Lectures

Brief Description

Reading Assignment

6/22 
Overview: What is Abstract Algebra? 
Set Theory handout and/or Section 1.2, skim Section 1.5 
6/23 
Motivating examples of groups 
Section 2.1, Section 1.3 
6/25 
Definitions and examples of groups 
Sections 1.4 and 2.1 
6/27 
More examples; the symmetric and dihedral groups 
Section 2.2 
6/28 (xhour) 
Proof Workshop 

6/29 
The symmetric and dihedral groups, Basic properties of groups 
Section 2.3 
7/2 
Subgroups 
No reading. (Optional: Section 4 of Gallian) 
7/4 
NO CLASS  Independence Day 

7/5 (xhour) 
Proof Workshop 

7/6 
Cyclic Groups 
Section 2.4 (up to the statement of Lagrange's theorem) 
7/9 
Cyclic groups (continued); Equivalence relations 
Section 2.4 (beginning with Lagrange's theorem) 
7/11 
Cosets and Lagrange's Theorem 
Section 2.5 (through the corollary to Theorem 2.5.5) 
7/12 (xhour) 
Proof Workshop 

7/13 
Homomorphisms and isomorphisms 
Section 2.5 (beginning with normal subgroups) 
7/16 
Cayley's Theorem and Kernels of Homomorphisms 
Section 2.6 
7/18 
Kernels (cont.) and Quotient Groups 
Section 2.7 
7/19 (xhour) 


7/20 
Quotient Groups (cont.) and Normal Subgroups 
None 
7/23 
MIDTERM EXAM 
Section 2.7 
7/25 
Quotient Groups and the First Homomorphism Theorem 
Section 3.2 (Skim Section 3.1 if you want to review the basics of the symmetric group) 
7/26 (xhour) 


7/27 
The Symmetric Group: Cycle decomposition 
Section 3.3 
7/30 
Even and Odd Permutations; The Alternating Group 
Sections 2.9 and 2.10 
8/1 
Direct Products of Groups and The Fundamental Theorem of Finite Abelian Groups 
Section 2.10 
8/2 (xhour) 
The Fundamental Theorem of Finite Abelian Groups (cont.); the more general classification problem 
Sections 4.1 and 4.2 
8/3 
Rings 
Section 4.3 
8/6 
Ring Homomorphisms and Ideals 
Section 4.4 
8/8 
Quotient Rings and Maximal Ideals 
Section 4.5 
8/9 (xhour) 
Polynomial Rings 
Section 4.6 
8/10 
Irreducibility of Polynomials 
Sections 5.3, 5.4 and 5.6 
8/13 
Roots of Polynomials and Field Extensions 
Sections 5.3, 5.4 and 5.6 
8/15 
Field Extensions (continued) 
None 
8/16 (xhour) 
Presentations 

8/17 
Presentations; The Splitting Field of a Polynomial 

8/20 
Presentations 

8/22 
Recap and brief overview of Galois theory 
