Office Hours: M 3:00-4:00pm, W 1:00-2:00pm, F 2:00-3:00pm
Prerequisites: Math 250A required, 115 and 250B recommended
Required Text: Lang, Algebraic Number Theory
Recommended Reading: Cox, Primes of the form x^2+ny^2
Syllabus: Roughly, we will cover algebraic number theory from
scratch, using Lang's book with examples and motivation from other
sources. Advanced topics such as class field theory and Tchebotarev
density will be discussed with an emphasis on the statements and
applications, so proofs of these will be omitted, and they will be
treated in the classical language of ideals rather than ideles and
Grading: Homework: 2/3rds of grade, final paper: 1/3rd of grade.
Homework: Homework will be assigned weekly, on Mondays, except
that they will be assigned the previous Friday when Mondays are holidays.
Final paper guidelines
The purpose of the final paper is twofold: to learn in detail about a topic
not covered in class, and to practice mathematical writing. As such, it will
be graded as much on clarity of writing as on any other factors.
The paper should be roughly 8-10 pages in default tex formatting. Using
latex with the amsart documentclass is recommended, but if you are
already familiar with another flavor of tex, you may use that instead.
There is no requirement of originality, but of course the paper should
be entirely in your own words.
The paper should be fully self-contained, and written like a research
article. In particular, it should have a brief introduction explaining the
main material to be discussed, and ideally some explanation of why it is
Material from lecture may be used without citation. Material closely
related to but not covered in lecture should be used with a specific
statement of the result needed, and a citation. Many of you will also have
to use results from other fields. These should always include a specific
statement and citation, and you should consult with me on which results
you are quoting.
I will attempt to type up and post lecture notes. If I have not prepared
notes for a lecture, I will give advance warning. Actual problem sets
are posted below, so feel free to ignore exercises mentioned in the