Lectures on finite fields

✍ Scribed by Hou, Xiang-dong

• Publisher: American Mathematical Society
• Year: 2018
• Tongue: English
• Leaves: 242
• Series: AMS Graduate studies in mathematics 190
• Category: Library

✦ Synopsis

Based on author's lecture notes, at University of South Florida.

Abstract:

The theory of finite fields encompasses algebra, combinatorics, and number theory and has furnished widespread applications in other areas of mathematics and computer science. This book covers basic facts about finite fields, polynomials over finite fields, Gauss sums, algebraic number theory and cyclotomic fields, zeros of polynomials over finite fields, and classical groups over finite fields.  Read more...

✦ Table of Contents

Content: Ch. 1. Preliminaries --
Ch. 2. Polynomials over finite fields --
Ch. 3. Gauss sums --
Ch. 4. Algebraic number theory --
Ch. 5. Zeros of polynomials over finite fields --
Ch. 6. Classical groups.

✦ Subjects

Finite fields (Algebra);Number theory -- Instructional exposition (textbooks, tutorial papers, etc.).;Number theory -- Forms and linear algebraic groups -- Forms and linear algebraic groups.;Number theory -- Algebraic number theory: global fields -- Algebraic number theory: global fields.;Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Finite fields and commutative rings (number-theoretic aspects).