu/~cav7/dept-pdfs/noah_tips.pdf

[19] https://gauss.math.yale.edu/~cav7/dept-pdfs/claire_thompson.pdf

[20] https://math.yale.edu/director-undergraduate-studies#overlay-context=undergrad-programs

[21] https://math.yale.edu/math-peer-mentor-program

[22] https://subscribe.yale.edu/browse?search=math+dus

[23] https://sites.google.com/yale.edu/yaledrp/project-suggestions?authuser=0

[24] https://sumry.yale.edu/

[25] https://yums.sites.yale.edu

[26] https://drive.google.com/drive/u/1/folders/1OazElzTAjlesznH3bY6PiKrArDEVw3fV

[27] mailto:Dimensionsatyale@gmail.com

[28] mailto:first.last@yale.edu

[29] https://poorvucenter.yale.edu/tutoring/quantitative-reasoning-science/small-group-and-1-1-tutoring