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Mathematical Proofs: Transition To Advanced Mathematics

Mathematical Proofs: Transition To Advanced Mathematics - 2nd edition

ISBN13: 978-0321390530

Cover of Mathematical Proofs: Transition To Advanced Mathematics 2ND 08 (ISBN 978-0321390530)
ISBN13: 978-0321390530
ISBN10: 0321390539
Cover type:
Edition: 2ND 08
Copyright: 2008
Publisher: Addison-Wesley Longman, Inc.
Published: 2008
International: No

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Mathematical Proofs: Transition To Advanced Mathematics - 2ND 08 edition

ISBN13: 978-0321390530

Gary Chartrand

ISBN13: 978-0321390530
ISBN10: 0321390539
Cover type:
Edition: 2ND 08
Copyright: 2008
Publisher: Addison-Wesley Longman, Inc.
Published: 2008
International: No
Summary

Mathematical Proofs: A Transition to Advanced Mathematics, 2/e,prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.KEY TOPICS: Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory.MARKET: For all readers interested in advanced mathematics and logic.

Table of Contents

0. Communicating Mathematics Learning Mathematics What Others Have Said About Writing Mathematical Writing Using Symbols Writing Mathematical Expressions Common Words and Phrases in Mathematics Some Closing Comments about Writing

1. Sets 1.1 Describing a Set 1.2 Subsets 1.3 Set Operations 1.4 Indexed Collections of Sets 1.5 Partitions of Sets 1.6 Cartesian Products of Sets Exercises for Chapter 1

2. Logic 2.1 Statements 2.2 The Negation of a Statement 2.3 The Disjunction and Conjunction of Statements 2.4 The Implication 2.5 More on Implications 2.6 The Biconditional 2.7 Tautologies and Contradictions 2.8 Logical Equivalence 2.9 Some Fundamental Properties of Logical Equivalence 2.10 Quantified Statements 2.11 Characterizations of Statements Exercises for Chapter 2

3. Direct Proof and Proof by Contrapositive 3.1 Trivial and Vacuous Proofs 3.2 Direct Proofs 3.3 Proof by Contrapositive 3.4 Proof by Cases 3.5 Proof Evaluations Exercises for Chapter 3

4. More on Direct Proof and Proof by Contrapositive 4.1 Proofs Involving Divisibility of Integers 4.2 Proofs Involving Congruence of Integers 4.3 Proofs Involving Real Numbers 4.4 Proofs Involving Sets 4.5 Fundamental Properties of Set Operations 4.6 Proofs Involving Cartesian Products of Sets Exercises for Chapter 4

5. Existence and Proof by Contradiction 5.1 Counterexamples 5.2 Proof by Contradiction 5.3 A Review of Three Proof Techniques 5.4 Existence Proofs 5.5 Disproving Existence Statements Exercises for Chapter 5

6. Mathematical Induction 6.1 The Principle of Mathematical Induction 6.2 A More General Principle of Mathematical Induction 6.3 Proof by Minimum Counterexample 6.4 The Strong Principle of Mathematical Induction Exercises for Chapter 6

7. Prove or Disprove 7.1 Conjectures in Mathematics 7.2 Revisiting Quantified Statements 7.3 Testing Statements 7.4 A Quiz of "Prove or Disprove" Problems Exercises for Chapter 7 8. Equivalence Relations

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Cover of Mathematical Proofs 3rd edition

Mathematical Proofs - 3rd edition

ISBN13: 978-0321797094
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