Instructor: Dr. Cordero
Office: 486 Pickard Hall
Office hours: MW 10-11:30 a.m. or by appointment.
Class webpage http://www2.uta.edu/math/cordero/courses.htm
About the course: In this course we will study fields, in particular finite fields in depth. We will begin the semester with a review of groups, rings and fields, in general. Then we will study field extensions, the Fundamental Theorem of Galois Theory, and splitting fields. The last half of the semester we will investigate the structure of finite fields and factorization of polynomials over finite fields. We will conclude with a look at some theoretical applications of finite fields.
The material is covered in the following books:
Abstract Algebra, David S. Dummit and Richard M. Foote
Algebra, Thomas W. Hungerford
Introduction to finite fields and their applications, Revised Edition, Rudolf Lidl and Harald Niederreiter
Homework and informal class presentations (60%)
Final Research Presentation (40%)
Weeks 1-3 Algebraic foundations
Weeks 4-6 Field extensions and Galois Theory
Weeks 7-13 Finite fields and polynomials over finite fields
Weeks 14-15 Research presentations
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