User:Marty/UCSC Math 222A Spring 2009

=Syllabus=

Mathematics Covered
The following is the official course guide description of the class:
 * Topics include algebraic integers, completions, different and discriminant, cyclotomic fields, parallelotopes, the ideal function, ideles and adeles, elementary properties of zeta functions and L-series, local class field theory, global class field theory. Courses 200, 201, and 202 are recommended as preparation.

We will follow these topics pretty closely, though in a different order and we will probably not get to class field theory within the 10-week quarter.

Text, Exercises, and Lecture
We will be following lecture notes, taken from a course by Marty's advisor Benedict Gross in 1999. These notes, taken by an audience member Sean Sather-Wagstaff, are quite thorough and full of examples. Gross's course was based somewhat on unpublished notes of his advisor, John Tate. The typed notes have been reproduced here, with permission from Gross.

Exercises will be written and due weekly. It is expected that students collaborate in completing these exercises. However, each week, one student will be required to present solutions to exercises for approximately 50 minutes.

Each week, there is approximately 3 hours and thirty minutes of class time. You can expect these 210 minutes to consist of approximately:
 * 10 minutes of breaktime.
 * 150 minutes of direct lecture and discussion.
 * 50 minutes of student lecture about exercises.

Grades
Grades will be determined by the quality of their problem solutions, as evidenced by written work and presentation. A final problem set will be given instead of an in-class exam.

Administration
All details of the course will be given on the SlugMath wiki. The URL for this course is. Students should create an account on the wiki by going to the wiki, and creating an account. Students should not edit the wiki, outside of discussion pages, without permission. Students can discuss problems and their solutions, using the discussion pages attached to wiki pages and user pages. Discussion and collaboration is highly encouraged.

For additional information and advice, Marty can be contacted easily by e-mail at weissman AT ucsc DOT edu. Office hours are readily available by appointment.

=Lecture Notes=

Lecture notes from Gross's course, from 1999, are contained in the following five PDF files:


 * [[Image:GrossNotes1.pdf]]
 * [[Image:GrossNotes2.pdf]]
 * [[Image:GrossNotes3.pdf]]
 * [[Image:GrossNotes4.pdf]]
 * [[Image:GrossNotes5.pdf]]

I am "whipping up" these notes into a more complete and prettier-looking book. The current draft can be found here:
 * [[Image:NumberTheory.pdf]]

Here are some final problems to work on. Please turn in (slide under my office door) as many problems as you are able to do by Wednesday, June 10, at 5:00 pm:
 * [[Image:FinalProblems.pdf]]

Thanks to Ted for sending in typo-reports on a regular basis -- the book is much improved, and I encourage all readers to report any errors to Marty.

Also, Ted has written a short SAGE notebook for this class. Quoth Ted, "On a different note, I created a notebook on sagenb.com that demonstrates how you can use sage to do the calculation portions of the problems from chapter 2. I have it published at I have a few changes in mind still, but right now it should be useful to anyone who wants to know how to do these simple calculations."

SAGE is a fantastic piece of software to play with, especially for number theory. It "wraps" other software like PARI, GAP, and many many others, so you don't really need anything else. It will even wrap software like Maple, if you have Maple installed on your computer. A standard distribution of SAGE includes many other software packages -- essentially all that are open source.

=Week-by-week=

Week 1

 * Days: MW, March 30, April 1.
 * Admin: Introductions. Syllabus.  Notes.  The Wiki.
 * Math: Lattices.  Some linear algebra over $\ZZ$.  The discriminant.  Integrality.

Week 2

 * Days: MW, April 6,8.
 * Problems:
 * Math:

Week 3

 * Days: MW, April 13,15.
 * Problems:
 * Math:

Week 4

 * Days: MW, April 20,22.
 * Problems:
 * Math:

Week 5

 * Days: MW, April 27,29.
 * Problems:
 * Math:

Week 6

 * Days: MW, May 4,6.
 * Problems:
 * Math:

Week 7

 * Days: MW, May 11,13.
 * Problems:
 * Math:

Week 8

 * Days: MW, May 18,20.
 * Problems:
 * Math:

Week 9

 * Days: W, May 27.  Monday is a holiday!
 * Problems:
 * Math:

Week 10

 * Days: MW, June 1,3.
 * Problems:
 * Math: