Math 3140
Abstract Algebra I
Fall 2019
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Instructor Information
Instructor
:
Tianyuan Xu (Eddy)
Email
:
tianyuan.xu@colorado.edu
Office
: Math. Building, Room 202
Office Hours
: Mon. 10:00-12:00, Wed. 10:00 - 11:00
Course Description
The main focus of the course is an introduction to group theory. We will study:
Definition of groups. Examples of groups arising from algebra, geometry and combinatorics.
Basic notions of group theory such as subgroups, cosets, conjugation and group homomorphisms. Lagrange's theorem. The isomorphism theorems.
Group actions on sets. The orbit-stabilizer theorem and its applications.
Optional topics chosen from the following list: classification of finitely generated abelian groups, group presentations, first steps in ring theory.
I will post a short lecture summary after each class
here
.
Recommended Text
Contemporary Abstract Algebra, Ninth Edition
by Joseph A. Gallian [
CU Bookstore
] [
Amazon
]
Algebra: Abstract and Concrete, Edition 2.6
by Frederick M. Goodman [
pdf
]