Math 71
Abstract Algebra
Last updated June 25, 2009 14:49:08 EDT

## Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly.
On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

Lectures Sections in Text Brief Description
9/26 0.1 Equivalence Relations and Partitions
9/28 0.3 The definition of Z/nZ
10/1 1.1 Definition of groups; examples; begin dihedral group
10/3 1.2 - 1.3 Dihedral and Symmetric groups
10/5 1.4 - 1.5, start 1.6 Matrix groups, Quaternions, Isomorphism
10/8 1.6, 2.1 Homomorphisms and subgroups
10/10 2.1 Subgroups
10/12 2.3 Cyclic groups
10/15 2.4, 3.1 Subgroups generated by a set; cosets
10/17 3.1, 3.2 Cosets and homomorphisms
10/19 3.2 More on cosets and Lagrange's theorem
10/22 3.3, 3.5 First Isomorphism theorem, the alternating group
10/24 1.7, 4.1, 4.2 Group actions and Cayley's theorem
10/26 4.2 Group Actions continued
10/29 4.3, 3.4 Groups acting by conjugations; the class equation; Holder program
10/31 4.5, 5.2, 5.4 Sylow theorems; Recognizing direct products; applications of Sylow theorems; fundamental theorem of finite abelian groups
11/2 5.2, 7.1 Fundamental theorem of finite abelian groups; Rings (basic definitions and examples)
11/5 7.2, 7.3 Polynomial Rings; homomorphism
11/7 7.3 Homomophisms; quotient rings
11/9 7.4 Quotient Rings and properties of ideals
11/12 8.1, 9.1 Euclidean Domains; Polynomial rings
11/14 8.2, 9.2 PIDs
11/16 8.3 gcds, irreducibles, primes
11/19 8.3 Unique Factorization Domains
11/21   Thanksgiving break: 11/21 - 11/25
11/26 9.3 Gauss' lemma and consequences
11/28 9.4 Irreducibility criteria
11/30 9.4 Extension Fields
12/3   Wrap it up

Thomas R. Shemanske
Last updated June 25, 2009 14:49:08 EDT