Topics in Algebra
Fall 2013
General Info | Day-to-day
Syllabus and homework assignments
wk | date | reading | topic | homework | |
1 | 6/20 | Ch 1.2, 1.3 | Intro; Sets | 1.2: 8, 12a, 21a; 1.3: 1, 2. | |
6/21 | Ch 1.5, 1.6 | Integers | 1.5: 4, 17; 1.6: 1, 8, 12. | ||
HW #1: Due Wed 6/25 | |||||
2 | 6/23 | Ch 2.1 | Groups | 2.1: 1abde, 8, 9. | |
6/25 | Ch 2.2, 1.4 | Permutations | 2.2: 1; 1.4: 9acf, 15, 34 | ||
6/27 | Ch 2.3 | Subgroups | 2.3: 1, 3, 8 | ||
HW #2: Due Wed 7/2 | |||||
3 | 6/30 | Ch 2.4 | Equivalence Relns | 2.4: 1a, 2, 4 | |
7/2 | Ch 2.4 | Lagranges Thm | 2.4: 5, 9, 31 | ||
HW #3: Due Friday 7/11 | |||||
4 | 7/9 | Ch 2.5 | Isomorphisms | 2.4: 25; 2.5: 1bcde, 2 | |
7/10 | Ch 2.5 | Homomorphisms | 2.5: 3, 4, 5 | ||
7/11 | Ch 2.6 | Factor Groups | 2.5: 15; 2.6: 3, 4, 5. | ||
HW #4: Due Wed 7/16 | |||||
5 | 7/14 | Ch 2.7 | Homomorphism Thms | 2.7: 2, 3, 6. | |
7/16 | Ch 2.7 | (continued) | 2.7: 4abc | ||
7/18 | Ch 2.8 | Cauchys Thm | 2.8: 2, 6, 7, 8 | ||
HW #5: Due Wed 7/23 | |||||
6 | 7/21 | 2.9 | Direct Products | 2.9: 2 | |
7/23 | 2.10 | Finite Abelian Groups | - | ||
7/25 | 3 | Symmetric Group | 3.2: 2ab; 3.3: 1ab | ||
7 | 7/28 | 4.1 | Rings | 4.1: 10a, 31, 32, 33a | |
7/30 | 4.2 | Quaternions | 4.2: 2 | ||
8/1 | 4.3 | Homomorphisms | 4.3: 4, 15 | ||
HW #6: Due Friday 8/8 | |||||
8 | 8/4 | 4.4 | Maximal Ideals | 4.4: 10, 11, 12, 13 | |
8/6 | 4.3 | Correspondence Thm | - | ||
8/8 | 4.5 | Polynomial rings | 4.5: 1, 2 | ||
HW #7: Due Wed 8/13 | |||||
9 | 8/11 | 4.5 | PIDs | - | |
8/13 | 4.5 | Unique factorization | - | ||
8/14 | 4.5 | Polynomial equations | - | ||
8/15 | 4.5 | Field Extensions | - | ||
10 | 8/18 | Chinese Remainder Thm | |||
8/20 | No class |