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Finite Fields, with Applications to Combinatorics

Kannan Soundararajan Stanford University, Stanford, CA
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Softcover ISBN: 978-1-4704-6930-6
Product Code: STML/99
List Price: $59.00 Individual Price:$47.20
Electronic ISBN: 978-1-4704-7242-9
Product Code: STML/99.E
List Price: $59.00 Individual Price:$47.20
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List Price: $88.50 Click above image for expanded view Finite Fields, with Applications to Combinatorics Kannan Soundararajan Stanford University, Stanford, CA Available Formats:  Softcover ISBN: 978-1-4704-6930-6 Product Code: STML/99  List Price:$59.00 Individual Price: $47.20  Electronic ISBN: 978-1-4704-7242-9 Product Code: STML/99.E  List Price:$59.00 Individual Price: $47.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$88.50
• Book Details

Student Mathematical Library
Volume: 992022; 170 pp
MSC: Primary 11; 05; 12;

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.

Undergraduate students interested in finite fields and combinatorics.

• Chapters
• 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

• Reviews

• The writing is very clear, and there are abundant cross-references and a good index in case you want to start in the middle of things rather than reading straight through. In particular the book is valuable if you already know about finite fields but would like to see some interesting applications. As abstract algebra texts go, this treatment is very concrete with lots of specific examples. The book has a strong number theory flavor and brings out how these abstract structures generalize the integers.

Allen Stenger, MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Volume: 992022; 170 pp
MSC: Primary 11; 05; 12;

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.

Undergraduate students interested in finite fields and combinatorics.

• Chapters
• 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
• The writing is very clear, and there are abundant cross-references and a good index in case you want to start in the middle of things rather than reading straight through. In particular the book is valuable if you already know about finite fields but would like to see some interesting applications. As abstract algebra texts go, this treatment is very concrete with lots of specific examples. The book has a strong number theory flavor and brings out how these abstract structures generalize the integers.

Allen Stenger, MAA Reviews
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.