Math 4000/6000

Modern Algebra and Geometry I

Call #: 81-658/01-659
Time, location: T Th, 11:00-12:15, 222 Boyd
Instructor: Patrick Corn, 527A Boyd, corn (at) math (dot) uga (dot) edu
Office hours: T 2-4, W 1-3:30. Extra office hours will always be available upon request.
Course web page: You're looking at it.
Final exam: Tuesday December 11, 12-3 pm.
Book: Abstract Algebra: A Geometric Approach, by Shifrin.
Course outline: We'll cover Chapters 1-4 and some of Chapter 5. The goal is to introduce students to the basics of field and ring theory, starting with familiar and concrete subjects (integers, real numbers) and moving to more abstract and interesting settings (polynomial rings, finite fields, field extensions).

6000 students will be given extra homework problems, and extra problems on the exams.
Homework and tests: There will be weekly homework assignments, posted on this webpage. Each assignment will contain regular problems and advanced problems. 6000 students must do all the problems, and 4000 students must choose at least two of the advanced problems to do in each assignment.

There will be three midterms (tentatively scheduled for 9/11, 10/9, and 11/13).

The grading will break down as follows:
Homework 25%
Midterms 15% each
Final 30%
A note on collaboration: I would like you to work on the weekly assignments in small groups of 2-4 people each. If you like, send me an email with your contact information and any preferences you might have, and I will help form study groups myself. I don't want you to work alone unless you're having no trouble with the class at all--and even if that is the case, you will still be strongly encouraged to collaborate with your fellow students.
Of course, group work will help you solve problems that you might not have solved on your own. Sometimes your study partners will solve a problem that you cannot; I merely ask that you write homework solutions in your own words, so that it is clear that you understand what you are writing. A less obvious benefit of group study is that the best way to test your reasoning is to explain it to your peers.

Homeworks

(Advanced problems are in red.)

Homework 1, due 8/23: Chapter 1.1: 4bcdij, 6 (You are NOT allowed to use the formula!), 7, 8, 16, 18.
Homework 2, due 8/30: Chapter 1.2: 1bdf, 8, 10, 13, 19, 20, 22.
Chapter 1.3: 7, 15. (This is the final version of this week's homework--the rest of the problems have been moved to next week.)
Homework 3, due 9/13: Chapter 1.3: 8, 9, 16, 20abfgh, 21cdfg, 25, 29, 30, 34.
Chapter 1.4: 1, 2ac, 5, 9, 11, 12, 13.
Homework 4, due 9/20: Chapter 2.3: 3, 4, 6, 8abdf, 9acfg, 10, 11, 13, 18, 21, 23.
Chapter 2.4: 10.
Homework 5, due 9/27: Chapter 3.1: 1ace, 2ad, 6, 10 (all of them!), 13, 14, 15, 16, 20.
Chapter 2.4: 5. (Do this one last.)
Homework 6, due 10/9: Chapter 3.2: 1, 2a, 3abcdf, 4abc, 6acd, 7, 11, 15.
Chapter 3.3: 2adefhi, 3acd, 6, 7, 10.
Homework 7, due 10/18: Chapter 4.1: 1, 3, 4adf, 6, 8, 10, 11, 13, 14, 16, 17, 18, 21.
Homework 8, due 11/1: Chapter 4.2: 1, 3acd, 4, 5, 8, 10, 11ae (the two parts TOGETHER are worth one red problem), 13, 14, 15, 17, 18, 21.
Homework 9, due 11/13: Chapter 4.2: 16acd, 20.
Chapter 4.3: 1ab, 2ab, 5, 8, 10cd, 10efg, 11.
Homework 10, due 12/6: Chapter 4.3: 13, 14, 15, 16.
Chapter 5.1: 4, 11abcgi, 11defh, 13, 19, 25.