| Date | Section/Topic | Homework |
| Tuesday 4/18 | § 3.1 Rings | Prove Propositions 1-5 given in class. Study the proof of Theorem 1.9 Problem # 6 on page 120. |
| Thursday 4/20 | § 3.2 Ideals. The Isomorphism Theorems | HW # 9. Due Thursday 4/27 Page 120 # 3, 6, 7, 15 |
| Tuesday 4/25 | § 3.2 Prime and maximal ideals | Page 133 # 3, 4, 7a |
| Thursday 4/27 | §3.3 Factorization in commutative rings | HW # 10. Due Thursday 5/4 Page 133 # 3, 4, 7a, 10, 20 |
| Tuesday 5/2 | § 3.3 Unique factorization domains | |
| Thursday 5/4 | § 3.3 and Review | |
| Tuesday 5/9 | Final Examination 11:00 a.m.-1:30 p.m. |
| Date | Section/Topic | Homework |
| Thursday 3/2 | § 2.1 Free abelian groups | |
| Tuesday 3/7 | § 2.1 Basis of free abelian groups | Classwork handout |
| Thursday 3/9 | § 2.1 Rank of free abelian groups | |
| MARCH 13-17 SPRING BREAK | ||
| Tuesday 3/21 | § 2.2 Finitely generated abelian groups | Handout # 3- Problems in Group Theory-Problems # 1-3 HW # 6. Due Tuesday 3/28 Prove the two corollaries of the Fundamental Theorem. Problem # 12 on page 82. |
| Thursday 3/23 | § 2.4 Group actions | 1. Prove the equivalent version of the class equation. 2.Complete the table of orbits and stabilizers. 3. Problems # 3, 9, 14 on page 92. |
| Tuesday 3/28 | § 2.4 Cayley’s theorem | HW # 7. Due Thursday 4/6 Proposition 4.8 and Corollary 4.10 |
| Thursday 3/30 | § 2.5 Sylow’s Theorems | Problems # 1, 10, 11, 13 on page 96 |
| Tuesday 4/4 | § 2.5 Sylow’s Theorems | 1. Show that a group of order 36 is not simple. 2. Handout # 4- Problems on Group Theory–Problems # 1- 103. HW # 8. Due Tuesday 4/11 Problems # 1, 10, 11, 13 on page 96 |
| Thursday 4/6 | § 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 |
| Tuesday 4/11 | Review Test # 2 | |
| Thursday 4/13 | Test # 2 |
| Date | Section/Topic | Homework |
| Tuesday 1/17 | §1.1 Semigroups, monoids and groups | Prove Proposition 1.3 on page 25.Problem 4, p.29. Give the Cayley table for the group of symmetries of the square.Prove Sn is non-abelian for n greater than 2.Problem 5, p.29. Prove the order of Sn is n!Problem 6 on page 29. |
| Thursday 1/19 | § 1.1 Groups § 1.2 Homomorphisms | Prove Proposition 1.4 on page 25.Problem 15 on page 30. |
| Tuesday 1/24 | § 1.2 Homomorphisms and subgroups | Pages 33-34 Problems # 1, 2, 6, 7, 9, 10, 11, 13, 17 HW # 1: Turn-in Problem # 6 on Tuesday January 31st. |
| Thursday 1/26 | § 1.3 Cyclic groups | Pages 36-37 Problems # 1, 3, 4, 5, 6, 8, 9 HW # 2: Turn-in Problem # 3 on Tuesday February 7. |
| Tuesday 1/31 | § 1.4 Cosets | Page 40 # 2, 3, 5 |
| Thursday 2/2 | § 1.4 Counting § 1.5 Normality | Page 40 # 6 Page 45 # 1, 2, 6, 7 |
| Tuesday 2/7 | § 1.5 Quotient groups and Isomorphism Theorems | Page 45 # 5, 9a, 10, 11, 16 HW # 3: Turn-in Problems: # 6 page 40; # 1, 7, 11, 16 pages 45-46 on Thursday 2/16. |
| Thursday 2/9 | § 1.5 Isomorphism Theorems | Problems in group theory (Handouts I and II) HW # 4: Turn-in Problems # 4, 6, 7, 9, 10 from Handout II on Tuesday 2/21. |
| Tuesday 2/14 | NO CLASS | |
| Thursday 2/16 | § 1.6 Symmetric group | Study the proof of Corollary 6.4. |
| Tuesday 2/21 | § 1.6 Alternating groups; Cayley’s Theorem | Page 51 # 2, 3, 4, 5, 7, 8, 10 HW # 5: Turn-in Problems # 3, 10 on Tuesday February 28. |
| Thursday 2/23 | Review Test # 1 | |
| Tuesday 2/28 | Test # 1 |