Course description: This is the first in a string of three courses, which is an introduction to algebraic and analytic number theory. In part I we will discuss the basics of algebraic number fields (their rings of integers, failure of unique factorization, class numbers, the Dirichlet unit theorem, splitting of primes, cyclotomic fields, and more).
Instructor: Claus Sorensen, csorensen [at] ucsd [etcetera]. Office hours by appointment in APM 6151.
Lectures: MWF 11-11:50, in APM 5402. (Beginning Fri Sep 29th.)Textbooks/notes:
-- [Neu] J. Neukirch, Algebraic Number Theory, Springer Berlin Heidelberg, 1999. (E-version available here.)
-- [RME] M. Ram Murty and J. Esmonde, Problems in algebraic number theory, Springer, New York, 2005. (E-version available here.)
-- [Bak] M. Baker, Algebraic Number Theory, Notes, v. 2017 (Georgia Tech).
-- [Mil] J. Milne, Algebraic Number Theory, Notes, v. 2017 (Univ. of Michigan)
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: Almost weekly problem sets (8 altogether, ~5 exercises each) posted below, due Wed in class; cf. the calendar.
Midterm exam: In-class, Wednesday Nov 8th.
Final exam: Take-Home. Due Tuesday, December 12th, 3 PM.
Grading: 30% Homework, 30% Midterm, 40% Final (you must take the final to pass the course).