Introduction to
              Mathematical Thinking
                Keith Devlin
              © Keith Devlin, 2012
   
   
 Publisher:
 Keith Devlin
 331 Poe St, Unit 4
 Palo Alto, CA 94301
 USA
 http://profkeithdevlin.com
   
   
   
   
   
 © Keith Devlin, 2012
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 reproduced or utilized in any form, electronic or mechanical, including photocopying,
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 Publication data
  Devlin, Keith, Introduction to Mathematical Thinking
  First published, July 2012
  ISBN-13: 978-0615653631
  ISBN-10: 0615653634
 Contents
 Preface
 What this book is about
 1  What is mathematics?
  1.1 More than arithmetic
  1.2 Mathematical notation
  1.3 Modern college-level mathematics
  1.4 Why do you have to learn this stuff?
 2  Getting precise about language
  2.1 Mathematical statements
  2.2 The logical combinators and, or, and not
  2.3 Implication
  2.4 Quantifiers
 3  Proofs
  3.1 What is a proof?
  3.2 Proof by contradiction
  3.3 Proving conditionals
  3.4 Proving quantified statements
  3.5 Induction proofs
 4  Proving results about numbers
  4.1 The integers
  4.2 The real numbers
  4.3 Completeness
  4.4 Sequences
 APPENDIX: Set theory
 Index