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.
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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