MAT3233
Modern Algebra
MAT 3233 Modern Algebra. (3-0) 3 Credit Hours.
Prerequisites: MAT2233 and MAT3003.
An introduction to modern algebra building up from concrete examples in elementary algebra and number theory which lead to the abstract theory of groups, rings, and fields. Topics include: Basic examples of groups. Cyclic groups. Permutation groups and cycle decompositions. Group homomorphisms. Normal subgroups, factor groups, and direct products of groups. Definitions and basic examples of rings, integral domains and fields. Ring homomorphisms. Ideals, factor rings, and direct products of rings. Unique factorization of integers and polynomials. Generally offered: Fall, Spring, Summer. Differential Tuition: $150.
Textbook
Lindsay N. Childs, A Concrete Introduction to Higher Algebra (3rd. ed.) Springer-Verlag (2009). ISBN: 978-0-387-74527-5
| Week | Sections | Topics | Student learning outcomes | |
|---|---|---|---|---|
| Example |
Chapter 1 |
Example | ||
| Example |
Chapter 2 |
The Integers | Example | Example |
| Example | Chapter 3 | Groups | Example | Example |
| Example | Chapter 4 | Cyclic Groups | Example | Example |
| Example | Chapter 5 | Permutation Groups | Example | Example |
| Example | Chapter 6 | Cosets and Lagrange’s Theorem | Example | Example |
| Example | Chapter 9 | Isomorphisms | Example | Example |
| Example | Chapter 10 | Normal Subgroups and Factor Groups | Example | Example |
| Example | Chapter 11 | Homomorphisms | Example | Example |
| Example | Chapter 13 | The Structure of Groups | Example | Example |
| Example | Chapter 16 | Rings | Example | Example |
| Example | Chapter 17 | Polynomials | Example | Example |
| Example | Chapter 18 | Integral Domains | Example | Example |
