Math 352: Abstract Algebra II Spring 2010

Complete solutions to HW #12 are available here.

Nearly complete solutions to HW #11 are available here.

Solutions to the two practice problems below are available here.

The third midterm is in class on Monday, May 3. It will cover chapters 21 and 32, and will consist of three questions, with at least one from chapter 21 and one from chapter 32. The problems will be similar to the examples done in class, and the problems on homework numbers 11 and 12. Your graded homework 12 will be available sometime this weekend.

To review for the exam, the best things are to understand the problems from homeworks 11 and 12, and to go over your notes from class. You can also work these problems as review problems (solutions will be posted here in the next two days): 1. Suppose that a is algebraic over Q and f(x) is a polynomial with coefficients in Q. Show that Q(f(a)) is an algebraic extension of Q. 2. Let E = Q(sqrt(3), sqrt(5)), and assume that [E:Q] = 4. Find the elements of Gal(E/Q) (recall they must permute the roots of any polynomial with rational coefficients, such as x^2 - 3), and use this to find all subfields of E containing Q. Is there an automorphism of E whose fixed field is Q?

For solutions to Exam 2, click here .

The second midterm is from 5:30-7:00 pm, on Monday, April 19, in the usual classroom. It will cover everything we have done in class from Chapters 18-20 in the book, in addition to the first two pages of Chapter 21. A practice exam is available here.

Solutions to the practice exam are available here.

Selected solutions to HW #9 are available here.

There will be a review session on Wednesday, April 14, from 6:30-8:00 pm, in the usual classroom.

For solutions to Exam 1, click here .

The first midterm is from 5:30-7:00 pm, on Monday, March 22, in the usual classroom). It will cover Chapters 13-18 in the book (only the part of Chapter 18 that the homework is on will be on the exam). A practice exam is available here.

Solutions to the practice exam are available here.

Selected solutions to HW #3 are available here.

Selected solutions to HW #2 are available here.