Math 521B

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

Syllabus: Here is the syllabus.

Furlough days: Due to the dramatic cuts to the CSU budget by the state of California–the same cuts that have resulted in a 32% increase to student fees–every CSU faculty is required to take 9 unpaid days off per semester. My furlough days are

Jan 26 (Tue)
Feb 9 (Tue) and 23 (Tue)
Mar 18 (Thu) and 24 (Wed)
Apr 5 (Mon) and 15 (Thu)
May 5 (Wed) and 12 (Wed)

Class will not meet, and I will not be available for office hours, phone or email consultation on these days. Please, understand that these are not holidays. The amount of material we are expected to cover has not been changed. This means that you will have to do more work on your own and learn some of the material without my help. It is obviously unreasonable to think that these furloughs will have no effect on your education. I know this and will take it into account when assessing your knowledge. But keep in mind that everything you do not learn, every skill you do not aquire will make you a less desirable employee, other than a less educated individual. It is particularly important that you do not skip class on the days that remain.

Online resources:

I use Blackboard to post your grades periodically throughout the semester

Homework:

Assigned	Due date	Read	Exercises
1/20	1/25	3.2	Turn in: Prove that multiplication of n by n real matrices is associative.
1/25	2/1	3.2	3.2.8, 10, 11, 17, 19
2/1	2/8	3.2, 3	3.2.1, 3, 14, 18, 27
2/8	2/15	3.3	3.2.15, 16, 21, 24, 25 Turn in on 2/10: Let G be a group and a an element of G. If a²⁰¹⁰=e and a¹⁰⁰¹=e, prove that a=e.
2/10	2/15		Turn in: Let G be an abelian group and H the set of all elements of finite order in G. Does H have to be a subgroup of G? If so, prove it; if not, give a counterexample.
2/15	2/22	3.3	Homework holiday. Prepare for the upcoming exam.
2/22	3/1	3.3	3.3.5, 8, 12, 14, 18 Turn in on 2/24: Let G be a group and H and K subgroups of G. Prove that HK is a subgroup of G if and only if HK=KH.
2/24	3/1	3.3	Turn in on 3/1: 3.3.14
3/1	3/8	3.3, 4	3.3.2, 11, 15-17
3/3	3/8		Turn in: Define the function f:Z₂ × Z₃ -> Z₆ by ([0], [0]) -> [0], ([0], [1]) -> [2], ([0], [2]) -> [4], ([1], [0]) -> [3], ([1], [1]) -> [5], ([1], [2]) -> [1]. Prove that this function is an isomorphism.
3/8	3/15	3.4	3.4.6, 15, 16, 18, 19, 24 Turn in: prove that isomorphism of groups is an equivalence relation.
3/15	3/22	3.4	Turn in on 3/17: 3.4.19 Prepare for the upcoming exam.
3/22	4/12	3.5	Read and digest 3.5. In particular, - Compare Thm 3.5.1 with Thm 1.1.4 - could you use Thm 1.1.4 to give a shorter proof of Thm 3.5.1? - Compare Prop 3.5.3 and Thm 1.3.5. - Can you find any analogies with Cor 3.5.4 in earlier sections? - Compare the proof of Cor 3.5.6 with the proof of Prop 1.4.8 via exercises 1.4.17, 29, 30. - Compare Lemma 3.5.8 and Exercise 3.2.26. 3.4.14, 17, 21, 22, 25 3.5.3, 6, 11 Turn in on 4/14: 3.4.21
4/12	4/19	3.6	3.5.4, 15, 19 3.6.4, 5, 18
4/14	4/19	3.7	Turn in: Prove that the group of symmetries of the cube and the group of symmetries of the regular octahedron have the same order.
4/19	4/26	3.7	3.7.2, 3, 7, 8, 20 Turn in: Prove that if A and B are n by n matrices, det(AB) = det(A) det(B). (Hint: use the definition of the determinant of a matrix in terms of elements of the symmetric group.)
4/26	5/3	3.7	3.7.9, 13, 16, 18, 19
5/3	5/10	3.7	3.7.6, 12, 14, 15, 20

The problem of the fortnight: The Mathematics Department in San Diego posts a new fun problem periodically. 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
Final exam pdf

Educational links:

A serious paper on teaching/learning at the university level by Prof. Steven Zucker
A more light-hearted, but very true guide on how to be on good terms with your professor (who assigns your grade) by Prof. Doug Andrews at Wittenberg University

Math 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.

M. Artin, Algebra, Prentice Hall. This is a textbook for a rather sophisticated undergrad algebra course. Artin likes matrices.
J.R. Durbin, Modern Algebra, Wiley. This is an undergrad text which covers a little more material than our book. It's quite concise.
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.
J.A. Gallian, Contemporary Abstract Algebra, Houghton Mifflin. A classic algebra text comparable in level and coverage to our textbook.
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: