Finite fields, with applications to combinatorics

Author(s)

• Soundararajan, Kannan

Bibliographic Information

Finite fields, with applications to combinatorics

Kannan Soundararajan

（Student mathematical library, v. 99）

American Mathematical Society, c2022

Note

Includes bibliographical references (p. 165-167) and index

Description and Table of Contents

Description

This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.

Table of Contents

Primes and factorization Primes in the integers Congruences in rings Primes in polynomial rings: Constructing finite fields The additive and multiplicative structures of finite fields Understanding the structures of $\mathbb{Z}/n\mathbb{Z}$ Combinatorial applications of finite fields The AKS primality test Synopsis of finite fields Bibliography Index

by "Nielsen BookData"

Details

• NCID: BC17479624
• ISBN:
  • 9781470469306
• LCCN: 2022037518
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: xii, 170 p.
• Size: 22 cm
• Classification:
  • LCC : QA247.3
  • DC23 : 512.7/4
• Subject Headings:
  • LCSH : Finite fields (Algebra)
  • LCSH : Combinatorial analysis
• Parent Bibliography ID:
  • BA42504671