Homework Assignments & Tentative Schedule
| Date |
Section |
Assignment | ||
|---|---|---|---|---|
| M |
8/31 |
Introduction |
Homework #1 |
|
| W |
9/2 | 0.1, 0.2 Handy facts |
Homework #2: Read Section 0.3 as needed, also read pages 13-14, and do a first reading (this means skip the details and read for the big picture) of Section 1.1. In Section 0.3 do Problems #12, #13, #14. |
|
| F |
9/4 |
0.3 The integers mod n and definition of a group |
Homework #3: Please do a more detailed reading of Section 1.1. Also complete Problems #5 and #15bd in Section 0.3, as well as Problems #9, #25 in Section 1.1. | |
| M |
9/7 |
LABOR DAY |
NO CLASS | |
| W |
9/9 |
1.1 Definition of a group |
Homework #4 | |
| F |
9/11 |
1.2 Dihedral groups |
Homework #5 | |
| M |
9/14 |
1.3 Symmetric groups |
Homework #6 | |
| W |
9/16 |
1.4 Matrix groups and 1.5 Quaternion Group |
Homework #7: Please read Section 1.4 as needed as well as Section 1.5. Please do Problems #3, #11 in Section 1.4 and in Section 1.5 Problem #2 ONLY for D8 and Q8. How do these two groups compare? |
|
| F |
9/18 |
1.6 Homomorphisms and isomorphisms |
||
| M |
9/21 |
1.6 More homomorphisms and isomorphisms |
Homework #8: Please do a first reading of Section 1.7 before class on Wednesday. Please do Problems #3, #4, #7, #8, #17, #23*. |
|
| W |
9/23 | 1.7 Group actions |
Homework #9: Read Section 1.7 as needed. Please do Problem #20 in Section 1.6 and Problems #3, #8 and #9 in Section 1.7. | |
| F |
9/25 |
1.7 More group actions |
|
|
| M |
9/28 |
Presentations by generators and relations |
Homework #10 | |
| W |
9/30 |
Midterm 1: Combo In Class/Take Home |
|
|
| F |
10/2 |
2.1 Definition of a subgroup |
Take Home portion of Midterm 1 due by 5:00 p.m. today | |
| M |
10/5 |
2.2 Important subgroups |
Homework #11: Please read Section 2.2 as needed. Here are the exercises - Section 1.7 #19; Section 2.1 #4, #11ac; Section 2.2 #4 for S3 only. |
|
| W |
10/7 |
2.2 Important subgroups continued |
Homework #12: Please do a first reading of Section 2.3 before class Monday. The following problems are due on the Wednesday after break: Section 2.1 #10; Section 2.2 #12abc, #14. | |
| F |
10/9 |
FALL BREAK |
NO CLASS | |
| M |
10/12 |
2.3 Cyclic groups |
||
| W |
10/14 |
Flexible use |
||
| F |
10/16 | Flexible use |
Homework #13: Read Chapter 2 as needed. Section 2.2 #12def; Section 2.3 #1, #5, #9, #12; Section 2.4 #14. |
|
| M |
10/19 |
2.4 Generating subgroups | |
|
| W |
10/21 |
2.5 Subgroup lattice |
Homework #14: Skim Section 3.1 (so read the definitions and statements of theorems and propositions, skip proofs and details). The following problems are due Monday next week: Section 2.3 #26 (phi is the Euler phi function, see p.7); Section 2.5 #6, #9a and Z45; Section 3.1 #6, #9. |
|
| F |
10/23 |
3.1 Quotient groups |
|
|
| M |
10/26 |
3.1 Quotient groups | Homework #15: Section 3.1 #3, #4, #5. | |
| W |
10/28 |
3.2 Cosets and Lagrange's Theorem |
||
| F |
10/30 |
Flexible use |
Homework #16: Section 3.1 #38, #39 and Section 3.2 #4, #16. | |
| M |
11/2 |
3.3 The Isomorphism Theorems | ||
| W |
11/4 |
3.3 The Isomorphism Theorems |
Midterm 2 distributed today by 5:00 p.m. | |
| F |
11/6 | Flexible use |
||
| M |
11/9 |
Diversion into geometry and topology | Midterm 2 due by 5:00 p.m. today |
|
| W |
11/11 |
3.5 The alternating group |
Homework #17 | |
| F |
11/13 |
3.5 The alternating group |
||
| M |
11/16 | 5.4ish Fundamental Theorem of Finite Abelian Groups | Homework #18 | |
| W |
11/18 |
7.1 Definition of a ring |
|
|
| F |
11/20 |
7.1 Types of rings |
Homework #19: Read Section 7.1 as needed. In Section 7.2 please read the part about polynomial rings. For Wednesday please do a first reading of Section 7.3. The following problems are due Wednesday next week: Section 7.1 #7, #13 (for part c see p.225 example 6); and Section 7.2 #1, #2. | |
| M |
11/23 |
7.2 Polynomial rings | ||
| W |
11/25 |
Flexible use | ||
| F |
11/27 |
THANKSGIVING BREAK | NO CLASS | |
| M |
11/30 |
7.4 Properties of ideals | ||
| W |
12/2 |
7.5 Rings of fractions | ||
| F |
12/4 |
Flexible use | ||
| M |
12/4 |
7.6 The Chinese Remainder Theorem | ||
| W
| 12/9
| Flexible use | Take Home Final distributed today by 5:00 p.m. | |
| Wed |
12/16 |
Take Home Final due today at 5:00 p.m. |