Advice for beginning Math PhD Students

  1. Familiarize yourself with the requirements for the Math PhD program by clicking around our math department website. For now, focus on the “Stage I” requirements. Most students are in Stage I for one to two years.
  2. Your main goal as a Stage I student is to master the material in the three core areas: topology, algebra, and analysis. The “alpha courses” are designed to help you meet this goal. These are Math 591, 592 (topology), Math 593, 594 (algebra) and Math 596, 597 (analysis). [If you are inclined toward applied math, there is an option to substitute Applied Analysis (Math 556, 572) for topology or algebra.]
  3. Make a plan now for achieving this goal. Remember that every student is different! Your office mate with a Master’s degree may pass some QR exam immediately upon arrival. However, another may choose to take alpha courses in topology and analysis this year and save algebra for year two. Both are reasonable plans likely to lead to timely completion of Stage I.
  4. Our department publishes a list of graduate courses offered each semester. Read and admire these courses, but do not let them entice you away from the goal of Stage I: to master the material of the three core areas.
  5. You will be assigned a doctoral committee advisor, whom you will meet in August. Come prepared to that meeting with your tentative plan for and/or questions about completing Stage I. Your advisor will help you choose courses and refine your plan.
  6. Usually, the only good reason to skip an alpha course is that you have passed the QR Exam in the corresponding subject. In some cases, a student might substitute certain “beta” courses (600 level). For example, a student who has solved many hard problems in a graduate course on the same topics as Math 593 might substitute Math 614 for Math 593 and plan to take Math 594 in the winter.
  7. Be ambitious, but reasonable and flexible. If you are tempted to take all three QR exams upon arrival in August, go for it! Adjust your plan after getting the results.
  8. First year students should generally avoid “topics courses” (most 700 and some 600 level courses), intended primarily for PhD candidates. These courses are more specialized and may not prepare you as well for writing your PhD. Take courses where you will turn in regular assignments, bond with your peers over difficult problems, and allow your professors to get to know you mathematically.
  9. Remember that you are also adjusting to teaching! Taking two intense courses of your own, with problem sets and exams, may be enough. Four demanding courses plus teaching is not recommended.
  10. Revisit and revise your plans and goals regularly. It is wise to take QR exams as soon as you think you have a chance of passing. There is no penalty for failing, as long as you pass by the deadline.
  11. Looking ahead, the main goal of a Stage II student is to find a dissertation advisor. We will help you! Although you should not worry about this yet, it is never too early to get to know professors and older students, both mathematically and personally. Similarly, it is never too early to keep an eye on the Seminar Offerings  or get involved once you feel adjusted and ready.  Start  by attending Junior Colloquium, at the very least.

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Karen Smith

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