Algebraic Reasoning and Mathematical Structures
MATH 623. Algebraic Reasoning and Mathematical Structures
Three Credit Hours (3).
Prerequisite: Undergraduate course in Modern or Abstract Algebra or permission of instructor.
Abstract algebra with a focus on topics directly related to high school algebra and geometry: basic number theory, rings of integers and polynomials, elementary group theory, fields, classical geometric constructions, and the insolubility of the quintic. Applications will be considered as time permits. A computer algebra system will be employed in examples and assignments.
Detailed Description of Course
1) Necessary Number Theory
2) Application (example: cryptography)
3) Polynomial Rings
4) Extension Fields and Applications
5) Group theory and other applications, as time permits
Detailed Description of Conduct of Course
Most classes will be in lecture format. A computer algebra system such as Maple will be used in examples and assignments. Assessment will be done by graded homework and tests.
Goals and Objectives of the Course
Having successfully completed this course, the student will be able to describe the classical hard problems of geometry and algebra, outline the solutions achieved, and prove some of the theorems discovered along the way.
Other Course Information
A computer algebra system will be required for the course. Maple, now used in undergraduate courses, is perfectly adequate and the most likely choice.
Review and Approval
Date Action Reviewed