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Algebra I (18.701)

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

Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory. It covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.

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. I rely on you to do the reading. Do it ahead of time if possible. Work the exercises in the course outline, but do not turn them in.

The problem sets are the most essential part of the course. As you should know from 18.701 (Algebra I), they require serious thought. Don't wait until the night before they are due to start working on them. You are encouraged to work in groups on these problem sets. However, each of you must write up your solutions alone.

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.