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Catalog Description: Elementary properties of the integers, sets and mappings, groups, rings, integral domains, division rings and fields. 3 credit hours.

Pre-requisite: Math 3120 Introduction to Linear Algebra.

• Develop a solid first understanding of three major algebraic concepts, namely groups, rings and fields, and the methods used to perform calculations in them
• Further develop the ability to correctly understand and interpret definitions and theorems (particularly in an abstract setting), and to write clear and correct proofs
• Prepare for more advanced study of algebra and other areas of mathematics that use algebra

1. Students will be able to write formal definitions of fundamental concepts of the course, e.g., group, ring, integral domain, field, homomorphism, isomorphism, quotient (factor) group/ring.
2. Students will be able to perform the basic computations of abstract algebra.
3. Students will be able to write clear and correct proofs of basic results in abstract algebra.
4. Students will be able to correctly write the statements of important theorems.
5. Students will be able to recognize when and how to apply important theorems.
6. Students will be able to work with and devise examples that illustrate basic concepts of the course.
7. Students will be prepared for more advanced study of algebraic structures and other areas of mathematics that use abstract algebra.

The work of the course will be divided into an introduction to the course (including Chapter 0) and 8 further modules that cover the chapters of the textbook listed below.

Modules 1-4: Groups: Chapters 1 - 11
Modules 5-7: Rings: Chapters 12 - 18
Module 8: Fields: Chapters 20 - 22

Test 1: due Friday, September 18
Test 2: due Friday, October 16
Test 3: due Wednesday, November 11
Final: due Monday, November 30 by 6 p.m.