Marquette University

Department of Mathematical and Statistical Sciences

Wim Ruitenburg's Fall 2023 MATH/SSC 4/5120-101. Recommended homeworks

Last updated: 6 December 2023
Comments and suggestions: Email   wim.ruitenburg@marquette.edu

6 December Section 11.5: 10, 11, 12
4 December Section 11.5. 7, 8, 9
Section 11.4: 16
1 December Section 11.5: 3, 4 (try with a very simple small G), 5, 6
29 November Section 11.5. 2
Section 11.4: 10, 12, 14
27 November Section 11.4: 4, 6, 9
20 November Section 10.4: 12, 13ac (try 13b), 14
Homework for points: From the book, 11.4.2, 11.4.3, and 11.4.5. Due 4 December
17 November Section 10.4: 6, 10, 11
15 November Section 10.4: 4abc, 5
Section 9.4: 36, 41, 42
13 November Section 9.4: 22, 25, 38, 39
10 November Section 9.4: 16, 26, 27, 28
8 November Section 9.4: 15 (also find all subgroups)
3 November Section 9.4: 10, 12
1 November Section 9.4: 3, 7, 8, 11
30 October Section 6.5: 17, 19, 21
27 October Section 6.5: 7, 12, 18
25 October Section 6.5: 1, 5abce
Homework for points: (1) Find elements of the 24 element cube group of orders 2, 3, and 4. (2) Find subgroups of sizes 6, 8, and 12 (it suffices to give generators, but explain why the sizes are 6, 8, or 12). Due 6 November
23 October In the 24-element cube group G, find an element of order 2, an element of order 3, and an element of order 4.
Find all subroups of the dihedral group D_7 (note that 7 is a prime number)
18 October Section 5.4: 31, 32ac, 34, 35, 36, 37ab
16 October Section 5.4: 12, 16, 23, 27
13 October Section 5.4: 2nf, 3ab, 4, 8
11 October Section 5.4: 1ab, 2b
Section 4.5: [Compute (1+i)^18], 23c, 28
9 October Section 4.5: 18dg, 19b, 20
6 October Section 4.5: 16a, 17c, 18cf
4 October Section 4.5: 3i, 5, 6, 11, 15ac
Complex numbers are easier with compplan.pdf and compexpo.pdf
2 October Section 4.5: 3abg, 4a
27 September Section 4.5: 1ab, 2a
With section 3.3: Find all subgroups of (Z_2 x Z_3). Find all subgroups of (Z_2 x Z_5)
25 September Section 3.5: 49, 50, 54
22 September Section 3.5: 31, 32 (tricky), 35, 48
20 September Section 3.5: 12, 17, 25, 26, 27, 28
18 September Section 3.5: 7, 8
Homework for points: 3.5.5 for a regular pentagon (called D_5), 3.5.6 for U(15), due 27 September
15 September Section 3.5: 1abc, 5, 6
Our class axiomatization of groups is at 180923_aata_grp.pdf
13 September Section 2.4: 23, 26, 28, 30
11 September Section 2.4: 12, 15ab, 18, 20
8 September Section 2.4: 1, 5, 10
1 September Section 1.4: 25, 26, 24ac
30 August Section 1.4: 19, 22bcd
28 August Section 1.4: 1, 2, 9, 11, 17