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Fall 2006 - Modern Algebra I
Homework Assignments
| Date | Assignment | Due | Solutions |
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| 8/28 |
| Read: | Chapter 1 |
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| Do: | pp
37-39: #2, 3, 12, 16 |
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| 9/6 | Coming soon |
| 8/30 |
| Read: | Chapter 2 (to page 50)
For
now, skip any references to Zn |
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| Do: | pp
37-39: #6, 8, 10 |
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| 9/6 |
| Read: | Chapter 2 (the rest) |
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| Do: | pp
53-56: #14, 16, 20, 32, 36 |
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| 9/13 | Available |
| 9/11 |
| Read: | Chapter 0 (through Modular Arithmetic) |
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| Do: | pp 23-26: # 4, 30
pp 54-56: # 8, 12,
24
And these two problems. |
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| 9/20 | Available |
| 9/13 |
| Read: | Chapter 3 (through Example 5) |
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| Do: | pp 67-71: # 4, 10, 12, 14, 28 |
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| 9/18 |
| Read: | Chapter 3 (the rest) |
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| Do: | pp 67-71: # 8, 16, 24, 34, 42 |
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| 9/27 | Available |
| 9/20 |
| Read: | Chapter 4 (through the corollaries of Theorem 4.2) |
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| Do: | pp 82-86: # 2, 8, 18, 28, 46, 54 |
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| 9/25 |
| Read: | Chapter 4 (through Example 5) |
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| Do: | pp 82-86: # 16, 20, 36, 40, 56 [Hint: Show that
U(2n) has two
elements of order 2, then apply (the solution to) #10 on page
67.] |
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| 10/11 | Available |
| 9/27 | |
| 10/2 |
| Read: | Chapter 5 (through Theorem 5.3) |
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| Do: | pp 112-115: # 2(prove your answer), 4, 18a, 24, 28,
32, 36, 46 |
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| 10/11 |
| Read: | Chapter 5 (the rest) |
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| Do: | pp 112-115: # 6, 8, 14 (Prove your answers), 18b, 22,
26 (Hint: every 3-cycle is even), 42, 50 |
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| 10/18 | Available |
| 10/16 |
| Read: | Chapter 6 (through example 7) |
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| Do: | pp 132-134: # 6 (we started this in
class), 18, 24, 32, 42
Extra credit: Show that Sn is
generated by any given n-cycle and a transposition. |
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| 10/25 | Available |
| 10/18 | |
| 10/23 |
| Read: | Chapter 6 (the rest) |
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| Do: | pp 132-134: # 10, 12 [Suggestion: Use
Theorem 6.5], 30
And these two problems. |
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| 11/1 | Available |
| 10/25 |
| Read: | Chapter 7 (through the proof of
Lagrange's Theorem) |
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| Do: | pp 148-151: # 2, 6, 8, 10, 14,
16 |
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| 10/30 |
| Read: | Chapter 7 (the rest) |
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| Do: | pp 148-151: # 18, 22, 30, 36 [Hint: Use
exercise 19, which we did in class, and proceed as in exercise 30 on p 134.], 38 |
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| 11/13 | Available |
| 11/1 |
| Read: | Chapter 7 |
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| Do: | pp 148-151: # 26, 28, 34, And show that
if H is a subgroup of G and a is in G
then the conjugate aHa-1 is also a
subgroup. |
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| 11/6 |
| Read: | Chapter 8 (through p 154) |
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| Do: | pp 165-168: # 4, 6, 12 (use the result of #4), 14, 20, 22 |
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| 11/15 | Available |
| 11/13 |
| Read: | Chapter 8 (the rest) |
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| Do: | pp 165-168: # 18, 28, 40, 44, 50, 52, 58 |
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| 11/29 | Available |
| 11/15 |
| Read: | Chapter 9 (through p 185) |
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| Do: | pp 191-195: # 4, 10, 12, 14,
18, 22, 28 |
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| 11/20 |
| Read: | Chapter 9 (through Cauchy's Theorem) |
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| Do: | pp 191-195: # 26 (see Isomorphism
Exercise #3 in HW #7), 42, 44 (prove, more generally, that [G:Z(G)] is
either 1 or composite), 46, 70 |
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| 11/27 |
| Read: | Chapter 10 (through p 205) |
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| Do: | pp 210-214: # 6, 10 (ignore the
questions about the ``kernel''), 14, 24a, 36, 52 |
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| 11/29 |
| Read: | Chapter 10 (the rest) |
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| Do: | pp 210-214: # 6, 10 (answer the questions about the ``kernel''), 16 (Hint: use the First
Isomorphism Theorem to show that any such homomorphism must be an isomorphism), 24bcd, 34, 38, 44 |
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| 12/4 | Not yet! |
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