Mathematics 351, Abstract Algebra
Topics, Fall 2003

The text is Hungerford, Abstract Algebra, 2nd edition. Topics to be covered, in order:

Sections Topics
1.1-1.3 Arithmetic in Z
2.1-2.2 Congruence classes, Zn
2.3 Zp, p prime
3.1-3.2 Rings and fields
3.3 Isomorphism and homomorphism
4.1, 4.4 Polynomial rings, divisibility, roots
4.2-4.3 Divisibility and unique factorization
4.5 Eisenstein's test, Fundamental Theorem
5.1-5.2 Quotient rings
6.1-6.2 Ideals and homomorphisms
7.1-7.2 Groups
7.3 Subgroups and congruences
9.1 Euclidean domains
9.2-9.3 (survey) Application to number theory
10.1 Vector spaces
10.2 Fields
15 Application to Euclidean geometry
7.4 Group isomorphisms, automorphisms
7.5 The Lagrange theorem
7.9 The symmetric and alternating groups
11.3 (part I) Solvable groups
11.1 The Galois group
11.3 Solvability by radicals


Main page, 351.