The pursuit of a PhD and career in mathematics is an exciting, challenging and sometimes daunting experience. The transition from undergraduate to graduate is the beginning a transition from student to professional mathematician and colleague. While you are remaining in academia, the role of a graduate student is considerably more complex than that of an undergraduate. In addition to learning how to develop a research program and solve problems (making you more an apprentice mathematician than a student), you will play valuable roles in: (i) the department's education mission as an instructor/TA; and (ii) the intellectual life of the department through a variety of venues, including: attending seminars and interacting with the visiting speakers, participating in (and organizing) reading seminars and research groups, and student chapters of professional organizations. Each of these is an important facet of the professional life of a mathematician.
Participate in seminars
Attend seminars. This is an excellent opportunity to learn about active areas of mathematics, important and interesting open problems, and various tools that can be used to tackle them.
Attend seminars outside your primary research interest(s), especially general audience talks such as: the Graduate-Faculty Talks, the Gergen Lectures and department colloquia. This broadens your view of the mathematical landscape and introduces you to ideas and machinery that can deepen your work. Mathematics is a deeply interconnected subject, and the best mathematicians are able to leverage these connections.
Interact with visitors
You are strongly encouraged to interact with visiting mathematicians (such as seminar speakers), especially those in your research areas. These interactions are valuable as they will broaden and deepen your view of the mathematical landscape and expand your professional contacts.
- The department funds a few graduate-student-sponsored colloquia each year. (These are distinct from the Graduate-Faculty Talks.) The department will provide a budget, but the graduate students will choose the speakers in consultation with the DGS (It is also recommended to discuss potential speakers with your mentor/advisor.) and organize the visit. Ask the DGS for details about the program, and submit any nominations to the graduate representatives. The 2019-2020 speakers are Jacob Lurie and Richard Schoen.
There is a lot of great advice from successful mathematicians, including:
- Terry Tao maintains an excellent and extensive collection of career advice from a number of sources.
- Dan Margalit's Mathematics Students Resource.
- Sara Billey's advice on how to be a successful student.
- Ravi Vakil's exercise for getting things out of talks.
- Katherine A. Ott's Notices article on attending conferences.
- Learn to give good talks. This is important: because more people will attend your talks than read your papers, this is how most people will know of your work. And a good talk can have a great influence on your career. (As a post-doc your current DGS was invited to apply for a tenure-track job after a seminar talk.) This is a skill that takes development and maintenance for most of us; invite critical feedback, it is invaluable. (The department's Graduate-Faculty Talks are a good place to practice.) When you attend a good talk, think about what makes it successful and incorporate these elements into your talks.
- AMS's Advice for New PhDs.
- Advice on the job search.
- The Math Dept at U Michigan has a great resource page.
Finally, CAPS offers (free) counseling on all manner of topics, including stress management and work-life balance.