Math 393 Homework, Autumn 2011
- Homework Set #1 (due Tuesday 6 September):
- 1.2, pp.25-26 (1-5,7-8,11), #6 is now extra credit.
- Homework Set #2 (due Tuesday 13 September):
- 1.4, pp.45-49 (2,3,7,8,11,12,15,18,31-35)
- Homework Set #3 (due Tuesday 20 September):
- 1.5, p.58 (43,52,54)
- 1.6, pp.66-68 (8-11,17,18,22,23,50,51,56)
- Homework Set #4 (due Tuesday 27 September):
- Create multiplication ('Cayley') tables for D3 and D4.
- 2.8, p.83 (1-9, 21)
- 2.9, p.94 (7-18)
- Homework Set #5 (due Tuesday 4 October):
- Compute the cosets for (i) 4Z of Z, (ii) <4> of Z_12, (iii) Right cosets as well as left cosets of {(1), (1 3)} in D_4.
- 2.10, p.101 (34,37,39,40,41,43)
- Homework Set #6 (due Tuesday 18 October):
- Prove that Z x Z is not cyclic.
- 2.11, p.110 (1, 3-7, 10, 22-25,29,39,46, EC(52))
- 3.13, p.133 (3-8, 13, 53)
- Homework Set #7 (due Tuesday 25 October):
- Show that C* does not have any proper subgroups of finite index.
- 3.13, p.133 (17,18,23,29,45,49,50)
- 3.14, p.142 (1-12,26,30,34,40)
- Homework Set #8 (due on Tuesday, 1 November):
- Homework Set #9 (due Tuesday 8 November):
- 4.18, p.174 (4-20,38,41,46)
- Homework Set #10 (due Tuesday 15 November):
- 4.19, p.182 (1,5-10,23,25,29)
- 4.20, p.189 (1-6,10,27,28)
- Homework Set #11 (due Tuesday 29 November):
- 4.23, p.218 (1,9,16-19,27,28,34,37)
- 4.26, p.243 (3,20,26,27,29)
- Homework Set #12 (due Tuesday 6 December):
- 5.27, p.252 (1,2,5-8,15-19,34,35)
- Construct fields with (i) 9 elements and (ii) 16 elements.