Course description: This is the first in a string of three courses, which is an introduction to algebraic and analytic number theory. In part A we'll discuss the basics of number fields (their rings of integers, failure of unique factorization, class numbers, the Dirichlet unit theorem, splitting of primes, cyclotomic fields, and more). In the sequels B and C, Kiran Kedlaya will treat local fields and zeta functions, respectively. The course will be relatively elementary; no extensive background needed. It should be of interest not just to number theorists, but to algebraic topologists etc. The plan is to cover I.1--I.10 in Neukirch's book, systematically, and supply with material from Milne's notes. You should have both.
Instructor: Claus Sorensen, csorensen [at] ucsd [etcetera]. Office hours M 2-3, or by appointment, in APM 6151.
Lectures: MWF 1-1:50, in APM 7421.
Textbook: Primarily Algebraic number theory (Springer) by J. Neukirch. As a supplement I recommend Milne's notes Algebraic number theory. You may also want to check out Lang, Frolich-Taylor, Cassels-Frolich (all with the same title).Prerequisites: Basic abstract algebra (such as 200ABC). Galois theory in particular will be useful, although we will review parts of it as we go along.
Homework: Weekly problem sets (~4 exercises)
Final exam: Take-Home. Due Monday, December 15th, 3 PM.
Grading: 50% Homework, 50% Final
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