The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs / Edition 4

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Overview

The Nuts and Bolts of Proofs instructs students on the primary basic logic of mathematical proofs, showing how proofs of mathematical statements work. The text provides basic core techniques of how to read and write proofs through examples. The basic mechanics of proofs are provided for a methodical approach in gaining an understanding of the fundamentals to help students reach different results. A variety of fundamental proofs demonstrate the basic steps in the construction of a proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.

  • 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

Audience: A primer for mathematics, computer science, engineering and physical science students presenting fundamental proof techniques.

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Editorial Reviews

From the Publisher
"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
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Product Details

  • ISBN-13: 9780123822178
  • Publisher: Elsevier Science
  • Publication date: 1/19/2012
  • Edition description: New Edition
  • Edition number: 4
  • Pages: 296
  • Product dimensions: 7.40 (w) x 9.10 (h) x 0.90 (d)

Meet 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.

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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? Direct Proof 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 Counterexamples 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 About Functions Relations The Basics of Groups Limits Cardinality and 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

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