Graduate Program Description

A central feature of the Columbia VIGRE proposal is a more cohesive teaching of the traditional branches of mathematics, with an exposure at an early stage to other scientific disciplines. In particular a restructured "core curriculum" will provide all new math graduate students - independently of their ultimate specializations - with a broad yet tightly interwoven introduction to the basic themes and techniques of modern mathematics.

The material is distilled from the most classical topics to state-of-the-art developments, and cuts across the traditional subdivisions. It is covered in a series of six one-year courses:

with large overlaps, and where the same ideas occur repeatedly in different guises. Besides lectures, the courses all incorporate round table discussions led by advanced graduate students and postdoctoral fellows that will be supported by the proposal.

All first year Ph.D. students will be required to take at least 3 of the 6 courses. Students taking Analysis and Probability can elect to take only one of the two follow-ups to Analysis and Probability I (either Analysis II or Probability II). Students taking Commutative Algebra can take one or both of the follow-ups (Algebraic Number Theory or Algebraic Geometry). First-year qualifying exams are given at the end of the first year, and consist of exams on the material in each of the courses. First year students are required to pass three qualifying exams. Second-year students are strongly encouraged to attend those of the courses they did not take in their first year.

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