Detailed Schedule -- Modern Algebra I

Fall 2018, Prof. Little

This is a tentative, evolving schedule. As always, topics may be added, deleted, or rearranged during the course of the semester. Any changes will be announced in class and here.

Date Class Topic Reading (Lee)
8/29 Course Introduction, Z, Zn 2.4, 2.5
8/31 A first example, the group S3 3.1
9/3 Groups 3.2
9/5 Basic properties of groups 3.3
9/7 Powers in a group; Problem Set 1 due; First problem day 3.4
9/10 Orders of elements, cyclic groups 3.4
9/12 Subgroups 3.5
9/14 Structure of cyclic groups; Problem Set 2 due; Second problem day 3.6
9/17 More on cyclic groups 3.6
9/19 Cosets and Lagrange's Theorem 3.7
9/21 Spare day; Problem Set 3 due; Third problem day 4.1
9/24 Normal subgroups 4.1
9/26 Normal subgroups 4.1
9/28 Factor groups; Problem Set 4 due; Fourth problem day 4.2
10/1 More on factor groups 4.2
10/3 Review for Midterm Exam I
10/5 or evening 10/4 Midterm Exam I 2.4, 2.5, Chapter 3, 4.1
10/8,10,12 Columbus Day Break -- no class 4.5
10/15 Group homomorphisms 4.3
10/17 Isomorphisms 4.4
10/19 The Isomorphism Theorems; Problem Set 5 due; Problem day 5 4.5
10/22 Isomorphism Theorems, continued, automorphisms 4.5, 4.6
10/24 Direct Products 5.1
10/26 Fundamental theorem of finite abelian groups; Problem Set 6 due; Problem day 6 5.2
10/29 More on the fundamental theorem 5.2
10/31 Elementary divisors and Invariant factors 5.3
11/2 Sn and cycle notation; Problem Set 7 due; Problem day 7 6.1
11/5 The alternating groups 6.2
11/7 An is simple for n ≥ 5 6.3
11/9 The classification of finite simple groups; Problem Set 8 due; Problem day 8 6.3
11/12 Normalizers and centralizers 7.1
11/14 Review for Midterm II See review sheet
11/16 Midterm Exam II, starting at 7:00am See review sheet
11/19 Symmetric and Alternating Groups 6.2-6.3
11/21,23 Thanksgiving Break -- no class 6.3
11/26 An is simple for n ≥ 5 6.3
11/28 Normalizers and Centralizers 7.1
11/30 Conjugacy and the Class Equation; Problem Set 9 due; Problem Day 9 7.2
12/3 CEFs administered; The Sylow Theorems 7.3
12/5 Proofs of the Sylow Theorems 7.4
12/7 Applications of the Sylow Theorems; Problem Set 10 due; Final Problem Day
The final exam for this course will be given at the time established for MWF 8:00am classes--Friday, December 14 at 8:00am.

Last modified: November 13, 2018