Math 113: Abstract Algebra, Course Outline

We will study groups, rings and fields loosely following our course text, A First Course in Abstract Algebra for most of the topics in Parts I - VI.

Almost certainly, we will deviate from the syllabus described below.

Lecture Date Textbook sections Topics
1 28 August 2007 § § 1 & 2 Introduction to groups and binary operations
2 30 August 2007 § § 3 & 4 Isomorphic binary structures and groups
3 4 September 2007 § § 4 & 5 Groups and subgroups
4 6 September 2007 § 6 Cyclic groups
5 11 September 2007 § 7 Generators of groups
6 13 September 2007 § 8 Permutation groups
7 18 September 2007 § 9 Orbits, cycles and alternating groups
8 20 September 2007 § 10 Cosets; Lagrange's theorem
9 25 September 2007 § 11 Direct products
10 2 October 2007 § 13 Homomorphisms
11 4 October 2007 § 14 Factor groups
12 9 October 2007 § 15 More on factor groups; simple groups
13 11 October 2007 § § 16 & 17 Group actions
14 16 October 2007 § 18 Introduction to rings and field
15 18 October 2007 § 19 Integral domains
16 23 October 2007 § 20 Fermat's Little Theorem
17 25 October 2007 § 21 Field of quotients
18 30 October 2007 § 22 Polynomial rings
15 1 November 2007 § 23 Factorization in polynomial rings
16 6 November 2007 § 24 Examples of noncommutative rings
17 13 November 2007 § 26 Homomorphisms and factor rings
18 15 November 2007 § 27 Prime and maximal ideals
19 20 November 2007 § 29 Extension fields
20 22 November 2007 § 30 Vector spaces
21 27 November 2007 § 31 Algebraic extensions of fields
22 4 December 2007 § 33 Finite fields
23 6 December 2007 § § 36, 37, 48, 53, 54, & 55 Preview of Galois theory