Math 254A (Number Theory)

This was the official course web page for Math 254A (Number Theory) at UC Berkeley, which I taught in the Fall 2001 semester. The web page for Math 254B is here.

The course description and syllabus for Math 254A can be viewed here.

Note added 19 Jul 2002: all PostScript files are now compressed using Gzip to save space.

Final exam info

The final exam was distributed in class Friday, November 30, and will be due in my mailbox at 5 PM on Monday, December 10. It is also posted here [TeX, DVI, PostScript]. There will be no class meetings at the scheduled time from this point onward. However, I will have extended office hours during the week of December 3, as follows: Monday and Friday 1-5 PM (with a break for tea; find me in 1015 Evans), Tuesday 10 AM-1PM. At other times, send me email and I'll respond as soon as possible. You can also contact Frank with questions.

Final exam corrections

Contact Info

For the professor

Kiran Kedlaya
757 Evans Hall
email: kedlaya(at)
Office hours: Monday and Thursday 1-2 PM, or by appointment, or just drop by. If the door is open, come right in; if not, go ahead and knock, but I reserve the right not to answer. I'm usually in my office immediately after lecture, and generally during late morning (before noon) and early afternoon (until 3 PM). I'm often at tea in 1015 Evans from 3 to 4 PM. I also will respond to questions by email, usually even over the weekend.

For the teaching assistant

Frank Calegari
1010 Evans Hall
email: fcale(at)
Office hours: Wednesday and Friday 2-3 PM. Frank is also often at tea from 3 to 4 PM.

Homework Policy

I'm willing to be flexible about late homeworks if you let me know in advance what the difficulty is and when you expect you'll be able to get the homework in. (Sending me an email over the weekend will usually satisfy this requirement, though earlier notice, say in class on Friday, is better.) I'm not trying to be an ogre about deadlines: I'm just trying to make sure no one falls behind, which is usually the kiss of death in a course like this.

About Magma

Some problems on the homework contain references to, or request code to be written in, the computer algebra package Magma. To run Magma on the Berkeley math department systems, type magma at any Unix prompt. (If you don't have access to the math department systems, see me and I'll see what I can do about getting you such access.)

The Magma home page includes HTML documentation; the same documentation can also be found in the folder /usr/local/Magma on the department network. Print copies of the Magma manual can also be found in room 708S (adjoining the computer cluster); please do not remove these.

Magma is not free software, but the math department has a site license. This means it is possible for department affiliates (or non-affiliates enrolled in a course using the program) to install Magma on their own computers. See Paulo Ney de Souza or one of the other computer staffers on the 9th floor for details.

Problem sets

Warning: corrections have not been made to these files. See here for corrections.

Lecture notes


Required: undergraduate algebra (Math 113 or equivalent). Possibly helpful: graduate algebra (Math 250 or equivalent). More specifically, we will use basic facts about groups, rings, fields, and Galois theory. Also possibly helpful: some familiarity with classical number theory.


For the most part, I will be following the recent English translation of Jürgen Neukirch's Algebraic Number Theory, published by Springer-Verlag. I have designated this a "recommended" text, rather than a "required" text, only because of its steep price tag. I also plan to distribute lecture notes, though these may lag slightly behind the lectures.

Other books worth looking at for various reasons are:

Recommended links

The Berkeley Number Theory Seminar meets Wednesdays from 3:10 to 4:00 PM in 891 Evans, and sometimes on Friday at the same time and place. Prospective students in number theory are encouraged to attend.

If you're shopping for an advisor in number theory, check out the Web pages of Robert Coleman, Hendrik Lenstra, Arthur Ogus, Bjorn Poonen, Ken Ribet, and Paul Vojta.

Some more possibly useful links:

Kiran S. Kedlaya (kedlaya[at]math[dot]mit[dot]edu)