There are many graduate school options available for math majors. This
page describes graduate school options in mathematics, especially for
those interested in academia.
If you want to go into academia, you will eventually need to get a Ph.D.
It is not necessary to get a master's degree before pursuing a Ph.D. Some
math majors from Pepperdine find it useful, however, to obtain a master's
degree first, to build up more background before attempting a Ph.D. program.
Pepperdine University does not offer either master's or Ph.D. degrees in
mathematics. Some universities have a single mathematics department, while
others have separate departments for fields like pure mathematics,
applied mathematics, statistics, computational mathematics, financial
mathematics, and so on.
Although math departments vary widely, the following are usually true:
To prepare for graduate school, you should take the following steps:
- Graduate school is much more self-motivated and results-driven.
There are rarely fixed deadlines, and grades are unimportant. But
if you do nothing, you will never get a Ph.D. The focus is not on
classes; it is on producing a dissertation advancing the field of
mathematics. There is no deadline, but you might run out of funding
if you do not work fast enough.
- There is no standard "number of years" it takes to get a Ph.D. Some
programs try to graduate their students in 3 to 4 years, while others
typically expect their students to stay for up to 10 years. More typically,
a Ph.D. program will take between 4 and 7 years.
- You don't usually pay for graduate school at the Ph.D. level. Typically
you can get research assistantships or teaching assistantships or both
to completely finance your tuition and still receive a stipend. If you
are accepted to a graduate program without funding, this may indicate that
they do not believe you will complete the program, and it may be a bad idea
to go there for graduate school. The funding, however, may be contingent
on your graduating in a certain number of years, and often is tied to your
thesis advisor, so that your thesis advisor may decide to no longer fund you.
You should also investigate Assistantships
and Graduate Fellowships in the Mathematical Sciences, an
annual publicattion of the AMS. The
National Science Foundation
also offers fellowships.
- You apply to the mathematics department, not the school. As a result,
the people deciding on your application are the math professors.
- There is often a qualifying exam, preliminary exam, or both. They
may be written or oral. On each you might have two attempts, and if you
fail both times, you are not accepted to the program (though you may
obtain a master's degree after completing the requirements). Sometimes
there is the option of taking this exam upon arrival.
- The first year or so is dedicated to preparing you for this exam.
The courses are only relevant to prepare you for the exams.
- The whole point to graduate school after your qualifying exams is
your thesis. Classes only matter as far as they help you solve your
- After passing whatever kind of qualfying exam, you need to find a
thesis advisor, who will guide you in finding a thesis problem. Your
goal is to solve this problem. The actual initial problem may not be
the problem you write your thesis on. If it is too easy, you may want
to develop it further. If it is too hard, you may want to try an easier
version. Or along the way, as you find interesting results, you may
decide to change the problem.
- The job market for Ph.D.'s who wish to go into academia is tight,
but not as tight as it used to be. It is impossible to predict what
the market will be like by the time you get your Ph.D.
- Take the GRE general test and the GRE Math Subject test. The GRE general
test is like the SAT, except is has logic puzzles as well. Often math
departments may be forced to require this score but generally ignore it
in admissions. The GRE Math Subject test tests mostly lower-division
knowledge like differential equations, linear algebra, calculus, and so on,
but there are a few upper-division questions like group theory, analysis,
and ring theory. It is not very strong on problem-solving and requires you
know some basic facts about each subject. Some graduate schools even
ignore this number as well. You should still take it anyway, and get a book
of sample questions.
- Application deadlines vary widely. Some start as early as December and
some are as late as May. Most commonly, deadlines will be during January.
- Look at webpages of possible schools. Make sure you know what you're
getting in to. If you have strong feelings as to what you want to study,
make sure there is enough of an opportunity to do that field, especially
making sure that there are at least a few tenured professors in that
subject or close to that subject.
- If you are particularly interested in a school, you can contact
professors or administrators at that school, and ask questions. At
some point you should ask administrators for names of current students
so you have some idea about what it's like to be a student there.
You should also take more courses than is merely required by the
Pepperdine math department. The more courses the better, of course,
but Complex Analysis is especially recommended.
If you have the opportunity to do so, do an undergraduate research
project, preferably publishing your results.