Courses in the Mathematics Ph.D. Program at the University of Michigan
(general guidelines)

This page provides general guidance regarding course choices for the students in the Ph.D. program in Mathematics at the University of Michigan. (For the AIM program/courses, please consult this page.) Its main goal is to help incoming graduate students design their first-year curriculum. In the table below, the courses are categorized, very roughly, into four tiers:

  • introductory courses aimed at advanced undergraduates, M.S. students, and Ph.D. students from other programs;
  • courses presenting foundations of the respective fields of mathematics at the beginning graduate level; among them, the core courses forming the basis of the Qualifying Review (QR) exams are shown in boldface;
  • advanced┬ácourses which require considerable familiarity with the foundations of the corresponding subject, either by succeeding in the foundational courses or by passing the QR exams in that subject; and
  • more specialized courses dedicated to topics of current research interest.

This classification is by no means rigid, and is provided as a general guidance only. Course syllabi may vary depending on year, instructor, and choice of topic. Please consult the current course descriptions for up-to-date information. The first priority for the incoming first-year student is to pass the QR, which requires passing approved combinations of written exams and core courses; please read Sections II-III on this page. The syllabi for the core courses (or, equivalently, for the QR exams) can be found here.

discipline introductory foundations advanced topics
Algebra 493-494 593-594 612-615, 711 619, 637, 715
Algebraic Geometry 631-632 731-732
Analysis 555 596-597 601-605, 650 609, 701-710, 793-794
Combinatorics 565-567 664 665, 669
Differential Equations 556-558, 572 656-658 756
Geometry 531-532 591 635 636
Logic 582 681 682-684 781
Number Theory 575 675-679 775-777
Probability 525-526 625-626
Topology 590 591-592 691-696 697, 791-792, 795-797

Additional information can be found on the graduate program website. See in particular the current course offerings, the list of all math graduate courses (including those not currently offered), and the list of all courses by area (including those not intended for graduate students in math). Some of those lists may be out of date; ditto for the table above. Please send corrections to