Considering Grad School FAQ:
Over the years I have had a number of students come to me with questions about going to graduate school in mathematics. I have collected some of the most common questions, along with my answers. Please remember that these answers reflect my personal opinions. Make sure that you get lots of other advice as well!
Prospective Graduate students should consult the Graduate Program Webpage for specific details on applying to and completing the Math Department's graduate program.

Question: How much does graduate school cost?
Answer: It may cost almost nothing. Most mathematics departments support most of their students through fellowships (i.e. free money) or assistantships (i.e. teaching of grading papers). This support often covers the full costs of tuition as well as living expenses, although there may be some fees to pay. Also, some schools do not include tuition as part of their support. You should read the support offer very carefully to determine exactly what is covered and what isn't.
It does happen that a school will accept more students than it has resources to support. In this case, support decisions may be based on the strength of the student's academic record in relation to the chosen program of study.
Very strong students should consider applying for outside support. Of particular note is the National Science Foundation Fellowship program. The preliminary application has an early November deadline. Application material may be downloaded from the above source. (At Purdue, the form may be obtained in room 160 of Young Grad House). The final application is due in December.
The Department of Defense also has three separate fellowship programs, each with its own application. Their deadline is midJanuary. There are also several programs for minorities. We should have fellowship information available on the Math Department Home Page shortly under Careers and Internships/Graduate School.

Question: Are my grades good enough?
Answer: There is a broad spectrum of graduate schools in the U.S with widely varying admission standards. The best advice is ``give it a try''. Some schools will accept marginal students for the Master's program on a `probationary' basis, insisting that they `prove themselves'. In such cases, they may not supply much in the way of support.
The most important factors in most admission decisions are: (a) your grades in math and mathrelated subjects (b) the courses you took (see below) (c) your recommendations and (d) the GRE scores (The Math Subject Area Test).
The importance of the recommendations cannot be over emphasized. They are weighed very heavily in admission decisions. They should be from mathematics professors. Many students feel that their professors do not know them well enough to write a recommendation. This is often a mistake. The professor knows them through their work. The good students stand out.
One final comment. You should also consider graduate work in a mathematics based field such as Applied Statistics (Master's level), Operations Research (often taught in Industrial Engineering Departments), Quality Control, Economics, Business, etc. Some schools even seek mathematics students for social science departments. Another possibility would be graduate work in Mathematics Education. This option is available even if your undergraduate degree is not in Math Ed. You should be aware, however, that many school corporations are reluctant to hire at the Master's or Ph.D. levels. They feel that such individuals are "over qualified" for their positions. Thus, an advanced degree in mathematics education is often a jumping off point for an academic career in education.

Question: You mentioned that I should take the `right' classes. What are the `right' classes?
Answer: For grad school in math, linear algebra, real analysis and abstract algebra are absolutely essential. Taking the honors versions (where available) is almost essential. You should also squeeze in as many other math classes as you can. Other valuable classes would include a second course in linear algebra, complex analysis, advanced calculus and topology.
A high ability student, who is hoping to go to one of the top ten graduate schools would typically be taking graduate classes by the senior year. Often, graduate classes can replace undergraduate classes in your program.
Warning: Graduate classes may be hazardous to your grades! This is only for the strongest of students. Such a program must be chosen only after careful deliberation with your professors and counselors.

Question: Is there a foreign language requirement for graduate school?
Answer: Yes. Most mathematics graduate programs demand a reading knowledge of one or two foreign languages. Often, these must be chosen from a specific list. Purdue only accepts French, German or Russian. If you have not had sufficient language study as an undergraduate, then you will probably need to take additional course work in graduate school. Most universities have reading classes designed specifically to help graduate students meet this requirement.

Question: Can I enter graduate school in the spring?
Answer: Some graduate schools will accept you for the spring. However, it is not recommended. By spring, most of the funds for support of graduate students will already be committed, so you may not get any support until the fall.

Question: When should I take the Graduate Record Examination?
Answer: For fall admissions, you should plan on taking the GRE in October of your senior year. If you miss October, December might also work, although some schools may not get the scores in time. (It can take as much as six weeks for the scores to become available.) Many application deadlines are early to mid January. However, a few are mid December. For spring admissions, contact the particular graduate school. Many programs require or encourage applicants to also take the GRE Math Subject Exam. Your application will certainly be more competetive if you take this exam and do well on it
Test dates and application material is available online. It is also available from the Dean of Student's Testing Service in 240 Schleman Hall.

Question: How will an advanced degree change my job opportunities?
Answer: The answer here is, of course, very dependent upon individual circumstances. Many positions in industrial "research and development" require at least a masters degree, either in mathematics or some related field. Often such people would be working closely with engineers, designing and testing new products. Similar comments would apply to Ph.D.'s in industry. For more information on careers in mathematics, see the Math Department Home Page: Careers and Internships.
For academic work at a university, a Ph.D. is required. The market for native speakers of English, whose primary interest is in teaching (as opposed to research), is very tight, but not impossible. For students seeking positions which allow time for research as well as teaching, the market is extremely tight and is expected to remain so for some time.

Question: How do I go about selecting a graduate school?
Answer: The graduate school must be selected to match your abilities. Most college libraries have information on graduate schools, including several rankings of graduate mathematics programs. (For example, see ResearchDoctorate Programs in the United States: Continuity and Change). You should also ask your professors for advice. (At Purdue, the Undergraduate Library has such information.)
Another source of information is the publication Assistantships and Fellowships in the Mathematical Sciences. This is published in the fall by the American Mathematical Society. It lists the assistantships and fellowships available for the following academic year. Copies are available in the Math Library and the Graduate Office (Math 630).
You should also check out the home page for any schools which interest you. The Math Department Home Page has a link to an extremely extensive list of math home pages.

Question: How important is my choice of graduate school?
Answer: It depends upon what your career goal is. If your primary goal is to do research at a university, then the graduate school is crucially important. At the best graduate schools, you will be exposed to the most current topics of research from the leaders of the field. A good recommendation from such a person can go a long way in helping to launch your career, particularly in the current tight market.
If your primary interest is in college teaching, then the choice is not as important. A small college would definitely prefer that you come from a nationally recognized graduate school. However, their main concern will be how well you do in a classroom.
For industrial work, the choice matters, but not nearly as much as in academic research. A company would be mainly interested in the over all strength of the academic program and its relevance to their needs. Often, companies recruit from schools where they have had success before.

Question: What is graduate school like?
Answer: As a beginning graduate student, you would usually take two to three advanced mathematics classes per semester. You would also be teaching classes (unless you had a fellowship). This sounds easy. It isn't. Graduate classes are vastly more demanding than undergraduate classes. Also, teaching takes an immense amount of time and energy.
At many universities, a Master's Degree may be earned without writing a thesis. Typically, a Master's Degree requires two years.
The Ph.D. program is, of course, more demanding. The amount of time required depends upon the student's preparation. It can take as few as four years. This is rare, however. Many students take six to sixandahalf years.
Most schools require that Ph.D. candidates pass "qualifying exams." At Purdue, these are a series of four written exams based on courses that the student has taken. They are usually taken during the second year of graduate study.
The next step, after "qualifiers", would be to find a thesis advisor. You begin by selecting an area of mathematics which interests you. You then approach a professor who specializes in this area and ask if s(he) would be willing to serve as your thesis advisor. Your thesis advisor would suggest what further classes you should take. The advisor might also recommend specialized reading. Eventually, the advisor will suggest a research topic for the thesis. At Purdue, you would also be required to pass `advanced topics' exams. The advanced topics exams are more specialized and usually cover topics related to the thesis.
The thesis must represent original, publishable research. This is not as frightening as it sounds. The advisor is expected to provide considerable guidance in the research. After the work is completed, you must `defend' the thesis. In mathematics, this means that you will give a talk to a committee of professors, outlining the major points of the thesis. It is very rare that a thesis is rejected. Usually, by the time the defense of the thesis comes around, the student is more of an expert on the thesis topic than all but the advisor.