### Homework Assignments

Homework assignments will be due each Wednesday. You should do all the problems listed, but turn in only the ones marked with *.

Due Date    Secn    Problems

Jan 29: 0.1:2, 5*, 6, 8, 10*, 14, 15*
0.2:3, 4*, 11
0.3:2*, 6, 16, 18*
0.4:8, 12, 14*, 17, 26*
0.5:8, 18*, 20

Feb 5: 1.1:5*, 11*, 12, 21*, 27
1.2:10, 20*, 27*, 28, 29*, 31, 35

Feb 12: 1.3:4*, 6, 16, 17, 19*
1.4:7, 10*, 15, 21*, 35
2.1:8*, 9, 13*, 20*, 33, 36

Feb 19: 2.2:4*, 7, 24*, 25*, 33
2.3:7*, 16*, 29
2.4:8*, 25, 27*

Feb 26: 2.5:5, 6*, 8*, 9, 17
3.1:3, 6*, 8*, 13, 14, 18*
3.2:3, 11*, 15*, 21

Mar 5: 3.1:14*, 20
3.2:21*
3.3:3, 6*, 19*, 20*

Mar 12: 3.4:1, 2, 3, 4*, 5, 6, 7, 9*, 15*
4.1:10, 15, 16*, 18*

Mar 19: 4.2:4, 10*, 11, 12*
4.3:1, 2*, 3, 4*, 5, 6*
4.4:5*, 14, 15*, 16, 22*

Apr 2: 4.5:4, 5, 6*, 9, 10*, 11*
14:*Let G=S4 be the group of rotations of a cube. Explain the conjugacy classes in G geometrically.

Apr 9: * If G is a subgroup of On and H is the intersection of G with SOn, show that the index of H in G is 1 or 2.
* Show that every orientation-preserving isometry of the plane is a product of two reflections.

Apr 16:No homework due.

Apr 23: 6.1:2, 5, 11, 13*, 15*, 16
6.2:2, 5*, 13, 14*
6.3:3*, 7, 12, 32, 33*
7.1:8, 9*, 13, 14*, 19*, 22, 23

Apr 30: 7.2:16, 21*, 22*, 25, 34, 35
7.3:2, 10*, 21, 28*, 29
8.1:2, 6, 9*, 15, 20*
8.2:1, 3, 5*, 7, 9*, 10

May 6: 8.3:1, 2, 3, 4, 5, 6*, 7, 9, 21*
8.4:1, 4*, 8, 13, 17, 19*, 22, 24, 26, 27
8.6:1, 6*, 11, 13, 18*, 26
8.7:1, 4*, 5, 6*, 16, 27, 30, 37