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Homework will be assigned daily and collected on Wednesdays.
You should attempt and do your best to complete the homework that goes with a given lecture before the next lecture.
If you need additional practice, there are hints and/or answers to the
odd numbered problems in the back of the book. (I may assign odd
numbered problems anyway, if I think they are important.)
HOMEWORK 1: Due Wednesday, September 29th.
Wednesday Sept. 22nd:
Read: Chapter 1 and the first two pages of Chapter 2.
Do: Chapter 1: 2, 3, 12
Bring your completed survey to class on Friday.
Friday, Sept. 24th:
Look at the sample starred problem, which is a solution to
problem 14 in Chapter 2. Decide whether you would give me credit
or no credit for my proof. We'll discuss this in class on Monday.
Read the rest of chapter 2.
Do: Chapter 2: 8, 20, 26* (first starred problem!), 28, 36
HOMEWORK 2: Due Wednesday, October 6th.
Monday, Sept. 27th:
Read: Chapter 3. There is one problem (19) about centers
and centralizers, which we will not discuss in class, so you should
read pages 63-64 carefully. You don't need to read about subgroup
tests, but you might want to glance at the theorems so that you know
they exist.
Do: Chapter 3: 2, 4, 10, 19 (this is in the back of the book, but your solution
should contain extra detail so that I can tell you've thought about it
and understand it), 40
Wednesday, Sept. 29th:
Read: Chapter 4. For now, just pay attention to the
statements of the theorems. We examined these theorems for the
case of Z_n in class, and next time, we'll talk about how to rewrite
our observations so that they look more like the theorems in the book.
Do: Chapter 4: 4, 10, 12, 16, 40 (note the group is Z, the set of integers, and not Z_n)
Friday, Oct. 1st:
Read: Chapter 4.
Do: Chapter 4: 42*, 62
HOMEWORK 3: Due Wednesday, October 13th. Resubmissions of the first starred problem are also due on 10/13.
Monday, October 4th:
Read: Chapter 5 (We'll do cycle notation on Wednesday, so you can wait until Wednesday to read that if you want).
Do: Chapter 5: 10, 17, 31, 34, 36. For odd numbered problems,
your answer should contain more detail than the answer in the back of
the book.
Wednesday, October 6th:
Read: The rest of chapter 5 (p. 108-9 are optional).
Do: Chapter 5: 18, 26, 28, 41, 48* (Z(S_n) is the center of S_n)
Friday, October 8th:
Read the first two pages of Chapter 10. We will talk about kernels on Monday.
Do: Chapter 10: 2, 3, 4, 10 (save the part about kernels for Monday)
HOMEWORK 4: Due Wednesday, October 20th. Resubmissions
of the second starred problem are due Monday 10/18. Last week's
starred problem is now this week's starred problem. Instead of a
new starred problem, there is extra credit (see the worksheet).
Monday, October 11th:
Read: Review the first two pages of Chapter 10. Read Chapter 6 up to p. 129.
Do: Chapter 10: 5, Chapter 6: 4, 5, 8
Wednesday, October 13th:
Read: Review Chapter 6 up to p. 129. Start Chapter 7, up to p. 143.
Do: Chapter 6: 7, 20, 22.
Friday, October 15th:
Read: Chapter 7 up to p. 143
Do: Chapter 7: 1, 2, 3, 8, 10, 14
HOMEWORK 5: Due Wednesday, October 27th. This
is a mini-homework, to give you extra practice with factor groups
before the exam. I highly recommend that you complete this by
Friday, before I hand out the midterm. Factor groups will make an
appearance on the midterm, and you will (as usual) be allowed to ask me
about these problems in office hours, even after the midterm starts.
Monday, October 18th, and Wednesday October 20th:
Read: Chapter 9, up to "Applications of Factor Groups."
Do: Chapter 9: 1, 2, 5, 6, 14, 27 (Save 1, 2, and 5 for Wednesday.)
The homework for Friday's lecture will go on Homework number 6.
HOMEWORK 6: Due Wednesday, November 3rd.
Read: Chapter 8 and the rest of Chapter 10
Do: Chapter 8: 6, 16, 34; Chapter 10: 11, 12, 13 (you must use the First Isomorphism Theorem for these 3 problems), 36
HOMEWORK 7: Due Wednesday, November 10th.
Monday, November 1:
Read: Chapter 11, but skip the proof, and Chapter 12.
Do: Chapter 11: 2, 15, 16.
Tuesday, November 2:
Read: Chapter 12.
Do: 2, 6, 18, 22, 38
Wednesday, November 3:
Read: Chapter 13.
Chapter 12: 44*, Chapter 13: 2, 4, 5, 8, 26
HOMEWORK 8: Due Wednesday, November 17th.
Monday, November 8:
Read: Chapter 13.
Do: Chapter 13: 16, 30, 51, 54
Wednesday, November 10:
Read: Chapter 14
Do: Chapter 14: 2, 6, 9, 20, 35 (The book suggests using theorems 14.3
and 4 but you can also do this using just what we learned in class
today. Either method is fine.)
Friday, November 12:
Read: Chapter 14:
Do: Chapter 7: 4, 5 (I want to emphasize that we're using the same
ideas to distinguish cosets that we used in group theory; You can even
treat H as an ideal of Z rather than a subgroup); Chapter 14: 29,
33, 36, 60*
HOMEWORK 9: Due Monday, November 29th.
Monday, November 15:
Read: Chapter 15 (You may skip the part on fields of quotients, but you may find it interesting).
Do: Chapter 15: 5, 6, 8, 10, 26
Wednesday, November 17 and Friday, November 19:
Read: Chapter 16
Do Chapter 16: 12, 17, 24 (I gave hints about this one in class)