Pries, Fall 2014, 466 Abstract Algebra I: Tentative Syllabus
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
Starts
8/25
9/1
9/8
9/15
9/22
9/29
10/6
10/13
10/20
10/27
11/3
11/10
11/17
14
15
12/1
12/8
Topics
Group actions:
permutation groups
conjugation and the class equation,
Burnside’s counting theorem
Sylow theorems
vector spaces
matrix groups, orthogonal matrices and rotations
representations of groups
Rings and ideals:
Principal ideals and unique factorization
Quotient rings
Quadratic rings
Factorization of ideals in ring extensions
Thanksgiving break
Applications to finite fields and quadratic reciprocity
Applications to algebraic geometry
Important dates:
Midterm Friday 10/17
Final Thursday 12/18 7:30-9:30 am
Textbooks:
Group actions: on-line resources Judson 12, Goodman 1.1-1.5, 4, 5, Garrett 13, Ash 5.1-5.4,
Wilkons 1.10-1.14. Dummit/Foote chapter 4.