Abstract Algebra
Math 4000/6000

Instructor: Victor Kreiman
Office: 318 Boyd Graduate Studies
Office Hours: TuWTh 4 - 5
e-mail Address: vkreiman@gmail.com

Textbook
T. Shifrin, Abstract Algebra: A Geometric Approach, Prentice Hall, 1996. An up-to-date list of typos can be found at http://www.math.uga.edu/~shifrin/AlgebraErrata.pdf.

Webpage
Course materials will be posted at eLearning Commons (https://www.elc.uga.edu).

Prerequisites
Math 3000 and Math 3200 with a grade of C or better.

Course Description
This is a rigorous mathematical course, based on proofs. The course will cover portions of chapters 1 - 5 of the textbook. We will mainly discuss algebraic objects called rings and fields, their definitions, structures, and properties. As we'll see, the study of rings and fields leads to a clearer and deeper understanding of mathematics you've learned in previous courses. It also introduces new and interesting results, connections, and directions in mathematics.

Homework
The only way to learn this subject is to spend a substantial amount of time thinking about it. This is one purpose of the homework assignments. To a much greater extent than in 2000 level courses, you will be required to solve homework problems which are not worked out in lecture or in the textbook. You may certainly discuss the problems with other students. However, I encourage you to first try to solve homework problems by yourself. Please feel free to ask me in office hours any questions you may have about the problems or the course in general.

Homework assignments will consist of basic problems, which are to be completed but not turned in; core problems, which are to be turned in; and challenge problems, which must be turned in, in addition to the core problems, by students enrolled in Math 6000. You must write your own solutions to the problems you submit for grading, with no assistance.

Proofs
Some of the assigned problems will require writing proofs. A proof is nothing more than a demonstration of the truth of an assertion. It must be mathematically sound and complete. It is important to remember, however, that a proof is also a form of communication. Thus, it must be clear, readable, and grammatically correct. Constructing and writing proofs is a good way to learn how to write mathematics effectively.

Grading
Your grade will be based on homework (23%), quizzes (10%), three one-hour exams (42%), and a comprehensive final exam (25%).

Missed work
Late homeworks will not be accepted, and there are no makeup exams.