**Student Mathematical Library**

Volume: 41;
2007;
175 pp;
Softcover

MSC: Primary 11;
Secondary 05

**Print 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

#### Supplemental Materials

# Finite Fields and Applications

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*Gary L. Mullen; Carl Mummert*

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

#### Readership

Undergraduate and graduate students interested in the theory of finite fields and applications.

#### Reviews & Endorsements

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 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

#### Table of Contents

# Table of Contents

## Finite Fields and Applications

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents iii4 free
- Foreword: MASS and REU at Pann StateUniversity v6 free
- Preface vii8 free
- Chapter 1. Finite Fields 112 free
- Chapter 2. Combinatorics 4354
- Chapter 3. Algebraic Coding Theory 7990
- Chapter 4. Cryptography 109120
- Appendix A. Background in Number Theory and Abstract Algebra 133144
- Appendix B. Hints for Selected Exercises 155166
- References 165176
- Index 171182
- Backcover Backcover1190