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
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
Final exam corrections
- 3: should refer to Problem Set 4.
- 7: Assume that K is not L.
- 10: in (a), the degree should be 6, not 5, or else the other parts
will not work.
For the professor
757 Evans Hall
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
1010 Evans Hall
Office hours: Wednesday and Friday 2-3 PM. Frank is also often at tea from
3 to 4 PM.
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.
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
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.
Warning: corrections have not been made to these files. See here for corrections.
- Solution set for Problem Sets 1 and 2: TeX,
- Problem Set 1 (due Sep. 5): TeX,
- Problem Set 2 (due Sep. 10): TeX,
- Problem Set 3 (due Sep. 17): TeX,
- Problem Set 4 (due Sep. 24): TeX,
- Problem Set 5 (due Oct. 1): TeX,
- Problem Set 6 (due Oct. 8): TeX,
- Problem Set 7 (due Oct. 15): TeX,
- No problem set due Oct. 22.
- Problem Set 8 (due Oct. 29): TeX,
- Problem Set 9 (due Nov. 5): TeX,
- Problem Set 10 (due Nov. 14): TeX,
- Problem Set 11 (due Nov. 21): TeX,
- Final Exam (due Dec. 10): TeX,
- August 27 (Mon): TeX,
- August 29 and 31 (Wed/Fri): TeX,
- September 5 and 7 (Wed/Fri): TeX,
- September 10, 12 and 14 (M/W/F): TeX,
- September 17 and 19 (M/W): TeX,
- September 19 (Wed) supplement: TeX,
- September 21 and 24 (F/M): TeX,
- September 26 (Wed): TeX,
- September 28 (Fri): TeX,
- October 1 and 3 (M/W): TeX,
- No new handout October 5: continuation of the previous handout.
- October 8 and 10 (M/W): TeX,
- October 12 (F): TeX,
- No classes October 15, 17, 19.
- October 22 and 24 (M/W): TeX,
- October 26 (F): TeX,
- October 29 (M): TeX,
- Supplement on the relative discriminant: TeX, DVI, PostScript
- October 31 (W): TeX,
- No class November 2.
- No new notes November 5 or 7; continuation of the previous handout.
- November 9 and 14 (F/W): TeX,
- No class November 12 because of the Veterans' Day holiday.
- No new notes November 14 or 16: continuation of the previous handout.
- November 19 and 21 (M/W): TeX,
- No class November 23 because of the Thanksgiving holiday.
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
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:
- Borevich and Shafarevich, Number Theory
- Cassels and Fröhlich, Algebraic Number Theory
(just the early chapters, for starters)
- Fröhlich and Taylor, Algebraic Number Theory
- Ireland and Rosen, A Classical Introduction to Modern Number
Theory (for background)
- Janusz, Algebraic Number Fields
- Marcus, Number Fields (lots of examples)
- Pollard and Diamond, The Theory of Algebraic Numbers
(assumes minimal prerequisites)
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
Ken Ribet, and
Some more possibly useful links:
- J.S. Milne has
printable notes from a variety of courses, including Algebraic Number Theory.
- The Number Theory
Web is the home of all things number-theoretic on the Web.
Kiran S. Kedlaya (kedlaya[at]math[dot]mit[dot]edu)