The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs

by Antonella Cupillari

Overview

This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course.

This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers is provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments.

Product Details

ISBN-13:	9780323990219
Publisher:	Elsevier Science
Publication date:	01/05/2023
Sold by:	Barnes & Noble
Format:	eBook
Pages:	416
File size:	24 MB
Note:	This product may take a few minutes to download.

About the Author

Antonella Cupillari is an associate professor of mathematics at Pennsylvania State Erie in Behrend College. She received her Laurea in Mathematics in Italy, and her M.A. and Ph.D. at the State University of New York at Albany. She has been a participant in the Mathematical Association of America/National Science Foundation Institute on the "History of Mathematics and Its Use in Teaching." Cupillari is the author of several papers in analysis, mathematics education, and the history of mathematics. She is also the author of the first edition of The Nuts and Bolts of Proofs.

Table of Contents

	List of Symbols	v
	Preface	xi
	Introduction and Basic Terminology	1
	General Suggestions	5
	Some Basic Techniques Used in Proving a Theorem of the Form "If A, then B"	9
	Direct Proof	12
	Related Statements	19
	Proof by Contrapositive	21
	How to Construct the Negation of a Statement	25
	Special Types of Theorems	33
	"If and only if" or Equivalence Theorems	33
	Use of Counterexamples	43
	Mathematical Induction	46
	Existence Theorems	55
	Uniqueness Theorems	58
	Equality of Sets	64
	Equality of Numbers	73
	Composite Statements	76
	Review Exercises	85
	Exercises Without Solutions	89
	Collection of "Proofs"	97
	Solutions for the Exercises at the End of the Sections and the Review Exercises	103
	Solutions for the Exercises at the End of the Sections	104
	Solutions for the Review Exercises	127
	Other Books on the Subject of Proofs and Mathematical Writing	147
	Books on Mathematical Writing	148
	Index	149

What People are Saying About This

From the Publisher

Demonstrates the construction of proofs to help students develop the skills they need to transition to higher-level, more abstract math courses

Editorial Reviews

"It is written with great accuracy and a level of enthusiasm necessary for the Herculean task of launching mathematical handle-turners into the world of mathematical thinking…for those required to teach ‘transition courses’, I recommend perusal of this book as a possible course text." —MAA online, December 3, 2013

From the Publisher