Applying to graduate school is similar to applying to college, except that you don’t need to apply for financial aid, because almost all graduate programs admit students with full support (tuition, benefits like health insurance, and a small salary) in the form of a teaching or research assistantship.
A Master’s Degree in mathematics generally allows you to get a more interesting or better paying job than you would get with a Bachelors Degree - it can open up the possibility of going into industry or teaching at a community college, for instance. And some people decide to start in a Master’s Degree program and then continue on with a Ph.D., although students in a pure mathematics Master’s program are less likely to receive full support from the institution. So if you are planning to get just a Master's degree, then in contrast to a Ph.D. program, you will probably end up paying for it yourself.
Information on Master’s degree programs: www.ams.org/profession/career-info/grad-school/emp-masters.
If you are planning on going to graduate school in mathematics, you should take as many math courses as possible while at Hamilton. In addition to the courses required for the major, Complex Analysis (318), the Senior Seminar in Topology (437), and Functional Analysis (315) are highly recommended.
Consider also the study abroad program in Budapest, Hungary (www.budapestsemesters.com). This semester-long program for undergraduate mathematics students is taught in English, and is a great way to get some extra preparation for graduate school along with a chance to take math courses that may not be offered at Hamilton.
Since part of your graduate work will include independent research, spending a summer doing mathematics research as an undergraduate serves as excellent preparation for graduate study. There are many undergraduate research programs (Research Experiences for Undergraduates) around the country, and all of them are very competitive. Below are some links to REU’s in the US:
In most of the REU programs, a group of 10 or so undergraduates work on a research team with a faculty member from the host institution. Students are granted stipends and sometimes assisted with housing and travel.
Talk with your advisor and/or any other math professor about your decision to go on to graduate school in mathematics. For help in choosing a program, browse the following websites, with links to graduate math department web sites and additional information:
It is not necessary to go to one of the top schools in order to get a good graduate education and a decent job once you graduate. You should probably plan to send out 5-8 applications, including one to a safety school. Do not apply only to schools in the top 10. If you know the area of mathematics that most interests you, it is better to attend a graduate program that is strong in that area rather than a more highly ranked program that is weaker in that area. If you don’t yet know the area of mathematics that most interests you, it is probably better to attend one of the larger programs that has researchers in a wide variety of fields.
Due dates for application materials usually range from early December to late January. Three important parts of your application are GRE scores, a personal statement, and letters of recommendation.
The GRE General Test is analogous to the SAT for undergraduate admissions. Information about the general test is available here: www.ets.org/gre.
More important for admission to a graduate program is the GRE Subject Test. About 50% of this test is Calculus, 25% algebra, and 25% other topics (real analysis, discrete math, general topology, geometry, complex variables, probability and statistics, and numerical analysis). Information about the subject test, including a practice booklet, is available here: www.ets.org/gre/subject/about/content/mathematics.
Find practice problems along with solutions for the subject test at this blog: sfmathgre.blogspot.com
Princeton Review has a book called Cracking the GRE Mathematics Subject Test: www.amazon.com/Cracking-Mathematics-Subject-Graduate-Preparation/dp/0375429727.
Plan to have taken both GRE tests by early fall. Most departments will not accept subject test results from exams taken later than December.
You will need 3 letters of recommendation from faculty members who know your work well, so make sure you get to know some of your professors so that they can write you a good letter. Request a recommendation letter in person and not by email, and be sure to give your letter writers plenty of advanced notice.
Try to visit the departments you are most interested in, and talk to both graduate students and faculty. Here is a slightly outdated and perhaps overly extensive list of questions to ask when choosing a graduate school: www.toroidalsnark.net/gradschoolqs.html.
As mentioned above, acceptance to most graduate programs in mathematics comes with a teaching/research assistantship or fellowship. A very competitive fellowship is offered by the National Science Foundation: www.nsfgrfp.org.