The Nuts and Bolts of Proofs,
Edition 4 An Introduction to Mathematical Proofs
By Antonella Cupillari

Publication Date: 05 Jan 2012
The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs provides basic logic of mathematical proofs and shows how mathematical proofs work. It offers techniques for both reading and writing proofs. The second chapter of the book discusses the techniques in proving if/then statements by contrapositive and proofing by contradiction. It also includes the negation statement, and/or. It examines various theorems, such as the if and only-if, or equivalence theorems, the existence theorems, and the uniqueness theorems. In addition, use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are covered in this chapter. The book also provides mathematical topics for practicing proof techniques. Included here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book invaluable.

Key Features

  • Jumps right in with the needed vocabulary—gets students thinking like mathematicians from the beginning
  • Offers a large variety of examples and problems with solutions for students to work through on their own
  • Includes a collection of exercises without solutions to help instructors prepare assignments
  • Contains an extensive list of basic mathematical definitions and concepts needed in abstract mathematics
About the author
By Antonella Cupillari, Associate Professor of Mathematics, Pennsylvania State Erie in Behrend College, Erie, PA, USA
Table of Contents

Chapter 1. Getting Started

Introduction and Basic Terminology

General Suggestions

Chapter 2. Basic Techniques to Prove If/Then Statements

What Does “If/Then¿ Mean?

The Negation of a Statement: AND/OR

Proof by Contrapositive

Proof by Contradiction

Chapter 3. Special Kinds of Theorems

“If and Only If¿ or “Equivalence Theorems¿

Use of Counter Examples

Mathematical Induction

Existence Theorems

Uniqueness Theorems

Composite Statements

Equality of Numbers

Chapter 4. Some Mathematical Topics on Which to Practice Proof Techniques

Basic Set Theory and Indexed Families

About Functions


The Basics of Groups


Sizes of Infinity

Chapter 5. Review Exercises

Exercises without Solutions

Collection of “Proofs¿

Solutions for the Exercises at the End of the Sections and the Review Exercises

Solutions for the Exercises at the End of the Sections

Solutions for the Review Exercises

Other Books on the Subject of Proofs and Mathematical Writing

Book details
ISBN: 9780123822178
Page Count: 296
Retail Price : £36.99

Intended for undergraduate math courses as a primer to assist engineering and physical science students on fundamental proof techniques