Math 371 - Summer 2011

Instructor: Ted Chinburg

Lectures MWTF 1 - 3:15 p.m., room 3C4 of DRL labs

Office: DRL 4E4, Ext. 8-8340.

Office hours: These will be on Skype, at times to be decided in class, and by appointment

E-mail: ted@math.upenn.edu

Math. Dept. Office: DRL 4W1, Ext. 8-8178.

Math. Dept. Undergraduate Program Information

Current homework and lecture schedule

Homework

Homework assignment 1 (Due Tuesday, May 31).

Homework assignment 2 (Due Monday, June 6)

Homework assignment 3 (Due Monday, June 13).

Homework assignment 4 (Due Monday, June 20).

Homework assignment 5 (Due Monday, June 27).

Homework assignment 6 (Due Thursday, June 30).

Course Guide

Course Goals:

This course continues math 370 from the spring semester of 2011. The focus of the course will be on constructing precise and complete mathematical proofs. Topics will include:

Ring theory
Factorization
Modules
Canonical forms of matrices
Field theory
Galois theory
Some further group theory, as time permits

Texts:

``Algebra" by Michael Artin, 3rd edition. The 2nd edition is also acceptable.

This is the book used in math 370 in the spring of 2011. I would strongly recommend that you get an account on library.nu. This is an amazing site for downloading texts of all kinds, including many mathematical texts which are by now almost impossible to obtain in print. Here is some additional advice about how to use the library.nu web site:

Once you've registered to use library.nu, your can search for book using the search window at the upper right corner of the library.nu web page.

If your search is successful, you will see a window with a picture of the book. Click on the name of the book. This will take you another page with a list of 'external links'. Clicking on one of these will lead you to a page from which you can download the book in one format or another. You may need to enter the password which is listed on the 'external links" page.

You may need to download some plug-ins to see some formats in which the books are available, e.g. the djvu plug-in, but this is usually straightforward.

Some of the downloading services create time delays in order to try to convince users to pay for premium services (which are not in fact very expensive). To avoid such delays, try downloading at times that are not likely to be popular with other users.

Electronic and web resources:

We will be using several different kinds of software to talk about course material. If you have time, it would be a good idea to try out some of the software below before we use it in class, if you don't already use it on a regular basis. In some cases, I would appreciate it if you could send me the information I will need to contact you, as described below.

We'll use Skype during online office hours as well as during course podcasts. It's possible to carry on a conference call with 24 people on Skype, and we have only 8 class members at the moment. So we can in fact have a conference call which includes everyone in class. Please send an e-mail to me at ted@math.upenn.edu with your Skype name so that I can put you on conference calls. If you think there may be times when it would be more convenient to reach you by phone, please also send a phone number I can use.
From time to time, I will put both streaming and downloading video on the web.
During conference calls, I will be using an online white board available from skrbl.com. Have a look at this sample white board. Feel free to write a message on the white board to test it! (PG-13 messages only, please.) At the start of a conference call I will send out the address of the whiteboard we will be using that day. Everyone should be able to write and to draw pictures on the whiteboard.

Office hours:

By appointment and by Skype in the evenings.

How to make attending lectures efficient:

Before each lecture, check the current homework and lecture schedule, and read the appropriate parts of the text. After each lecture, you should review your lecture notes, reread the corresponding sections of the book and solve related homework problems.

Homework:

Homework will be due at the beginning of the first class in a given week. There will be two kinds of problems on the homework.

The first kind, labelled Type A, are problems you should work on and write up on your own. The purpose of these problems is to provide practice in writing complete proofs and mathematical arguments.
The second kind of problem, labelled Type B, are problems you can work on with one or two other students. I will ask people to be prepared to explain at the board during class the solutions to Type B problems which they worked out with their group. You will not need to turn in written solutions to Type B problems. The purpose of these problems is to get some practice at explaining mathematical ideas and arguments to other people.

There will be no class on Monday, May 30, because of the Memorial Day holiday. So the first homework set will be due Tuesday, May 31, and you should be prepared to discuss the Type B problems in class on the homework that day.