Mathematics 25600: Basic Algebra III, Spring 2017

Course information

The final exam on June 5th covers the following sections of Fraleigh:
• Group Theory: 34, 35, 16, 36, 37
• Field Extensions: 31, 32, 33
• Automorphisms and Galois Theory: 48, 49, 50, 51, 53, 54, 55, 56

Assignment 1, due on Friday, April 7th. From Fraleigh: Section 34, Problems 4, 6, 8; Section 35, Problems 4, 6, 25, 26, 28

Assignment 2, due on Friday, April 14th. From Fraleigh: Section 16, Problem 12; Read Section 17 and do Problem 7*; Section 36, Problems 6, 13, 15, and 22

*: For this problem, the answer is given in the back of the book, so the important part is to show how you arrive at the answer.

Assignment 3, due on Friday, April 21st. From Fraleigh: Section 37, Problems 4 and 5; Section 31, Problems 6, 12, 23, and 31; Section 32, Problems 4 and 10; also do the following problem

Assignment 4, due on Friday, April 28th. From Fraleigh: Section 31, Problems 33 and 37; Section 33, Problems 12 and 13

Assignment 5, due on Friday, May 5th. From Fraleigh: Section 48, Problems 34, 36, 37 ; Section 49, Problems 6, 9, 11

Assignment 6, due on Friday, May 12th. From Fraleigh: Section 50, Problems 6, 16*, 21, 22, and 23 ; Section 51, Problems 7, 9, and 11

*: The hint to part a suggests you use Exercises 7--9. Problem 23 will provide you with the answer to Exercise 8.

Assignment 7, due on Friday, May 19th. From Fraleigh: Section 51, Problems 4 and 14; Section 53, Problems 12, 16, 17, 21, 22, 25

Here the group of a polynomial over F is the Galois group of its splitting field over F.

Assignment 8, due on Friday, May 26th. From Fraleigh: Section 54, Problems 8, 11*, 12; Section 55, Problems 1, 2, 14, 15

*: Read the section on Symmetric Functions at the beginning of Section 54 before doing this problem.

Chapter 1 of Finite Group Theory by I. Martin Isaacs

A few resources on approximate angle trisection (caveat: I haven't gone through any of these carefully): 1, 2, 3

General formula for the roots of a quartic equation