Math 110A: General Course Outline
Catalog Description
    110A. Algebra. (4) Lecture, three hours; discussion, one hour. Requisite: course 115A. Not open for credit to students with credit for course 117. Ring of integers, integral domains, fields, polynomial domains, unique factorization. P/NP or letter grading.
Textbook
    T. Hungerford, Abstract Algebra, 2nd Ed., Brooks Col.
Reviews & Exams
    The following schedule anticipates 24 days of instruction, with 2 holidays and 4 days for exams and reviews. If there is extra time, one could do section 6.3 - the structure of R/I when I is prime or maximal and/or section 4.6 - irreducibility in R[x] or C[x].
Schedule of Lectures

Week
Pages
Topics
1
2-20
Division Algorithm, divisibility, primes, and unique factorization.
2
24-40
Congruence and congruence classes, modular arithmetic, Z/pZ when p is a prime.
3
42-62
Definition and examples of rings, basic properties.
4
66-79
Isomorphims and homomorphism of rings. Review and first midterm. [Note: The book does isomorphism first then homomorphism. The order should probably be inverted.]
5
80-92
Polynomials and the Division Algorithm, divisibility in F[x], irreducibles, and unique factorization.
6
100-115
Polynomial functions, roots, and reducibility, irreducibility in Q[x].
7
119-123
Review, second midterm. Congruence in F[x] and congruence classes.
8
123-133
Congruence class arithmetic, the structure of F[x]/(p(x)) when p(x) is irreducible.
9, 10
134-153
Ideals and congruence, quotient rings and homomorphisms.

Comments

Outline update: 4/98
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