A Ph.D. graduate student in mathematics听must pass two preliminary exams to successfully meet their听graduation requirements. A description of this requirement听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.听
Syllabi
Below is a list of the syllabi for the exams.
Recommended Textbooks
Algebra:
- D. Dummit and R. Foote, Abstract Algebra: Chapters 1鈥�14 and Appendix I, but skipping sections 9.6, 10.4, 10.5, 11.5.
- T.听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,听Introduction to Topological Manifolds
Analysis
- C. Apostol, Mathematical Analysis
- G. Folland, Real Analysis
- H. Royden, Real Analysis听听听
- W. Rudin, Real and听Complex Analysis
Student Led Study Groups
Students may (and are encouraged to) form student led study sessions for any of the three prelim topics.听 Talk to the Graduate Assistant for information about possible funding.听 It is recommended that you speak with graduate students who have already passed the exam听to discuss study strategies as well as to get solutions to past exams.