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 Factor groups 4.2
9/28 More on factor groups; Problem Set 4 due; Fourth problem day 4.2
10/1 Group homomorphisms 4.3
10/3 Isomorphisms 4.4
10/5 Midterm Exam I Chapter 3, 4.1-2
10/8,10,12 Columbus Day Break -- no class 4.5
10/15 The Isomorphism Theorems 4.5
10/17 The Isomorphism Theorems, continued 4.5
10/19 Automorphisms; Problem Set 5 due; Problem day 5 4.6
10/22 Direct products 5.1
10/24 Fundamental theorem of finite abelian groups 5.2
10/26 More on the fundamental theorem; Problem Set 6 due; Problem day 6 5.2
10/29 Elementary divisors and Invariant factors 5.3
10/31 Spare day 6.1
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 Conjugacy and the Class Equation 7.2
11/16 Midterm Exam II 4.3-4.6, Chapters 5, 6
11/19 The Sylow theorems 7.3
11/21,23 Thanksgiving Break -- no class 7.3
11/26 Proofs of Sylow theorems 7.3
11/28 Applications to structure of finite groups 7.4
11/30 More applications to structure of finite groups; Problem Set 9 due; Problem Day 9 7.5
12/3 A final topic TBD
12/5 A final topic TBD
12/7 A final topic TBD; course wrap-up; Problem Set 10 due
The final exam for this course will be given at the time established for MWF 8:00am classes. Watch for annoucement from the Registrar's Office.

Last modified: August 14, 2018