Be careful to justify your solution when a homework problem calls for it.
| Date | Section/Topic | Reading (page numbers) | Problems | Due |
|---|---|---|---|---|
| 8/24/11 | 0. Sets and relations | 1–8 | §0: #3, 5, 7, 11, 12, 13, 15, 16, 17, 25, 28, 31, 32 | 8/31/11 |
| 8/26/11 | 1. Introduction | 11–18 | §1: #3, 7, 11, 13, 19, 23, 29, 33, 35, 37, 39, 40 | 8/31/11 |
| 8/29/11 | 2. Binary operations | 20–25 | §2: #2–8, 12, 14–18, 23, 24 | 8/31/11 |
| 8/31/11 | 3. Isomorphisms | 28–34 | §3: #1, 2–4, 6–7, 17, 20–23, 26–29 | 9/7/11 |
| 9/2/11 | 4. Groups | 36–43 | §4: #1–3, 7, 10, 11–13, 19, 22, 23, 25 | 9/7/11 |
| 9/5/11 | 4/5. Groups/subgroups | 43–45, 49–52 | §4: #26–28, 31–33; §5: 1, 2, 5, 11–12, 14 |
9/14/11 |
| 9/7/11 | 5. Subgroups | 53–55 | §5: #20, 22, 23, 26, 36, 39, 42, 44, 53, 54 | 9/14/11 |
| 9/9/11 9/12/11 |
6. Cyclic groups | 59–65 | §6: #1, 5, 11, 14, 15, 17, 20, 21, 22, 25, 30, 31, 32 | 9/14/11 |
| 9/12/11 | 7. Generators and Cayley digraphs | 68–72 | §6: #36, 37, 38, 42, 44, 49; §7: #1, 6, 7, 9, 10, 16, 17, 18, 19 (Hint: see #9) |
9/21/11 |
| 9/14/11 | 8. Permutation groups | 75–81 | §8: #1, 5, 6, 8, 10, 11, 17, 18, 23, 24 | 9/21/11 |
| 9/16/11 | 8. Cayley's theorem | 81–83 | §8: #30, 31, 35, 39, 41, 43, 47 | 9/21/11 |
| 9/19/11 9/21/11 |
9. Orbits, cycles, even and odd permutations, alternating groups | 87–93 | §9: #1, 6, 7, 10, 13, 14, 15, 19–23, 29, 34 | 9/28/11 |
| 9/23/11 | 10. Cosets | 96–100 | §10: #1–4, 6–7, 12, 13, 15, 19, 20–24 | 9/28/11 |
| 9/23/11 9/26/11 |
10 Lagrange's Theorem | 100–101 | §10: #27, 30–34, 37, 41, 43 | 9/28/11 |
| 9/28/11 | 11. Products | 104–110 | get started on §11 HW | 10/12/11 |
| 9/30/11 | 11. Finite abelian groups | 104–110 | §11: #1, 2, 7, 8, 9, 13, 14, 18, 20, 24, 32, 36, 46, 47 | 10/12/11 |
| 10/3/11 | Review | |||
| 10/5/11 | Exam 1 | Covers all material up to and including Section #10 | ||
| 10/7/11 | 13. Homomorphisms | 125–129 | §13: #1–5, 9, 10, 16, 17, 22, 24, 25, 28, 29 | 10/26/11 |
| 10/10/11 | 13. Homomorphisms | 129–133 | §13: #32, 33, 34, 39, 42, 47, 48, 49, 52 | 10/26/11 |
| 10/12/11 | 14. Factor groups | 135–139 | §14: #1–2, 7, 9–10 | 10/26/11 |
| 10/14/11 | 14. Factor groups | 139–141 | §14: #17, 18, 20, 23a-d, 24, 30 | 10/26/11 |
| 10/15/11 – 10/23/11 |
Fall break | |||
| 10/24/11 | 14. Factor groups - summary | 135–141 | ||
| 10/26/11 | 15. Simple groups | 144–148 | §15: #1–5, 19, 28 | 11/2/11 |
| 10/28/11 | 15. Simple groups | 149–151 | §15: #30, 31, 34 | 11/2/11 |
| 10/31/11 | 15. Simple groups | |||
| 11/2/11 | 18. Rings and Fields | 167–170 | §18: #3, 5, 7, 9, 11, 14, 15, 16, 17, 19 | 11/9/11 |
| 11/4/11 | 18. Rings and Fields | 171–174 | §18: #20, 22, 23, 24, 25, 27, 28, 33, 37, 38 | 11/9/11 |
| 11/7/11 | 24/19 Quaternions/Domains | 177–179, 224–226 | §19: #1–4, §24: 4–7 | 11/9/11 |
| 11/9/11 | 19. Domains | 177–182 | §19: #5, 7, 9, 11, 12, 14, 15–18, 23, 29 | not collected but on exam |
| 11/11/11 | 19. Domains | |||
| 11/14/11 | Review | |||
| 11/16/11 | Exam 2 | Covers §§13,14,15,18,19 plus quaternions (§24) | ||
| 11/18/11 | 20. Fermat's and Eulers theorem | 184–189 | §20: #1–10 | 11/30/11 |
| 11/21/11 | 20. Fermat's and Eulers theorem | |||
| 11/23/11 – 11/27/11 |
Thanksgiving holiday | |||
| 11/28/11 | 21. Field of Quotients | 190–196 | §21: #1, 2, 4, 5, 6–11 | 12/7/11 |
| 11/30/11 | 22. Polynomials | 198–207 | §22: #1, 2, 6, 7, 9, 13, 17, 22, 23, 25 | 12/7/11 |
| 12/2/11 | 22. Polynomials (ctd); 23. Factorization | 209–214 | §23: #2, 4, 6, 8, 9, 11, 13 | 12/7/11 |
| 23. Factorization (ctd); 26. Ideals | 209–218 | §23: #14, 16, 18, 20, 21, 25, 26, 27, 28 | ||
| 26. Ideals, Factor rings; | 237–243 | §26: #3, 4, 17 | ||
| 29. Field extensions, 31:Algebraic extensions | 265–272, 283–286 | §29: #1, 3, 9, 10, 11, 13 31: 1–6 | ||
| 32. Geometric constructions | 293–299 | |||