Math 3124, Modern Algebra
(9:05-9:55 AM MWF, McBryde 212)

Final grades: The grades have been submitted to the registrar.  Most of you did a decent job on the final, even though it was long and hard.  And quite a few of you did a very nice job.  You can view the break-down, although it doesn't have names or id numbers, so you'll have find yourself based on your HW or exam scores.  You may stop by my office to look at your exam, although I will spend less time there during the summer.  If you want to find me for sure, e-mail me and I'll tell when I am there next.  I will be out of town May 15-25

Final exam: Here is the final in pdf.  And here are the solutions with some remarks of how to do and how not to do problems, and why these problems are interesting.

Syllabus: Check the syllabus for office hours, locations, and general advice on how to do well in the course. Or here is a pdf version to print.

Homework assignments:

Assigned	Due	Read	Do but don't turn in	Do and turn in
				On your own	You may discuss
1/19	1/27	Appendix A-C, I.1, 2	A.1-5, I.1.4, 6, 14	I.1.21	I.1.28
1/21	1/27	I.3	I.2.7, 11, 17, 18	I.2.20	I.2.24, 26
1/23	1/27	I.3	I.2.10, 12, 13
1/28	2/2	I.4	I.3.1-8, but don't worry about associativity, commutativity, and identity, I.3.9, 19	I.3.21	I.3.20
1/30	2/2	I.4	I.3.1-8, 11, 13, 29	I.3.28	I.3.23, 30
2/2	2/9	I.4, II.5	I.3.10, 12, 14-18, 27	I.3.24	I.3.22
2/4	2/9	II.6	I.4.1, 4, 10, II.5.1-11, 17	II.5.12	I.4.16
2/6	2/9	II.6, Appendix D	II.5.13, 14, 18 (do only Table 5.1), 20, 21	II.5.15, 22
2/9	2/16	II.7	II.6.1, 3, 5, 7, 12	II.6.6	II.6.15
2/11	2/16	II.7	II.6.1, but rewrite the permutations in cycle notation first, II.6.10	II.6.11
2/13	2/16	II.7	II.5.24 (you may want to do 23 first), II.6.4	II.6.14	II.5.23
2/16-2/20		II.8	No new homework.
2/23	3/1	II.8	II.7.1, 8, 10-12, 14, 21, 23, 24	II.7.22	II.7.13
2/25	3/1	III.9	II.7.3, 4, 15, 16, 18-20	II.7.17	II.7.23
2/27	3/1	III.9	II.8.1, 2, 4, 7-10, 12, 14, 15	Bonus exercise below.	II.7.25
3/1	3/15	IV.14	III.9.1, 5-9, 15-17, 20, 21	III.9.18	III.9.22
3/3	3/15	IV.14	III.9.2-4, 10, 11, 13, 16, 19		III.9.14
3/5	3/15	IV.14	III.9.12	III.9.9	III.9.19
3/15-19		IV.15	No new homework.
3/22	3/29	IV.16, 17	IV.14.3, 6, 15, 20, 24, IV.15.4, 7, 12, 14, 30	IV.14.14	IV.15.20
3/24	3/29	IV.17	IV.14.28, 30-32, IV.16.3, 7, 11, 14, 15, 17, 18	IV.16.10	IV.16.19
3/26	3/29	IV.18	IV.14.25, 37, 38, IV.16.15, IV.17.7, 8, 14-16, 22, 23, 26, 32	IV.17.24	IV.17.27
3/29	4/5	IV.19	IV.17.2-4, 9-12 (see Example 17.3 for what a subgroup lattice is), 18-21, 29-31	IV.17.25, bonus exercise below
3/31	4/5	IV.19	IV.18.1-6, 9	IV.18.8	IV.18.10
4/2	4/5	IV.20	IV.18.7 IV.19.1-10, 17, 18	IV.19.25	IV.18.15
4/5	4/12	IV.20	IV.17.17 IV.19.11 (Hint: What could the order of an element be in this group?), 24, 27 Catch up on all the exercises from last week you haven't done.	IV.19.26
4/7	4/12	IV.20	IV.19.14-16, 27, 30, 31, 33	IV.19.12 (This question has a mistake. It should read: "Is there a noncyclic abelian group of order 39?")	IV.19.28, 29, 32
4/9	4/12	III.10, 11	No new homework.
4/12-16	4/19	III.12, 13	No new homework.
4/19	4/26	V.21	III.11.9, 14, 18 III.12.7, 10, 20 III.13.12, 13, 19	III.12.18	III.12.21
4/21	4/26	V.22	V.21.3-6, 9, 10, 25, 28	V.21.17	V.21.23
4/23	4/26	V.23	III.12.14, 16 III.13.6 V.21.7, 8, 12, 24, 34, 35	V.21.29
4/26	5/3	V.24	V.22.3-6, 12, 14, 15	V.22.11	V.22.9
4/28	5/3	V.24	V.23.1, 4, 7-9, 13, 15, 22	V.23.10	V.23.21
4/30	5/3	V.25	V.23.5, 11, 12 V.24.2, 4, 6, 10, 12 (we've done all of it, just review the relevant theorems and proofs in your notes or in the book), 18, 19	V.23.18	V.24.22
5/3-5	No more homework.

Bonus exercise assigned 3/29 (due 4/5): Find the mistake in the proof of Theorem 17.1.(c) for extra credit.

Bonus exercise assigned 2/27 (due 3/1): Let f : R² --> R² be a map which preserves distances, that is d(f(x), f(y)) = d(x,y) for all x, y in R². Prove that f must be one-to-one and onto, hence it is a permutation. (That this is a bonus exercise means you don't have to do it, but if you do, you can get extra points for it possibly resulting in a score of more than 100% on this HW set.)

Solution to Exercise I.4.16: pdf file.

Exam solutions:

• First hourly exam pdf.
• Second hourly exam pdf.
  
• Third hourly exam pdf.
  

Other books: Here are a few other algebra textbooks you may want to consult.

• M. Artin, Algebra, Prentice Hall.  This is a textbook for a rather sophisticated undergrad algebra course.  Artin likes matrices.
  
• J.A. Beachy and W.D. Blair, Abstract algebra, Waveland Press.  This is an undergrad textbook, whose level is closest to our text's.
• I.N. Herstein, Topics in algebra, Wiley.  This is a classic textbook used by many undergrad and some graduate level algebra courses. It's more sophisticated than our course, but you may still get some good ideas from it.
• I.N. Herstein, Abstract algebra, Wiley.  This is a lighter version of the above book. In fact, it's often referred to as "baby Herstein."
• T.W. Hungerford, Algebra, Springer-Verlag.  This is a graduate level textbook in the Graduate Texts in Mathematics series. It is a good reference.
• A. Papantonopoulou, Algebra: pure & applied, Prentice Hall.  This is a book with lots of examples. Its level is a little more sophisticated than our course, but you could still understand many of the examples.
• J.J. Rotman, Advanced modern algebra, Prentice Hall.  This is another graduate level textbook and could also serve as a good reference.