Mathematical Proofs A Transition to Advanced Mathematics 2nd Edition by Gary Chartrand, Albert Polimeni, Ping Zhang 0321390539 978-0321390530

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ISBN-10 ‏ : ‎ 0321390539

ISBN-13 ‏ : ‎ 978-0321390530

Author:   Gary Chartrand, Albert Polimeni, Ping Zhang

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.

Mathematical Proofs A Transition to Advanced Mathematics 2nd Table of contents:

0
Communicating Mathematics
0.1 Learning Mathematics 2
0.2 What Others Have Said About Writing 3
0.3 Mathematical Writing 5
0.4 Using Symbols
0.5 Writing Mathematical Expressions 8
0.6 Common Words and Phrases in Mathematics 10
0.7 Some Closing Comments About Writing 12
1 Sets
1.1 Describing a Set 14
1.2 Subsets 18
1.3 Set Operations 23
1.4 Indexed Collections of Sets 27
1.5 Partitions of Sets 31
1.6 Cartesian Products of Sets 33
Chapter 1 Supplemental Exercises 35
2 Logic
2.1 Statements
2.2 Negations 41
2.3 Disjunctions and Conjunctions 43
2.4 Implications 45
2.5 More on Implications 49
2.6 Biconditionals 53
2.7 Tautologies and Contradictions 57
2.8 Logical Equivalence 60
2.9 Some Fundamental Properties of Logical Equivalence 62
2.10 Quantified Statements 65
2.11 Characterizations 76
Chapter 2 Supplemental Exercises 78

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