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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 corecourses forming the basis of the Qualifying Review (QR) exams are shown in boldface;
  • advanced courses 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 page. See in particular the current course offerings, the list of math graduate courses, 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 Some of those lists may be out of date; ditto for the table above.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 math-grad-office@umich.edu.