Abstract algebra is about groups, rings, and fields, and is basically impossible. But if you can make any sense of it, you might find it slightly interesting. Groups are hopelessly complicated, unless they're finite and abelian, in which case they're insultingly simple. Rings seem very dry, but eventually turn out to be connected to geometry, which makes them interesting; but it takes years to get there, so why bother? Fields seemed pretty manageable, until Galois related them to groups again, which made them hopelessly complicated. In any case, abstract algebra has had a profound effect on our culture, as the following figures show:
Fig.1 - Evariste Galois, 1811-1832.
Fig.2 - Bowie at his best, 1977.
Prerequisites
Math 54, officially, but math 55 may also be helpful.
Textbook
There is no required textbook for the class - You can use the notes George and I wrote up as the textbook. However, you are encouraged to consult other sources. Some texts I like are "Algebra" by Artin, "Topics in Algebra" by Herstein, and "Abstract Algebra" by Dummit and Foote.
Grading
The grade is out of 400 points, distributed as follows: 125 points for each of two exams, 120 points for HW (8 assignments at 15 points each), and 30 points for class participation (coming to lectures, office hours, etc).
You must take at least one exam to pass the course. In the event of a serious medical emergency, you may miss ONE exam if you have written documentation of your illness. You cannot miss both exams.
Homework
Homework is due every Monday (and also Wednesday on an exam week), either in class or under my office door by 4PM. No late Hw will be accepted, so if you can't finish just submit what you have so far.
In doing your homework, you should work with others, but please write the names of your collaborators at the top of the assignment. You must write clearly - points will be taken off if your explanations are confusing or illegible. When writing proofs, you must use complete sentences.
Exams
There are two exams, on July 17th and August 14th, weighted equally at 125 points. Both will take the entire class period and will be held in 70 Evans as usual.
Lectures
We meet for two hours each session. The first fifty minutes will be a lecture. After a ten minute break, the second hour will be a problem session.
