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It is very important that you practice doing as many problems as you can. It is not enough to understand the concepts; you must be good at executing them or you will run out of time on exams. Therefore, you should do as many of the other problems in the text as you need to in order to feel comfortable with each concept. You may also find more practice problems in Allan Clark's (recommended) text, Elements of Abstract Algebra, available on reserve in the Madden Library.
You should follow the homework policy outlined in the syllabus for the problems to be turned in. In particular, please remember to follow all the format rules. I will announce in class when the problems from each section will be due and will update this list online from time to time.
All problems due on the same day should be stapled together in one packet.
| Section | Exercises | Due |
|---|---|---|
| 1.1 | 2, 3, 5, 7, 9, 12 | 8/27 |
| 1.2 | 1, 3, 7, 9, 13* | 9/3 |
| 1.3 | 3, 4, 7, 8, 10, 14**, 18, 22*, 24*, 25* | 9/10 |
| 1.4 | 1, 3, 5, 6, 7 | 9/10 |
| 2.1 | 1, 5, 8, 9, 13, 14, 15, 17 | 9/17 |
| 2.2 | 3, 4, 7, 13(a-d); also read and convince yourself of #11, 12 | 9/17 |
| 2.3 | 1, 3, 5, 7, 9, 10, 12 | 9/24 |
| 3.1 | 1, 7, 12, 14, 15, 19 | 10/11 |
| 3.2 | 2, 3, 8, 10, 11, 16(a,c), 20 | 10/11 |
| 3.3 | 6, 7, 8, 12, 13, 14 | 10/15 |
| 3.4 | 1, 2, 4, 9***, 13, 14, 17* | 10/15 |
| 3.5 | 2, 4, 11, 13, 19* | 10/22 |
| 3.6 | 11, 15*, 16, bonus problem† | 10/22 |
| Matrices assignment | 10/22 | |
| 3.7 | 3, 6, 7, 9, 10, 12 | 10/29 |
| 3.8 | 2, 5, 7, 8, 11, 13, 23, 26* | 11/5 |
| 4.1 | 1, 2, 4, 5, 9 | 11/19 |
| 4.2 | 1, 2, 4-7(a,b), 11, 16 | 11/19 |
| 4.3 | 2, 4, 6, 9††, 12 | 11/19 |
| 5.1 | 1, 2, 5, 13, 16, 17, 19 | 12/3 |
| 5.2 | 3, 4, 7, 15 | 12/3 |
| 5.3 | 1, 4, 10(a,b), 13, 14 | 12/3 |
* Bonus problem (extra credit only)
** "Units digit" = ones digit. For example, the units digit of 10,369 is 9.
*** Please see me if you need help multiplying matrices.
† Prove that conjugation preserves cycle shape.
†† Hint: To show the forward implication, suppose n = mq + r, and show that r = 0.
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| Last updated 10/30/2004 |