| 1 December |
Section 11.5: 2, 3, 4 (try with a very simple small G), 5, 6 Section 11.4: 4, 6, 9, 10, 12, 14, 16 |
| 24 November | Section 10.4: 4abc, 5, 6, 10, 11, 12, 13ac (try 13b), 14 |
| 15 November |
Section 6.5: 1, 5abce, 7, 12, 17, 18, 19, 21
Homework for points: We only look at the cube group of 24 elements. All elements can be written as 3 by 3 matrices with determinant equal to 1. (1) Find elements of orders 2, 3, and 4. (2) Find a non-cyclic subroup of size 4. (3) Find subgroups of sizes 6, 8, and 12 (it suffices to give generators, but explain why the sizes are 6, 8, or 12). Due 25 November. |
| 26 October |
Section 5.4: 1ab, 2bnf, 3ab, 4, 8, 12, 16, 23, 27, 31, 32ac, 34, 35, 36, 37ab
Find all subgroups of (Z_2 x Z_3). Find all subgroups of (Z_2 x Z_5) |
| 14 October | Examwork for points: the clock group |
| 7 October | Section 4.5: 1ab, 2a, 3abgi, 4a, 5, 6, 11, 15ac, 16a, 17c, 18cdfg, 19b, 20, [Compute (1+i)^18], 23c, 28 |
| 20 September |
Section 3.5: 1abc, 5, 6, 7, 8, 12, 17, 25, 26, 27, 28, 31, 32 (tricky), 35,
38, 49, 50, 54
Homework for points: three proofs |
| 11 September | Section 2.4: 1, 5, 10, 12, 15ab, 18, 20, 23, 26, 28, 30 |
| 4 September | Section 1.4: 1, 2, 9, 11, 17, 19, 22bcd, 24ac, 25, 26 |