Course Descriptions

General Information (Catalog listing)

01:640:451-452 Abstract Algebra I,II (3,3)
Rigorous study of abstract algebraic systems including groups, rings, and fields.
Prerequisites: Permission of department and instructor. For students preparing for graduate study in the mathematical sciences.

This course forms part of the Honors Track sequence. Special permission is required for admission to Math 451. Requests for admission are evaluated based on the student's prior achievements, level of interest, and potential for success in the course.

Required Textbook

Michael Artin; Algebra (second edition); Prentice-Hall, 2011 (560 pp.); (ISBN: 0-13-241377-9; ISBN13: 9780132413770).
See also the  Master Textbook List page.

Short Description

Groups: axiomatic formulation, subgroups, isomorphisms, cosets, quotient groups
Symmetry: actions of groups on sets and vector spaces
Theory of groups: groups of finite order, Sylow theorems, free groups, generators and relations
Representations of groups: representing groups via linear transformations

Topics, in approximate order

Groups and subgroups
Group homomorphisms and isomorphisms
Cosets and Lagrange’s theorem
Conjugation and normal subgroups
Quotient groups
Group actions
Groups of isometries
Groups of permutations
The orbit-stabilizer theorem
Groups of finite order
Sylow theorems
Free groups, generators and relations
Group representations
Characters
The regular representation

As time allows, with the instructor’s discretion, some additional topics may also be covered, such as the following:
Finite groups of Lie type, finite simple groups, classifying abelian groups, linear groups.

Sample Syllabus

Spring 2013

Schedule of Sections

Previous semesters