Where to Go to Graduate School?
Most accredited universities have graduate programs, and the web site of a university and its catalog should have ample information about them.
The university where you attend(ed) undergraduate school may have a graduate program that interests you, but be aware that it is common practice to not attend the same university for graduate study. If you get your undergraduate degree in the mathematics department at University X, and then you go to graduate school in the mathematics department at University X, it gives the impression that you did what was most comfortable rather than accepting the challenge of applying elsewhere and entering an unfamiliar environment. Also, your understanding of the subject matter will have been shaped entirely by a single department, which is not good. Finally, when you are a graduate student in the same department where you did your undergraduate studies, faculty members may have a difficult time seeing you as other than an undergraduate student. None of these realities is ideal, though there are students who are willing to live with them.
If you selected a university for your undergraduate studies based on academics, you needed one where the major you wanted was offered, but hopefully you also checked on the structure of the undergraduate program and its reputation and whether the institution was accredited. An example of an accrediting agency is the Western Association of Schools and Colleges Senior College and University Commission (WSCUC; formerly WASC). For information, go to https://www.wascsenior.org/about/purposeofaccreditation, where it says, in part, “The WASC accreditation process aids institutions in developing and sustaining effective educational programs and assures the educational community, the general public, and other organizations that an accredited institution has met high standards of quality and effectiveness.”
When looking for a university to apply to for graduate school, your attention should be not just on a department, but rather a specific research area of the subject matter (within that department) that you want to be the emphasis of your graduate work. A few of many examples of areas of mathematics are combinatorics, probability, topology, and numerical analysis. If you want to do research as part of earning a graduate degree, you should explore the research reputations of faculty members at prospective universities in your area of interest. What is the quality of their research? What academic journal articles have they been published? How prestigious are the journals in which their articles have appeared? Faculty members in your undergraduate program may be willing to share their impressions of graduate programs elsewhere and the faculty members connected to those programs.
Preparation for Applying to Graduate School
If graduate school is the path that you decide to take, you need to be prepared for applying. Whereas applications to UC San Diego’s undergraduate programs are handled by the central campus Admissions office, applications to UC San Diego graduate programs are reviewed and decided on by the Graduate Division and the department that a student applies to. UC San Diego is referred to here just as an example. As mentioned elsewhere, it is not recommended that you attend graduate school at the same campus where you were an undergraduate student.
Long before you are ready to apply to a graduate program, carefully read all application instructions. Why? There may be undergraduate courses that faculty in the prospective department want applicants to take. Do you want to discover this in your senior year of undergraduate study, when you have no time to take additional courses?
Applying to a reputable graduate program is a highly competitive process, and faculty members on admissions committees are quite selective. Each year, there could easily be hundreds of people applying for just a few openings.
These are routinely required when applying to graduate school:
– Completed application forms, which nowadays are usually entirely online. Give yourself ample time to thoughtfully gather information and prepare responses sought in the application form. Be accurate. Your application risks being rejected due to perceived (or actual) deception.
– Undergraduate transcripts. Unofficial transcripts may be allowed during the application process, but official transcripts will be needed if you are offered admission to a program. It could take a week or two to have a transcript mailed from your undergraduate institution to a graduate institution of interest.
– List of undergraduate major courses taken and your GPA for those courses
– Letters of recommendation from people (mostly faculty members) who can attest to your capacity for excellence in graduate study in the major. Extra letters are not necessarily better; admissions committee members will be more persuaded by the quality and depth of letters rather than whether you exceeded the maximum quantity requested (usually three). For a faculty member to be able to honestly write a detailed letter of recommendation about you, s/he needs to know you as an individual. That will not happen simply because you sat in her/his class for a quarter. Did you attend class punctually, regularly, and stay for the full class period? Were you attentive and actively engaged in learning experiences? Did you frequently visit the faculty member in office hours to discuss the course material? Did you make opportunities to talk to the member about his/her research and your goals? Was the professor able to see for her/himself that you are self-driven with high standards and perseverance? Did s/he see that you have a passion for the subject and are exceptionally talented in it? It is up to you to help faculty members get to know you professionally. If you do not make that happen long before applying to graduate schools, the letters of recommendation that members write for you may be weak and looked at nonpersuasively by admissions committee members. For example, a letter that says little more than that you earned a certain grade in a certain course taught by the author is not telling readers much that cannot be independently determined from your transcript.
– Scores on the General Record Examination (GRE) General Test transmitted from Educational Testing Service (ETS) directly to each department that you apply to. (A graduate program may also require that you take a GRE subject test.) GRE tests take months of frequent (ideally, daily) study to prepare for. At the ETS website, you can read the rules governing the GRE test(s) that you need to take.
– Personal statement. This is your only opportunity to “speak” directly to an admissions committee. Use it wisely. You are communicating with people whose entire impression of you is formed from the application materials. What do you want committee members to know that will give them a better understanding of you as a candidate for graduate study in the major? As you write, be aware of how what you say will be received by readers. You will not be able to see their reactions and then respond with qualifying information. You get one chance at a personal statement, and so it needs to be the best that you can make it. You want to be admitted to their program; if it is a reputable one, admissions committee members will look for top candidates who are likely to complete the program in the allowable time and add to its prestige.
– Answers to additional questions. Answer completely and truthfully, but also succinctly.
Regardless of whether a graduate program’s application materials state that prior research work is a requirement, you are wise to consider engaging in meaningful research under faculty supervision while you are an undergraduate student. It is good to allow yourself at least a year to do this. The UC San Diego Department of Mathematics encourages students to see faculty members whose research areas interest them to inquire about possible research work. The Department has no formal way channel for announcing when research positions are available.
Other sources for learning about research opportunities:
(1) Research Experience for Undergraduates (REU): Typically run over a summer, they offer research in small groups in different areas of mathematics. They are a great way to see other university campuses and interact with a new set of professors and researchers. The Mathematical Association of America lists REU positions.
(2) The UC San Diego Research Experience & Applied Learning (REAL) portal, “offers research, internship, international, service learning, entrepreneurial, leadership, and other co-curricular opportunities that help students build real-world skills by applying knowledge gained in the classroom”. An advantage of the REAL is that it allows students to post a brief profile of themselves and their career goals.