Graduate School in Mathematics
Types of graduate programs
There are several types of graduate programs that mathematics students
might be interested in. In addition to mathematics, Canisius math majors have gone
to graduate school to study economics, finance, education, physics, philosophy,
classics, history of science, architecture, biomedical engineering, and medical school.
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“Professional” masters programs: A professional master’s degree is
considered a terminal degree: in other words, you do not expect to go on to
further study. These are usually designed to prepare graduates for a
recognized profession. Examples are librarians, social workers, or teachers,
among others. For teachers there are again choices: whether to get a master’s
degree in general education or one specifically in mathematics education.
The more specialized degree is slightly more prestigious than the general one,
but either will gain you increased recognition and expertise. Such programs
typically require one to three years of full-time study. The website below has
information on professional programs in mathematics:
http://www.ams.org/profession/career-info/grad-school/emp-masters
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Master’s programs in mathematics or statistics: This degree will prepare
students for jobs that require a higher level of proficiency than an
undergraduate degree, or as preparation for further study. Such programs
typically require two to four years of full-time study. Some programs require
only coursework, some require coursework with a comprehensive exam, and
some require coursework with a thesis, an individual project done under the
supervision of a faculty advisor.
Doctoral programs: This degree prepares students for a career as a
professor at a college or university or as a researcher in the private, public or
government sector. Such programs typically require four to seven years of
full-time study. All doctoral programs require a dissertation, an individual
project done under the supervision of your advisor resulting in a new piece
of mathematics. Here is a blog by and for graduate students in mathematics:
http://mathgradblog.williams.edu/
Preparing for graduate study
First, remember that graduate school is hard work and not to be undertaken
lightly. The qualities that make a good graduate student are the same ones that
make a good student (and, of course, a good mathematician): intelligence, initiative,
self-discipline, intellectual curiosity, and persistence. These are the properties
graduate schools will be looking for. While you are still an undergraduate, you
should take the opportunity to develop these characteristics.
In addition, it is good to expose yourself to a lot of different types of
mathematics, so you can first choose a graduate program that matches your
interests and then an advisor in that subfield. As an undergraduate, you will not
have the opportunity to take courses in every specialty, but you can at least narrow
the field down a bit. Do you like pure math or statistics and applied math better? Do
you think visually or analytically? Try to distinguish between liking the content of a
course versus liking the professor who happens to be teaching it.
Some graduate schools require reading knowledge of a foreign language,
usually your choice of French, German, or Russian. Two semesters of study is
usually sufficient to take the proficiency exam, which usually consists of translating
a mathematics article from the language into functional English, with the aid of a
dictionary. Since the equations are the same in any language, this isn’t as hard as it
might be in another field. Check the requirements of any graduate schools you’re
thinking about.
Try to get some exposure to research. Attend the seminar talks so you can
see lots of different mathematics that we may not offer courses in. Another way to
try out what research is like is to work on an individual project under the guidance
of a professor, either for a seminar talk or as an independent study course. Often tis
sort of work culminates with a presentation at Ignatian Scholarship Day. Attend
conferences. The Seaway chapter of the MAA (Mathematical Association of America)
has two local conferences each year and Canisius often sends some faculty and
students to these. We also frequently send students to the Hudson River
Undergraduate Mathematics Conference in April:
https://apps.skidmore.edu/pls/apex/f?p=115:1:4136755819932908::NO:::
Women students can attend the Nebraska Conference for Undergraduate Women in
Mathematics in late January/early February:
http://www.math.unl.edu/~ncuwm/13thAnnual/
There are also summer research programs, called REUs (Research
Experiences for Undergraduates). These typically last 8 weeks, though some are as
short as two or four weeks. Students usually live on campus and either take
advanced courses or work in teams on research projects. Students are paid a decent
stipend and often write a paper that can be presented at conferences or even get
published. We have had students attend REU’s at Carleton College, William and
Mary, Arizona, Texas A & M, and Brigham Young. Information on these programs
can be found at the sites below:
http://www.nsf.gov/crssprgm/reu/list_result.cfm?unitid=5044
http://www.maa.org/students/undergrad/
Choosing graduate schools
First think about what suits you best. Large schools have certain advantages
such as a greater variety of courses and specialties and more fellow graduate
students to work and socialize with, while smaller schools will be more intimate and
can be more supportive (but not always!). Do not let geography tie you down. It’s
good to leave Buffalo and experience other places. You should apply to at least five
to ten graduate schools. Be candid (to yourself) about your abilities. Ask for advice
from your professors and try to choose a spectrum of schools, some at a level
slightly higher than you judge yourself, some at a lower level, and some that you feel
are just the right level. Here are some places to start looking for graduate programs:
http://graduate-school.phds.org/
http://chronicle.com/article/NRC-Rankings-Overview-/124743/
http://grad-schools.usnews.rankingsandreviews.com/best-graduate-schools/topscience-schools/mathematics-rankings
http://www.ams.org/profession/career-info/grad-school/grad-school
Applying to graduate school
You should choose where to apply by Thanksgiving of your senior year. Most
graduate schools have deadlines starting in December or January. Then check out
the websites for each program and note the deadlines and what each school wants
in the way of application materials. Typically, they will want an official transcript
that you can have sent by the Registrar in Bagen Hall. They will ask for an
application fee, of course. Note that many schools will waive or discount this in
cases of financial hardship. You will need to write an essay or statement of purpose
and you should tailor this to each program you apply to. Ask faculty members for
help with this if you’re not sure what to say. Remember that Canisius has a very
good local reputation but many universities will not have heard of us. It is your job
to make a strong case. And you will need at least three letters of recommendation.
These should be from professors that know your work (and, of course, think highly
of your ability). The graduate programs will consider most carefully letters from
research mathematicians who have taught you in advanced courses, rather than
lower level teachers.
Most schools require you to take the GRE exam (Graduate Record
Examination). There are two exams, a general exam that is much like the SAT, and a
much harder subject exam that covers much of the undergraduate courses in
mathematics. Check on deadlines for those and study for them. Perhaps take a
commercial course or form a study group with other students. The Career Center
has some material, especially on the general GRE exam.
http://www.ets.org/gre/
Paying for graduate school
Many graduate programs in mathematics offer some form of financial aid.
The most prestigious form of this is a research assistantship, for which you will need
to study under a professor and work on research. More commonly, a lot of students
get teaching assistantships, for which the student will either lead small discussion
groups (sometimes called recitation sections) for students enrolled in large lecture
classes or teach a small introductory class, usually under the supervision of an
experienced teacher. Most of these pay you enough to live on, but certainly not
extravagantly. After all, they would prefer that you stay home and study rather than
be able to afford to go out. Many assistantships also cover tuition, which is a huge
financial benefit. Many graduate students in mathematics can graduate without
additional student loans.
Some schools automatically consider all applicants for these assistantships,
but some require a separate application. Check on this when you’re preparing your
application materials. Experience in grading and working for the Mathematics
Tutoring Center is excellent preparation for a teaching assistantship, but remember
that the graduate school is first interested in whether you will succeed in your
studies, and after that in how good a teacher you will be. The site below has
information on all the graduate programs in the U.S.:
http://www.ams.org/profession/career-info/grad-school/grad-school
Choosing where to go
Most graduate programs using a rolling admissions procedure. This means
that as applications come in, they sort them into three piles: definitely yes, definitely
no, and a lot of maybe’s. The yes’s will get acceptance letters immediately and the
no’s get rejection letters (which build character!). In turn, some of their accepted
students will have made other plans, so they will turn to the maybe pile and pick out
some more students to make offers to. Thus, your letters of acceptance and rejection
can trickle in gradually. If things go well, you will get acceptance letters from several
schools. Now is the time to learn everything you can about these programs. Ask your
professors, think again about what areas of mathematics you find most appealing,
and consider whether you fit the program. Some people thrive under competition
and pressure and some collapse under the same circumstances. You know best what
you need. Look at the financial aid package, but as long as you don’t need to run up
an excessive debt, don’t just take the school that offers the most money. Try to visit
the schools and meet with the graduate director. Make a point of also meeting some
of the graduate students and try to get a sense of what the program is like.
Of course, schools would prefer that you accept them as quickly as possible.
Once you select a school and commit to a program, it is very unprofessional to go
back on your word. This has happened in extreme circumstances, but it is very much
frowned on. However, before you commit yourself, if there are programs you are
very interested in but that you haven’t heard from, you can call and ask the graduate
director politely when they might be making up their minds. You can even tell them
that you have another offer and explain your deadline. Sometimes they will expedite
their decision in such cases.
Drs. Kahng and Kinsey
2/9/11