**Pure and Applied Undergraduate Texts**

Volume: 26;
2016;
217 pp;
Hardcover

MSC: Primary 00;

Print ISBN: 978-1-4704-2899-0

Product Code: AMSTEXT/26

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

**Electronic ISBN: 978-1-4704-3496-0
Product Code: AMSTEXT/26.E**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

#### Supplemental Materials

# The Tools of Mathematical Reasoning

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*Tamara J. Lakins*

This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.

#### Readership

Undergraduate students interested in advancing beyond computation-oriented mathematics courses to proof-based courses.

#### Reviews & Endorsements

Lakins' book is a nice, solid exposition of the tools students need as they transition to abstract mathematical thinking.

-- Michele Intermont, MAA Reviews

#### Table of Contents

# Table of Contents

## The Tools of Mathematical Reasoning

- Cover Cover11
- Title page iii4
- Contents vii8
- Preface ix10
- Chapter 1. Language, Logic, and Proof 116
- Chapter 2. Techniques of Proof 2540
- Chapter 3. Induction 5368
- Chapter 4. Sets 6782
- Chapter 5. Functions 93108
- Chapter 6. An Introduction to Number Theory 131146
- Chapter 7. Equivalence Relations and Partitions 155170
- Chapter 8. Finite and Infinite Sets 167182
- Chapter 9. Foundations of Analysis 191206
- Writing Mathematics 209224
- Bibliography 211226
- Index 213228
- Back Cover Back Cover1233