Graduate Courses in Mathematics
A typical graduate student entering the pre-PhD program will usually spend one or two years (depending on their previous background) taking classes in preparation for the PhD qualifying examinations.
In the first year (which may be skipped by students with a strong background), students usually take three 500 level sequences, chosen from 544/5/6 algebra, 513/4/5 analysis, 531/2/3 topology/geometry and 564/5/6 probability/statistics. In the second year, students usually take three 600 level sequences, chosen from 616/7/8 real analysis, 634/5/6 algebraic topology, 647/8/9 abstract algebra, 637/8/9 differential geometry (offered every other year), and 616/672/673 probability theory (offered every other year).
The PhD qualifying examinations are taken in two of the 600 level sequences chosen from the following three categories: (1) algebra; (2) analysis or probability; (3) geometry or topology. Students are to at least complete a 500 level sequence in the third area complementary to the two areas in which they take their exams. After passing the PhD qualifying examinations, students take Advanced Courses and Seminars, as well as reading courses in their chosen area of specialization.
You can find out more about graduate courses offered from the following links: