**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.)

-- [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).

**Assignments:**

- HW 1 (Due 10/11): Problem set 1
- HW 2 (Due 10/18): Problem set 2
- HW 3 (Due 10/25): Problem set 3
- HW 4 (Due 11/01): Problem set 4
- HW 5 (Due 11/15): Problem set 5
- HW 6 (Due 11/22): Problem set 6
- HW 7 (Due 11/29): Problem set 7
- HW 8 (Due 12/06): Problem set 8