Finite Fields, with Applications to Combinatorics (Paperback)

Kannan Soundararajan

ISBN 10: 1470469308 / ISBN 13: 9781470469306

Published by American Mathematical Society, Providence, 2023

About this Item

Paperback. 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. Uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. The book constructs all finite fields from scratch and shows that they are unique up to isomorphism. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781470469306

Bibliographic Details

• Title: Finite Fields, with Applications to Combinatorics (Paperback)
• Publisher: American Mathematical Society, Providence
• Publication Date: 2023
• Language: English
• ISBN 10: 1470469308
• ISBN 13: 9781470469306
• Binding: Paperback
• Condition: new

About this title

Synopsis

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.

About the Author

Kannan Soundararajan, Stanford University, CA.