Course Descriptions

16:640:551 - Abstract Algebra I

Fall 2021 - Jerrold Tunnell

Course Description:

This will be a basic graduate algebra course discussing such algebraic structures as categories, monoids and groupoids, groups, rings, and modules. Since categories form a basic structure having many applications as diverse as physics or computer science, we will begin there. Examples of algebraic objects will be emphasized throughout, as well as connections with other areas of mathematics. The first three chapters of the text will form the kernel of the course, with additional topics introduced in the lectures.

1. Categories and functors

2. Groups and homomorphisms

3. Rings, ideals and principal ideal domains

4. Modules, homomorphisms and structure theorems

Course Format: There will be weekly homework assignments, as well as longer term projects.

Text:

Jacobson, BasicAlgebra I

Prerequisites:

Familiarity with basic algebra such as polynomials, vector spaces, etc.

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Schedule of Sections:


 Previous Semesters