Mathematical Proofs: A Transition to Advanced Mathematics

✍ Scribed by Gary Chartrand, Albert D. Polimeni, Ping Zhang

• Publisher: Pearson
• Year: 2007
• Tongue: English
• Leaves: 240
• Edition: 2
• Category: Library

✦ Synopsis

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

00-preface......Page 1
0-communicating math......Page 10
01-Sets......Page 16
02-Logic......Page 26
03-Direct_contrapositive_proof_odd......Page 43
04-Direct_contrapositive_proof_contd......Page 54
05-Existence and proof by contradiction......Page 65
06-Math Induction......Page 76
07-Prove or Disprove......Page 90
08-Equivalence Relations......Page 100
09-Functions......Page 111
10-Cardinalities of Sets......Page 123
12-Proofs in Calculus......Page 135
Answers......Page 150
ch14......Page 167
ch15......Page 185
ch16......Page 216
an......Page 236