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

by Antonella Cupillari

Overview

The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.

* The "List of Symbols" has been extended.
* Set Theory section has been strengthened with more examples and exercises.
* Addition of "A Collection of Proofs"

Product Details

ISBN-13:	9780080537900
Publisher:	Elsevier Science
Publication date:	09/08/2005
Series:	The Nuts and Bolts of Proofs Series
Sold by:	Barnes & Noble
Format:	eBook
Pages:	192
File size:	4 MB

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

Introduction and Basic Terminology
General Suggestions
Some basic Techniques Used in Proving a Theorem of the Form :If A then B”
Direct Proof
Related Statements
Proof by Contra positive
How to Construct the Negation of a Statement
Special Kinds of Theorems
“If and only if” or Equivalence Theorems
Use of Counterexamples
Mathematical Induction
Existence Theorems
Uniqueness Theorems
Equality of Sets
Equality of Numbers
Composite Statements
Limits
Review Exercises
Exercises without Soultions
Collection of Proofs
Solutions of the Exercises at the End of the Sections and the Review Exercises
Other Books on the Subject of Proofs and Mathematical Writing

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