Preparing for Graduate School in Mathematics

If you love math and want to learn it in depth, then graduate school can be
an ideal way to immerse yourself in the subject and to develop your
problem-solving and theory-building abilities. There is a broad spectrum of
math graduate schools, from highly competitive top departments to more
easy-going programs. Luckily, excellent mathematicians are not just
concentrated in a few places.

This being said, it pays to carefully plan your undergraduate program, so
you can take full advantage of what graduate school has to offer. Here are
guidelines for students interested in applying for grad school in pure
mathematics. If you are intersted in applied mathematics you should speak
with your advisor because there are a few important differences in what is
recommended.

Coursework

  • The core courses in the Mathematics BS are absolutely necessary: MATH 235 (or 173), MATH 236, MATH 240, MATH 265, and MATH 282.
  • If a course has an honors version, take it! (specifically MATH 236H, 240H, 265H) Standard level courses are good, but honors versions go deeper and are specifically designed as preparation for graduate level courses.
  • Take two semesters of algebra (MATH 236H and MATH 237) and two semesters of analysis (MATH 265H and MATH 266). If you are unable to take MATH 266, then MATH 440 or MATH 453 are suitable replacements.
  • Take an intro programming course like CSC 161 or 171. Having basic programming skills is useful even if your focus in pure math.
  • Do NOT skip courses in sequence! It can be detrimental to take courses when you are unprepared. For example, it is never recommended to take graduate level analysis (MATH 471) without first taking MATH 265 or 265H. While you may survive MATH 471 without taking MATH 265H, merely surviving is not the goal. Moreover, it is difficult to "test out" of courses in grad school so it is likely you would need to take real analysis again in any case.
  • Do not be afraid to branch out. In graduate school your studies will become more focused in a few areas, but as an undergraduate you have an opportunity to take a variety of different topics such as probability, combinatorics/graph theory, number theory, ODEs, geometry, etc. Being well-rounded is very important as mathematics is intertwined.
  • Quality over quantity! Avoid taking more than three mathematics courses in a single semester. You should strive to master the material in every mathematics course you take and you do not want to burn yourself out. The expectations in graduate school are very high and the sooner you get into the right mindset, the better.
  • Sample schedules can be found here.

Subject Test GRE

  •  Info about GRE and GRE prep will go here

Undergraduate Research

Participating in research as an undergraduate is highly rewarding and can significantly increase your chances of admission to a grad program in mathematics. For more information about how to get involved in research visit our undergraduate research page.

Recommendation Letters

All graduate programs ask for three or more letters of recommendation:

  • For a grad program in mathematics, most (if not all) of your letters should come from math faculty. A letter from a professor in a related field (e.g. physics or computer science) that can comment on your mathematics or problem-solving ability also helps.
  • Ask professors that know you best! Getting an A in a class does not necessarily mean you will get a good letter from that professor. If you have have never had a conversation with the professor, they will be hard-pressed to write personal comments about you. Fluffy, generic letters that simply say "he or she got an A in my class" will not help you. Get to know your professors!
  • Give your letter writers sufficient notice ahead of deadlines (one month is safe). Give them a list of the programs you are applying to with deadlines.

Assistantships

Don't pay for grad school, let them pay you! Almost all PhD candidates in mathematics are on assistantship either as a teaching assistant (TA) or research assistant:

  • Assistantships are generally offered at time of admission to the program. They usually pay your tuition in full and offer a stipend (e.g. $ 15000-25000 annually) so you can concentrate on your studies instead of working.
  • Most often it will be a teaching assistantship unless you already have research experience or have a connection with a professor coming in.
  • As a TA you will be required to run recitations and teach your own classes after a few years in the program.
  • Apply to be a mathematics TA as an undergraduate. It is very helpful to gain teaching experience prior to grad school.

Do Your Homework Before You Apply

Be sure to read program websites to familiarize yourself with the program:

  • It is important to find programs which are a good fit for you. Look for programs that have several professors in your field(s) of interest.
  • Personalize your cover letters. It is good to mention specific areas of research or professors in the dept. which you are applying. Departments look for students that seem particularly interested in their program. Sending a generic letter is not a deal breaker, but does not maximize your chances of getting noticed.

Resources For Finding The Right Program

  • You can find theses and future plans for recent honors BA/BS Mathematics students here.
  • More advice and external links helpful for narrowing down programs can be found here.