Preparing for Graduate School in Mathematics
The admission process for PhD programs in mathematics is highly competitive. Being underprepared for graduate school not only hurts your chances of admission, but also makes it more difficult to successfully complete the program if/when you get there. While aspects of an applicant's record will be weighted differently depending on the program, there are specific things you can do to increase your chances of being admitted to a strong program and ultimately thrive in the field. 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.
- The core courses in the Mathematics B.S. are absolutely necessary: MTH 235 (or 173), MTH 236, MTH 240, MTH 265, and MTH 282.
- If a course has an honors version, take it! (specifically MTH 236H, 240H, 265H) Standard level courses are okay, but honors versions go deeper and are specifically designed as preparation for graduate level courses.
- Take two semesters of algebra (MTH 236H and MTH 237) and two semesters of analysis (MTH 265H and MTH 266). If you are unable to take MTH 266, then MTH 440 or MTH 453 are a suitable replacements.
- Take an intro programming course like CSC 161 or 171. Having basic programming skills is necessary 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, while you may survive MTH 467 without taking MTH 282, merely surviving is unhelpful and does not impress anyone. Regardless of the level of understanding in MTH 467, it is highly unusual that you will "test out" of Complex Analysis in graduate school, and you will be forced to take it again anyway.
- 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
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.
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.
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.