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Finite Fields and Applications

Gary L. Mullen Pennsylvania State University, University Park, PA
Carl Mummert University of Michigan, Ann Arbor, MI
Available Formats:
Softcover ISBN: 978-0-8218-4418-2
Product Code: STML/41
List Price: $41.00 Individual Price:$32.80
Electronic ISBN: 978-1-4704-2150-2
Product Code: STML/41.E
List Price: $38.00 Individual Price:$30.40
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List Price: $61.50 Click above image for expanded view Finite Fields and Applications Gary L. Mullen Pennsylvania State University, University Park, PA Carl Mummert University of Michigan, Ann Arbor, MI Available Formats:  Softcover ISBN: 978-0-8218-4418-2 Product Code: STML/41  List Price:$41.00 Individual Price: $32.80  Electronic ISBN: 978-1-4704-2150-2 Product Code: STML/41.E  List Price:$38.00 Individual Price: $30.40 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:$61.50
• Book Details

Student Mathematical Library
Volume: 412007; 175 pp
MSC: 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 error-correcting 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.

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

• 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.

• 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 self-study. 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 user-friendly 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 412007; 175 pp
MSC: 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 error-correcting 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.

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.