MATH 402 (Algebraic Structures)
| DESCRIPTION |
This is the less theoretical of the two upper level
undergraduate abstract
algebra courses. (Student's planning graduate work in mathematics
should take the other course in abstract algebra, MATH 403.) The
course covers the basics of groups, rings, integral domains and fields.
There will be a detailed study of several groups, and a study of the
properties
of integers and polynomials. Emphasis is on the origin of the
mathematical
ideas studied and the logical structure of the subject. (This course is
not open to mathematics graduate students. Credit will only be given
for
one of Math 402 and 403.) The last item in the list of topics could be
replaced by other topics in algebra, for example, coding theory or
crystallographic
groups. |
| PREREQUISITES |
MATH 240 or equivalent |
| TOPICS |
Preliminaries
Induction
Equivalence relations
Functions
Groups
Groups and symmetries
Finite groups
Cyclic groups
Subgroups
Permutation groups
Cosets and Lagrange's Theorem
External direct product
Normal subgroups and factor groups
Homomorphisms
The structure of finite abelian groups
Rings
Introduction to rings
Integral domains
Ideals and factor rings
Ring homomorphisms
Polynomial Rings
Division Algorithm
Unique Factorization of Polynomials
Divisibility in Integral Domains
Fields
Extension Fields
Algebraic Extensions
Finite Fields
Geometric Constructions
Constructible numbers
Trisecting an angle
Duplicating a cube
Squaring a circle |
| TEXT |
Text(s)
typically used in this course. |
|
