| Date | Section/Topic | Homework |
| Tuesday 1/20 | §1.1 Semigroups, monoids and groups | Problem 4, p.29. Give the Cayley table for the group of symmetries of the square. Problem 5, p.29. Prove the order of Sn is n! Prove Sn is non-abelian for n greater than 2. Problems 13, 14 pp. 30 |
| Thursday 1/22 | § 1.1 Properties of Groups | Prove Proposition 1.3 on page 25.Problem 6 on page 29.Prove Proposition 1.4 on page 25.Problem 15 on page 30. |
| Tuesday 1/27 | UTA CLOSED | |
| Thursday 1/29 | § 1.2 Homomorphisms and subgroups | Pages 33-34 Problems # 1, 2, 6, 7, 9, 10, 11, 13 HW # 1: Turn-in Problems # 6 and # 11 on Tuesday February 10th |
| Tuesday 2/3 | § 1.3 Cyclic groups | Pages 36-37 Problems # 1, 3, 4, 6, 8, 9 HW # 2: Turn-in Problem # 3 on Thursday February 12. |
| Thursday 2/5 | NO CLASS | |
| Tuesday 2/10 | § 1.4 Cosets and counting | Page 40 # 2, 3, 6 |
| Thursday 2/12 | § 1.5 Normality | Page 45 # 1, 2, 5, 6, 7, 9a HW # 3: Turn-in Problems: # 6 page 40; # 1, 7 page 45 on Thursday 2/19. |
| Tuesday 2/17 | § 1.5 Quotient groups | Problems in group theory (Handout I ) |
| Thursday 2/19 | Test # 1 | |
| Tuesday 2/24 | § 1.5 Isomorphism Theorems | Pages 45-46 # 11, 16 HW # 4: Turn-in Problems: # 11, 16 pages 45-46 on Thursday 3/5. |
| Thursday 2/26 | § 1.6 Symmetric group | Study the proof of Corollary 6.4. Page 51 # 2, 3, 4 |
| Tuesday 3/3 | § 1.6 Alternating group. Cayley’s Theorem | Page 51 # 5, 8HW # 5: Turn-in Problems pp. 51-52 # 3, 5 on Thursday 3/12 |
| Thursday 3/5 | § 1.8 Direct products. § 2.2 Finitely generated abelian groups | Handout (Chapter 5) p. 156 # 1; p.165 # 1 a, b; 2 a, b, c Handout problems on group Theory # 3-7 |
| Tuesday 3/10 | § 2.2 Invariant factors. Elementary divisors | Handout (Chapter 5) p.165 # 3 a, b, c Handout Problems on Group Theory # 21-25, 29HW # 6: Turn-in Problem # 12 p.82 on Tuesday 3/24 |
| Thursday 3/12 | § 2.4 Group actions | |
| March 16-20 | Spring break | |
| Tuesday 3/24 | § 2.4 Group actions | Page 92 # 3, 9, 14 Handout Problems in Group Theory II-All |
| Thursday 3/26 | Test # 2 | |
| Tuesday 3/31 | § 2.5 Sylow’s Theorems | Problems # 1, 10, 11, 13 on page 96 |
| Thursday 4/2 | § 2.5 Sylow’s Theorems | 1. Show that a group of order 36 is not simple. 2. Handout – Problems on Group Theory–Problems # 1- 6 3. Handout-Problems on Sylow Theorems-# 1-10 HW # 7. Turn in Problems # 1, 10, 11, 13 on page 96 on Thursday 4/9 |
| Tuesday 4/7 | § 2.6 Finite groups | Study the proof of Proposition 6.3 and Proposition 6.4 See link below for a listing of groups of small order. http://www.math.usf.edu/~eclark/algctlg/small_groups.html Pages 99-100 # 3, 4, 10 HW # 8. Turn in Problems # 1,3, 5 from Handout Problems in Group Theory and problems # 3, 4 from page 99 on Thursday 4/16 |
| Thursday 4/9 | § 2.7 Solvable groups. | Pages 106-107 # 2, 10, 14 |
| Tuesday 4/14 | § 2.7 Nilpotent groups | |
| Thursday 4/16 | § 3.1 Rings and homomorphisms | HW # 9. Due Thursday 4/23 Page 120 # 3, 6, 7, 15 |
| Tuesday 4/21 | Review Test # 2 | |
| Thursday 4/23 | Test # 2 | |
| Tuesday 4/28 | § 3.2 Ideals. The Isomorphism Theorems | Page 133 # 3, 4 |
| Thursday 4/30 | § 3.2 Quotient rings. The Isomorphism Theorems | HW # 10. Due Thursday 5/7 Page 133 # 3, 4, 7a, 10 |
| Tuesday 5/5 | § 3.2 Prime and maximal ideals | Page 134 # 20 |
| Thursday 5/7 | §3.3 Factorization in commutative rings | Page 140 # 1 |
| Tuesday 5/12 | Final Examination 11:00 a.m.-1:30 p.m. |