This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

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Description

This course discusses the basic elementary facts about the integers, groups, rings, integral domains, and fields. It is recommended strongly for all students planning to go to graduate school in mathematics. 

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH461, MATH340); and 1 course with a minimum grade of C- from (MATH341, MATH241); and minimum grade of C- in MATH310.


Level of Rigor

Advanced


Sample Textbooks

Contemporary Abstract Algebra, by J. Gallian

Abstract Algebra, by I.N. Herstein


Applications

Chemistry, Engineering, Physics, and Astronomy


If you like this course, you might also consider the following courses

MATH406, MATH456, MATH404, MATH405


Additional Notes

Duplicate credit with MATH402

Students interested in grad school in MATH should strongly consider this course

Topics

Groups

Definition and examples

Subgroups

Normal subgroups and quotient groups

Homomorphisms

Isomorphism theorems

Cyclic groups

Permutation groups, Cayley's Theorem

Rings

Definition and examples

Polynomial rings

Ideals and quotient rings

Integral domains

Euclidean domains, unique factorization

Prime ideals, maximal ideals

Fields

Quotient fields

Extensions

Algebraic extensions

Impossibility of trisection of angle