Homework |
You may be tested on the proofs of the
following theorems on exams (so test yourself, with the book closed, to
make sure you can do them).
Mid 1: 3.1-3.6, 4.1, 4.4(i,ii), 4.7, 5.3.
Mid 2:
5.1-5.3, 5.4(i), 6.1(i).
Mid 3: 10.3, 10.4, 11.3, 12.2-12.4.
|
HW # |
Due | Read | Do |
|---|---|---|---|
| F 12/18 9am-noon, Fowler 113 |
The final exam will cover all HW assignments, with a bit of emphasis on HWs 22-25. You should also know the proofs of the theorems listed above, except Theorems 10.3 and 12.4ii. Here is last year's final exam. |
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25 |
M 12/7 | Read Theorem 14.1 (may skip its proof). | Sec 14: 3, 7, and also do this problem. |
24 |
F 12/4 | Sec 14, p. 133-137, up to (but not including) Corollary 14.5. May skip Theorem 14.1 and its proof. | Sec 14: 1ae, 4, 5. Please see these notes. |
23 |
W 12/2 | Nothing. | Sec 13: 8, 9, |
22 |
M 11/30 | Sec 13 p. 121-125. | Sec 13: 1-3, 5, 19. |
| M 11/23 | Will cover HW 14-21. Here's last year's Mid3. Our exam will be different (but somewhat similar). Problem 1 is from Sec 13, which we haven't covered yet. |
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21 |
W 11/18 | Sec 12 p. 112-113, 115. | Sec 12: 15, 19-21, 29, 30. Also, prove Theorem 12.3. |
20 |
M 11/16 |
Sec 12 p. 114-115 up to but not including Theorem 12.6. (We'll cover
p. 112-113 later). Learn the proof of Theorem 12.4. |
Sec 12: 4, 5, 7, 8, 12-14. For #4, detailed proofs are not necessary, but do give brief justifications for your answers; in particular, if you claim two groups are isomorphic, give an isomorphism between them, but you don't need to prove that your map is indeed an isomorphism (though you should verify it for yourself). Also, prove that if G is a non-abelian group, then there exist elements a, b in G such that a^(-1)b^(-1) does not equal b^(-1)a^(-1). |
19 |
W 11/11 | Sec 12 p. 109-111. | Sec 12: 1-3. |
18 |
M 11/9 | Sec 11 p. 105. | Sec 11: 21-26. |
17 |
F 11/6 | Sec 11 p. 102-104. | Sec 11: 10, 14, 16-20. |
16 |
W 11/4 | Sec 11 p. 99-101. Learn the proof of Theorem 11.3. | Sec 11: 1, 3, 4, 6, 7, 11-13. |
| F 10/30 | Covers HWs 7-13.5, plus proofs of Theorems 5.1-5.3, 5.4(i), 6.1(i). Here's last year's Mid2. Our exam will be different (but somewhat similar). |
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15 |
W 10/28 | Review for the midterm. | Sec 10: 6-9, 16, 21 |
14 |
M 10/26 | Read Sec 10 up to and including Theorem 10.4 and its proof. Also read the proof of Theorem 10.3. | Sec 10: 1-3, 5, 11, 13. |
13.5 |
F 10/23 | Read p. 88 (first page of Sec 10), to prepare for Friday. | Sec 9: 6, 7, 12, 14. Sec 5: 23. |
13 |
W 10/21 | Sec 9. We didn't get to cover this in class; but the first three pages should be review for you (equivalence relations). | Sec 9: 4, 5. |
|
12 |
F 10/16 | Sec 8 p. 75-76. |
Sec 8: 15, 20. Also do the fifteen puzzle problem. Hint for 20: Let A be the set of all odd elements of H, B the set of all even ones. Show if A is nonempty, then |A| <= |B| and |B| <= |A|. |
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11 |
W 10/14 | Sec 8 p. 72-74. |
Sec 8: 5, 12, 17, 24, Hint for 27a: Let f=(1,2), g=(1,2,...,n). Find g f g^(-1). Find g^2 f g^(-2). Find g^i f g^(-i). |
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10 |
M 10/12 | Sec 8 p. 69-71. Play the Game of 15 (the "Fifteen Puzzle") for a couple of minutes if you've never played it before. |
Sec 8: 2, 3, 11, 13, 16. |
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9 |
F 10/9 |
Read Sec 8 p. 66-68. Take a quick look at Sec 7; it's a review from Discrete Math; refresh your memory if you feel rusty with any of it. |
Sec 6: 4-8, 10, 11. Sec 8: 1, 4, 7, 8, 10, 18. Hint for Sec 8, #10(a): See the proof of Theorem 6.1(i); this problem is different, but similar in some ways (I'm not saying use Thm 6.1; just get ideas from its proof). You'll also need to prove the following fact: the product of disjoint nontrivial permutations is not the identity. |
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8 |
M 10/5 | Sec 6. Proof of Theorem 6.1(i) may be on exams. | Sec 6: 1-3. |
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7.5 |
F 10/2 | Learn proofs of Theorems 5.1-5.3, 5.4(i) (they may be on exams). |
Sec 5: 6-9, 17-22. Hint for 6(a): use one of the theorems in the section. A good way to test yourself to see if you've learned the proof of Theorem 5.4(ii) is to try to prove #18a without using this theorem. (Also, note that 18a easily implies Theorem 5.4ii.) Solution of 5.21 |
| W 9/30 | The exam will cover HWs 1-6, plus
proofs of Theorems 3.1-3.6, 4.1, 4.4(i,ii), 4.7, 5.3. Here's last year's Mid1. Our exam will be different (but somewhat similar). |
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|
7 |
M 9/28 | Sec 5: 11, 12, 14-16. | |
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6 |
F 9/25 | Sec 5 pages 43-48. | Sec 5: [1a-g], 2, 3, 4, 5, 10. |
|
5 |
F 9/18 W 9/23 |
Sec 4: p. 38-40. |
Do at least the first half by Friday, so you
can ask questions. Sec 4: [1, 2], [4, 5], 6, [7], 8-10, 11, 13, 16, 17, 22, 23, 25. Square brackets [ ] mean: if you find these problems very easy, you don't have to turn them in --- but they may be on exams, so make sure you can do them! |
|
4 |
W 9/16 F 9/18 |
Read Sec 4: p. 33-38 up to Theorem 4.4. You may skip the proof of Thm 4.2 (but if you've never seen it, I recommend at least a quick look). |
Sec 4: 18-21. We did part of 18 in class; now try to do it without looking at your notes. Hints: for #19, use Theorem 4.1; for #21, use #20. Note: I added problem 14 to HW 3; I just realized that since you'll still be working on #15, it's better to do #14 first. |
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3 |
M 9/14 | Sec 3. | Sec 3: 1, 3-7, 9-12,
14, 15, 16. Use #14 to do #15. |
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2 |
F 9/11 | Sec 2 p.20-22; may skip the proof (but not
the statement) of the Division Algorithm. We will continue with Sec 3 on Friday. |
Sec 2: 4a, 7, 8, 10. |
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1 |
W 9/9 | Section 1 (may skip Example 5). Section 2, up to and including Example 7. Also, please make sure to read the Syllabus. |
Sec 1: 3acg, 4, 5, 6acg, 9. Sec 2: 1, 2a, 3, 5, 6. |