| Date | Topic | Homework | Due date | Reading assignment |
| Tuesday 3/4 | Group actions | Study the examples given in class. Study the actions given on p.43 (#4), p. 52 (#1, 2) | pp. 41-45, 51-53 | |
| Thursday 3/6 | Transitive group actions | Study the actions given on p.113 (#2, 3, 4) and on p.115 (# 4, 5). | pp.112-117 | |
| Tuesday 3/11 | Cayley’s Theorem | Do problems # 4, 5, 6, 13, 14, 15, 16, 18 on pages 44-45 | 3/27 HW # 7 | pp. 118-121 |
| Thursday 3/13 | The class equation | Do problem # 8 on page 53. Handout II on Groups | 4/1 HW # 8 | pp.122-129 |
| March 17-21 | Spring Break | Spring Break | Spring Break | |
| Tuesday 3/25 | No class. Work on Handout II. | pp. 133-144. | ||
| Thursday 3/27 | The Sylow Theorems | Study the following: Examples on page 144 Propositions 21 and 23 Corollary 22 on page 145. | pp. 144-146 | |
| Tuesday 4/1 | The Sylow Theorems Take home test (Test # 3 given out.) Due Tuesday April 8. | Handout III on Groups. | pp. 152-165 | |
| Thursday 4/3 | Direct product. Finitely generated abelian groups. | p. 147 # 13, 18, 30 pp. 156-15 7# 1, 18 a-c pp.165-166 # 1 a, b; 2 a-c; 3 a-c; 4 | 4/15 HW # 9 | pp. 188-194 |
| Tuesday 4/8 | Abelian groups. Nilpotent groups. | Handout IV on Nilpotent Groups | pp. 194-199 | |
| Thursday 4/10 | Solvable groups | Problem # 8 on page 198. Handout V on Solvable groups. pp. 173-174 # 1, 2, 4, 7, 10 | 4/22 HW # 10 | pp. 223-230 |
| Tuesday 4/15 | Introduction to Rings | pp. 230-231 # 1, 2, 3, 4, 7, 9, 11, 15, 21 | ||
| Thursday 4/17 | Ring homomorphisms. Ideals | p. 237 # 1 p.249 # 16, 18, 22, 24a, 27, 28 | ||
| Tuesday 4/22 | Review | |||
| Thursday 4/24 | Test # 4 | |||
| Tuesday 4/29 | ||||
| Thursday 5/1 | ||||
| Tuesday 5/6 | Final Exam 11:00 am-1:30 pm |
| Date | Topic | Homework | Due date | Reading assignment |
| Thursday 2/7 | Cosets | |||
| Tuesday 2/12 | Normality. Quotient groups. | Prove the following: 1. Corollaries to Lagrange’s theorem. 2. Prove the equivalent definitions of normal subgroup. 3. If , then . 4. If A and B are normal subgroups of G, then their intersection is also normal in G. 5. If N is a normal subgroup of G and , then . | 2/21 HW # 4 | pp. 89-100 |
| Thursday 2/14 | The isomorphism theorems | 1. pp. 85-88 # 3, 4, 22, 24, 30, 31, 36 2. pp. 95 # 1, 4, 5, 8 3. Study the statements and proofs of Propositions 13, 14, and 15 on pages 93-94. 4. Study the proof of the Proposition given in class. | 2/21 HW # 4 | pp. 101-105 |
| Tuesday 2/19 | Simple groups | Handout I on Groups -ALL | 2/26 HW # 5 | pp. 106-110 |
| Thursday 2/21 | Alternating groups | 1. Show that if G is a simple group, then any homomorphic image of G is either isomorphic to G or of order one. 2. p111 # 1, 2, 3 | 3/6 HW # 6 | |
| Tuesday 2/26 | Examples | |||
| Thursday 2/28 | Test # 2 |
| Date | Topic | Homework | Due date | Reading assignment |
| Tuesday 1/15 | Introduction to groups: Definitions and Examples | pp 21-23 # 1,2, 6, 9aStudy the proof of Proposition 2 (p.20) | 1/24 HW # 1 | pp 16-25; 29-32 |
| Thursday 1/17 | Properties of groups. Dihedral and Symmetric groups | Prove: Sn is a non-abelian group for all n greater than or equal to 3.pp. 21-23 # 11, 18, 20, 22, 23, 25, 29,31, 32, 34pp. 32-33 # 1, 4, 6, 7p.36 # 1 | 1/24 HW # 1 | pp 36-39; 46-48 |
| Tuesday 1/22 | Homomorphisms and isomorphisms | Prove: The normalizer of a subset A of G is a subgroup of G.Prove: The centralizer of a subset A of G is a subgroup of G.Prove: Isomorphism of groups is an equivalence relations.pp. 39-41 # 1, 2, 3, 4, 8, 17 pp.48-49 # 10 a | 1/31 HW # 2 | pp 49-51, 54-56 |
| Thursday 1/24 | Normalizers and centralizers. Cyclic groups | Prove directly that Z(G) is a subgroup.Prove Claim 3 from class. pp 52-53 # 3, 5 (a, b), 6Study the proof of Theorem 4 on p. 56 | 1/31 HW # 2 | pp 56-64 |
| Tuesday 1/29 | Generators | Study the proof of Propositions 5, 6 on p. 57.Compute <a> for all all a in Z/36Z.Study the proof of Theorem 7 on p. 58.If H and K are subgroups of a group G, is HUK a subgroups of G? Prove or give a counterexample.pp 60-61 # 1, 2, 3, 4, 10, 11p. 65 # 1, 5, 6 | 2/7 HW # 3 | pp 66-71 |
| Thursday 1/31 | Lattices of subgroups | p. 71 # 2 (a, c, d), 9 (a, b) | 2/7 HW # 3 | |
| Tuesday 2/5 | Test # 1 |