Math 521B

Math 521B, Abstract Algebra
(5:35-6:50 MW in C-8)

Final exam: The final is at 5:35-7:35 on Wed, 5/14 in our usual classroom. It is a comprehensive exam and covers Chs 5-9 in the text.

Syllabus: Here is the syllabus.

Online resources:

Homework: Remember that you do not have to turn in the HW. However you should keep up with it. This is why we have target dates. You should have completed your HW by the target date and have it in a form that you would be confident relying on at the next exam. You can of course come back to it and revise it afterwards.

Assigned	Target date	Read	Exercises
1/23	1/30	Ch 5 pp. 94-102	5.10, 30, 34, 36, 38, 54
1/30	2/6	Ch 5 pp. 100-109	5.24, 28, 31, 44, 50
2/6	2/13	Ch 5 pp. 100-109 Ch 6 pp. 120-124	5.3, 9, 11, 12, 18, 22, 26
2/13	2/20	Ch 6 pp. 120-124	5.6, 8, 26, 42, 52
2/20	2/27	Ch 6 pp. 125-132	6.22, 24, 32, 36, 42
2/27	3/5	Ch 6 pp. 125-132	6.6, 18, 26, 29, 41
3/5	3/12	Ch 7 pp. 137-142	6.2, 10, 16, 20, 30, 40
3/12	3/19	Ch 7 pp. 137-143	6.12, 38 7.6, 8, 12, 32 (What does this have to do with cosets?)
3/19	3/26	Ch 7 pp. 133-147	7.10, 16 (Hint: look at the proof of Fermat's Little Theorem for inspiration), 20, 22, 36
3/26	4/9	Ch 9 pp. 177-184	7.18, 28, 30, 34, 38 (Hint: Look at the left of cosets kH where k is in K. How many distinct ones can you have? Compare this with the number of elements in K.)
4/9	4/16	Ch 9 pp. 179-187	9.2, 4, 8, 42, 50, 66
4/16	4/23	Ch 8	9.12, 36 (Think about why this problem is in this chapter.), 45, 46, 48, 56
4/23	4/30	Ch 8	9.58, 64, 68, 70 8.1
4/30	5/7	Ch 9 pp. 187-190 Ch 10	8.4, 8, 12, 22, 38 9.30

The problem of the fortnight: The Mathematics Department in San Diego posts a new fun problem every two weeks. If you'd like to submit a solution, give it or e-mail it to me, so that I can fax them all together to San Diego. Winners receive prizes.

Exam solutions:

First hourly exam pdf
Second hourly exam pdf
Third hourly exam pdf
Final exam pdf

Useful links: The links below lead to sites with encyclopedias of math terms. You can use them to find definitions, examples, and some theorems.

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

J.A. Beachy and W.D. Blair, Abstract algebra, Waveland Press. This is an undergrad textbook, whose level is closest to our text's. This was originally meant to be the textbook for our course. I've put my copy on reserve in the library. Check it out!
M. Artin, Algebra, Prentice Hall. This is a textbook for a rather sophisticated undergrad algebra course. Artin likes matrices.
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.

Some scholarship opportunities for prospective teachers: