Math 581e: Algebraic Number Theory (Fall 2012) -- Syllabus



This is a graduate-level course on algebraic number theory (though undergraduates are welcome!). This course will be mostly theoretical (we will prove a lot of results), augmented by tutorials about how to compute with the objects we encounter. We will give complete proofs of the two main theorems of algebraic number theory: finiteness of class groups and the unit theorem. You will also learn how to use Sage to compute with all of the objects discussed in the course. The course textbook is available online.

Main Course Topics


In addition to general mathematical maturity (you know what a proof is, and you've written some), I will assume that you are familiar with finite groups, linear algebra, commutative rings, ideals, elementary number theory, Galois theory of fields, topology of Rn, and the Sage mathematics software.

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