MAD 6617-001 Abstract Structures

Selected Topics in Finite Fields

Spring 2005

 

Course Information

 

Course Objectives

To learn the fundamentals of  finite fields. 

 

Prerequisites

MAS 5311 (Algebra I) and MAS 5312  (Algebra II)

 

General Information

Instructor:             Xiang-dong Hou, PH.D.

Office:                    PHY 355

Office Hours:        Tuesday 11:00 – 12:00, Wednesday 12:00 – 1:00 pm, other times by appointment

Phone:                   974-2561

E-mail:                    xhou@math.usf.edu

Web:                      http://www.math.usf.edu/~xhou/courses.htm

                                (Or USF Math Dept --> People --> Faculty --> Xiang-dong Hou --> Other Pages)

References:           R. Lidl and H. Niederreiter, Introduction to finite fields and their applications, Cambridge ; New York : Cambridge University Press, 1994.
                                R. Lidl and H. Niederreiter, Finite Fields, 2nd ed. Encyclopedia of Mathematics and its Applications, 20. Cambridge University Press, Cambridge, 1997.
Lecture Notes:      @http://www.math.usf.edu/~xhou/courses.htm Notes will be updated throughout the course.

 

Tentative coverage
Basic properties of finite fields
Polynomials over finite fields
Exponential sums
Zeros of polynomials over finite fields
General linear group and affine linear group over finite fields.

 

Grading

 The course grade is determined by homework.