Students who are considering graduate school in mathematics should start preparing for this goal well before the senior year. This page describes some of the considerations to keep in mind as you move through the math major.
Two Types of Graduate Programs
Graduate programs come in two flavors: master’s programs and Ph.D. programs. A typical master’s program is 2 years of courses while a Ph.D. program has 2 years of courses and 3 years of work on a Ph.D. thesis, which is original research. There are very few purely master’s programs in math, and the main purpose of pursuing a master’s degree is to prepare for a Ph.D. program elsewhere, so this page focuses on preparing for a Ph.D. program.
Coursework in College
Start taking upper-level math courses as soon as you can in the core areas of algebra, analysis, and geometry/topology. Specifically, take Math 3146 (Complex Variables), Math 3150 and 3151 (Analysis I and II), 3160 (Probability), Math 3210 (Abstract Linear Algebra), Math 3230 (Abstract Algebra I),and Math 3330 (Topology). Aside from 3146 and 3160 these courses have a common prerequisite of a C or better in either Math 2142Q (part of the Advanced Calculus sequence) or Math 2710 (or its W version Math 2710W), so if you need 2710 or 2710W then take it as soon as possible, which is right after Calculus II (Math 1132Q or 1152Q). Start taking 3000-level math classes right after you have taken 2142Q or 2710/2710W. Note: a lot of the motivation for topology comes from analysis, so it’s advisable to take Math 3150 before Math 3330 or its graduate counterpart Math 4310 (see below), even though 3150 is not an official prerequisite. Our graduate complex analysis course Math 5120 is a more rigorous alternative to Math 3146.
- Those interested in graduate school in pure math should also take a couple of courses from among Math 3231 (Abstract Algebra II), Math 3240 (Number Theory), Math 3250 (Combinatorics), Math 3260 (Logic) and Math 3370 (Differential Geometry), depending on your interests.
- Those interested in graduate school in applied math should also take Math 3410 (Differential Equations for Applications), Math 3435 (Partial Differential Equations), and Math 3510 and Math 3511 (Numerical Analysis I and II).
- All students interested in graduate school in math should take some of the first-year graduate courses that are cross-listed in the undergraduate catalog: Math 4110 (Analysis), Math 4210 (Abstract Algebra), or Math 4310 (Topology).
- If you want to write a senior thesis in math as part of graduate school preparation, see the bottom of this page for advice about when to start the process.
Some of the courses listed here (3231, 3260, 3330, and 3370) are not offered every year (see this page for a schedule), so plan ahead to fit in all the courses you need. If 3330 (undergraduate topology) does not fit then 4310 (graduate topology) could be taken instead.
Opportunities Outside of UConn
Demonstrate your interest in math by participating in a math summer program in college, such as an REU program (a regularly updated list of such programs is here) or the Park City Math Institute Undergraduate Summer School. REU programs require students to still be in college, so the summer after junior year is the last time to apply (students finishing their freshman year are unlikely to be accepted). Consider also semester-long math programs elsewhere such as Penn State’s MASS program, the Budapest Semesters in Mathematics, or Math in Moscow.
GRE Exams
Most math graduate programs in the US require applicants to take the GRE (Graduate Record Exam). There are two GRE tests: the GRE General Test that applicants to all programs (not just in math) take, and the GRE Math Subject Test. There is a math portion on the general test, which will be very easy for math majors. What matters more is your score on the math subject test. You must work rapidly to get through all the questions on the math subject test, so it’s important to prepare well. Start preparing several months ahead of time, e.g., in the summer between junior and senior years if you take the test in the fall of your senior year. Pro tip: the math subject test has calculus on it, and some past UConn students have said that being a Q Center tutor helps them remember how to do calculus computations long after they’ve finished calculus.
Applications
The most important part of an application to graduate school, besides a strong transcript of upper-level coursework, is the recommendation letters. Generally three are required and they should all be from mathematicians. Seek out letter writers by the middle of the fall semester of your senior year. People to get letters from are those who know your mathematical abilities well. This includes, but is not limited to,
- instructors of upper-level (especially proof-based) courses,
- faculty you have done an independent study with,
- a senior thesis advisor,
- an REU research supervisor.
Letters from either long-term or short-term faculty in the math department are okay, but try to have at least two letters written by long-term faculty. They are on the math department’s Regular Faculty webpage, while short-term faculty are on the department’s Postdoctoral and Visiting Faculty webpage.
No minimum number of applications will guarantee an admission somewhere, but based on past experience of UConn students you should apply to over 10 programs, and at least 15 if possible. Look beyond the northeastern US.
Note: If you want to apply to math Ph.D. programs outside the US then you need to know how those programs are organized differently from American programs. First of all, no GRE scores are needed (it’s a purely American phenomenon). Second, you would usually be admitted because a particular faculty member wants to work with you, so you need to show a specific research interest. American Ph.D. programs in math do not generally require students to commit to a particular research area or research supervisor when applying. Third, Canadian graduate math programs admit all students as master’s students and they are allowed to move on to the Ph.D. program only after doing well enough in courses.
Funding Graduate School
Unlike college, Ph.D. programs in math do not require you to pay tuition. Admitted students get a tuition waiver in exchange for doing some grading or teaching, for which they get a stipend. Most Ph.D. students cover expenses in graduate school with the stipend.
The US government offers two national graduate fellowships, sponsored by the National Science Foundation and the Department of Defense. These fellowships cover expenses for a few years without requiring a student to teach or grade. Only students with outstanding course grades and some additional mathematical experience will be competitive applicants.
Graduate School, but not in Math
Math majors can be attractive candidates for graduate school in math-related disciplines other than mathematics itself, such as statistics, biostatistics, economics, or computer science. For example, Ph.D. coursework in statistics and economics requires real analysis, so a math major who does well in a year-long real analysis sequence in addition to other challenging math courses will get noticed. The Harvard economist Greg Mankiw wrote on his blog “If you are thinking about a Ph.D. program in economics, you are advised to take math courses until it hurts.” Math majors should have a higher pain threshold for math courses than economics majors.
Want to Know More?
The UConn math club has a panel discussion on preparing for graduate school near the end of each spring semester involving faculty and graduate students. Attend this at least once before your senior year. At other times of the year, if you have questions about getting ready for graduate school ask around to find faculty who are knowledgeable about the process and willing to talk with you about it.