Courses:

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Linear Algebra (18.700), Analysis I (18.100), or permission of instructor

You should have some familiarity with proofs. And though you need to be comfortable with matrix operations, we won't go over the first chapter on matrices systematically. Study that chapter yourself.

Artin, M. Algebra. Englewood Cliffs, NJ: Prentice-Hall, 1991. ISBN: 9780130047632.

Groups, vector spaces, linear transformations, symmetry, bilinear forms, and linear groups. I believe that all of the topics are interesting and useful. The table of contents for chapters 2 through 8 of the text provides an overview, but time constraints will force us to skip some of the topics in those chapters.

Weekly problem sets will be graded. There will be three quizzes during the regular class hour, and no final exam. To receive a passing grade for the course, you must submit solutions to at least 75% of the problems on the weekly assignments. Assuming that this is done, weighting in the final grade will be roughly 25% for the homework and 25% for each quiz.

The course outline contains reading assignments and exercises on the topic of each lecture. Going through each topic systematically in class can get boring, so I will not do that. I rely on you to do the reading. Do it ahead of time if possible. Just a few minutes before class will help your understanding a lot. Work the exercises in the course outline, but do not turn them in. Most of them should not be too hard, once the material has been absorbed. I've tried to keep the number of exercises that are pure drill to a minimum, so there may be times when you need additional practice.

The problem sets are the most important part of the course. They will contain some extensive and difficult problems, and require hard work. You won't be able to complete them in one sitting. I recommend that you get together with other students to work on these assignments. However, the solutions that you hand in must be written entirely by you. Consulting existing solutions, such as from previous years' problem sets or from the web, is not permitted.

In past years a few students have had trouble finishing their assignments on time, and fall further behind each week. To avoid the stress that this causes, and for the sake of the graders, I've instituted a firm rule: Written assignments must be handed in on the day they are due. It is better to hand in an incomplete assignment than to put it off, hoping to finish the work in the future.

I don't hand out solutions because it is hard to find interesting problems, and I want to be able to use the ones I have collected again.