**Pure and Applied Undergraduate Texts**

Volume: 31;
2018;
314 pp;
Hardcover

MSC: Primary 11; 37;

**Print ISBN: 978-1-4704-3097-9
Product Code: AMSTEXT/31**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

**Electronic ISBN: 978-1-4704-4672-7
Product Code: AMSTEXT/31.E**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

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#### Supplemental Materials

# An Experimental Introduction to Number Theory

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*Benjamin Hutz*

This book presents material suitable for an
undergraduate course in elementary number theory from a computational
perspective. It seeks to not only introduce students to the standard
topics in elementary number theory, such as prime factorization and
modular arithmetic, but also to develop their ability to formulate and
test precise conjectures from experimental data. Each topic is
motivated by a question to be answered, followed by some experimental
data, and, finally, the statement and proof of a theorem. There are
numerous opportunities throughout the chapters and exercises for the
students to engage in (guided) open-ended exploration. At the end of a
course using this book, the students will understand how mathematics
is developed from asking questions to gathering data to formulating
and proving theorems.

The mathematical prerequisites for this book are few. Early
chapters contain topics such as integer divisibility, modular
arithmetic, and applications to cryptography, while later chapters
contain more specialized topics, such as Diophantine approximation,
number theory of dynamical systems, and number theory with
polynomials. Students of all levels will be drawn in by the patterns
and relationships of number theory uncovered through data driven
exploration.

#### Readership

Undergraduate students interested in number theory.

#### Reviews & Endorsements

If you see the value of stressing calculation and computers in a first course in number theory, then this book is one that you will want to take a good look at the next time you teach number theory.

-- Mark Hunacek, MAA Reviews

#### Table of Contents

# Table of Contents

## An Experimental Introduction to Number Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- Introduction 114
- Chapter 1. Integers 518
- Chapter 2. Modular Arithmetic 3952
- Chapter 3. Quadratic Reciprocity and Primitive Roots 6578
- Chapter 4. Secrets 91104
- Chapter 5. Arithmetic Functions 109122
- Chapter 6. Algebraic Numbers 143156
- Chapter 7. Rational and Irrational Numbers 157170
- Chapter 8. Diophantine Equations 187200
- Chapter 9. Elliptic Curves 221234
- Chapter 10. Dynamical Systems 247260
- Chapter 11. Polynomials 275288
- Bibliography 299312
- List of Algorithms 303316
- List of Notation 305318
- Index 307320
- Back Cover Back Cover1330