Softcover ISBN:  9780821844182 
Product Code:  STML/41 
List Price:  $41.00 
Individual Price:  $32.80 
Electronic ISBN:  9781470421502 
Product Code:  STML/41.E 
List Price:  $38.00 
Individual Price:  $30.40 

Book DetailsStudent Mathematical LibraryVolume: 41; 2007; 175 ppMSC: Primary 11; Secondary 05;
This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications.
The first chapter is devoted to the theory of finite fields. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields.
Each of the remaining chapters details applications. Chapter 2 deals with combinatorial topics such as the construction of sets of orthogonal latin squares, affine and projective planes, block designs, and Hadamard matrices. Chapters 3 and 4 provide a number of constructions and basic properties of errorcorrecting codes and cryptographic systems using finite fields.
Each chapter includes a set of exercises of varying levels of difficulty which help to further explain and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises related to this material. Appendix B provides hints and partial solutions for many of the exercises in each chapter. A list of 64 references to further reading and to additional topics related to the book's material is also included.
Intended for advanced undergraduate students, it is suitable both for classroom use and for individual study.This book is published in cooperation with Mathematics Advanced Study Semesters.ReadershipUndergraduate and graduate students interested in the theory of finite fields and applications.

Table of Contents

Chapters

Chapter 1. Finite fields

Chapter 2. Combinatorics

Chapter 3. Algebraic coding theory

Chapter 4. Cryptography

Appendix A. Background in number theory and abstract algebra

Appendix B. Hints for selected exercises


Additional Material

Reviews

The book provides a brief introduction to the theory of finite fields and to some of their applications. It is accessible for advanced undergraduate students.
EMS Newsletter 
This book gives a quick, clear introduction to finite fields and discusses applications in combinatorics, algebraic coding theory, and cryptography. ... The work contains more than 100 exercises, appendixes on number theoretic and algebraic background, exercise hints, and a list of 65 references.
CHOICE Magazine 
The book is very well written and most stimulating. In addition, it is well suited for selfstudy. The student having a course using this book or anyone studying it will be substantially rewarded. On the whole, the authors succeed in providing a nice introduction to an active field of research.
Mathematical Reviews 
Altogether, this undergraduate text is an extremely carefully written introduction to the subject for beginners, which stands out by its remarkable features: instructional mastery, lucidity, diversity, profundity, topicality, and userfriendly determination. Being a lovely invitation to this current topic of mathematical (and interdisciplinary) research, the book is perfectly suitable both for classroom use and for individual study.
Zentralblatt MATH


RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications.
The first chapter is devoted to the theory of finite fields. After covering their construction and elementary properties, the authors discuss the trace and norm functions, bases for finite fields, and properties of polynomials over finite fields.
Each of the remaining chapters details applications. Chapter 2 deals with combinatorial topics such as the construction of sets of orthogonal latin squares, affine and projective planes, block designs, and Hadamard matrices. Chapters 3 and 4 provide a number of constructions and basic properties of errorcorrecting codes and cryptographic systems using finite fields.
Each chapter includes a set of exercises of varying levels of difficulty which help to further explain and motivate the material. Appendix A provides a brief review of the basic number theory and abstract algebra used in the text, as well as exercises related to this material. Appendix B provides hints and partial solutions for many of the exercises in each chapter. A list of 64 references to further reading and to additional topics related to the book's material is also included.
Intended for advanced undergraduate students, it is suitable both for classroom use and for individual study.
Undergraduate and graduate students interested in the theory of finite fields and applications.

Chapters

Chapter 1. Finite fields

Chapter 2. Combinatorics

Chapter 3. Algebraic coding theory

Chapter 4. Cryptography

Appendix A. Background in number theory and abstract algebra

Appendix B. Hints for selected exercises

The book provides a brief introduction to the theory of finite fields and to some of their applications. It is accessible for advanced undergraduate students.
EMS Newsletter 
This book gives a quick, clear introduction to finite fields and discusses applications in combinatorics, algebraic coding theory, and cryptography. ... The work contains more than 100 exercises, appendixes on number theoretic and algebraic background, exercise hints, and a list of 65 references.
CHOICE Magazine 
The book is very well written and most stimulating. In addition, it is well suited for selfstudy. The student having a course using this book or anyone studying it will be substantially rewarded. On the whole, the authors succeed in providing a nice introduction to an active field of research.
Mathematical Reviews 
Altogether, this undergraduate text is an extremely carefully written introduction to the subject for beginners, which stands out by its remarkable features: instructional mastery, lucidity, diversity, profundity, topicality, and userfriendly determination. Being a lovely invitation to this current topic of mathematical (and interdisciplinary) research, the book is perfectly suitable both for classroom use and for individual study.
Zentralblatt MATH