Preliminary Exams

A Ph.D. graduate student in mathematics must pass two preliminary exams to successfully meet their graduation requirements. A description of this requirement can be found on the Degree Requirements page. Below is a list of resources available for those preparing for the exams. The dates of the upcoming exams can be found on the Academic Calendar

Syllabi

Below is a list of the syllabi for the exams.

Recommended Textbooks

Algebra:

  • D. Dummit and R. Foote, Abstract Algebra: Chapters 1–14 and Appendix I, but skipping sections 9.6, 10.4, 10.5, 11.5.
  • T. Hungerford, Algebra
  • N. Jacobson, Basic Algebra I
  • S. Lang, Algebra

Topology/Geometry

  • J. Munkres, Topology
  • G. Bredon, Topology and Geometry
  • J. Lee, Introduction to Smooth Manifolds
  • J. Lee, Introduction to Topological Manifolds

Analysis

  • C. Apostol, Mathematical Analysis
  • G. Folland, Real Analysis
  • H. Royden, Real Analysis   
  • W. Rudin, Real and Complex Analysis

Student Led Study Groups

Â鶹ÒùÔº may (and are encouraged to) form student led study sessions for any of the three prelim topics.  Talk to the Graduate Assistant for information about possible funding.  It is recommended that you speak with graduate students who have already passed the exam to discuss study strategies as well as to get solutions to past exams.