# Mathematical Proofs: A Transition to Advanced Mathematics, 3rd Edition

## Book Description

*Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition*, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

### Table of Contents

Chapter 1 Sets

Chapter 2 Logic

Chapter 3 Direct Proof and Proof by Contrapositive

Chapter 4 More on Direct Proof and Proof by Contrapositive

Chapter 5 Existence and Proof by Contradiction

Chapter 6 Mathematical Induction

Chapter 7 Prove or Disprove

Chapter 8 Equivalence Relations

Chapter 9 Functions

Chapter 10 Cardinalities of Sets

Chapter 11 Proofs in Number Theory

Chapter 12 Proofs in Calculus

Chapter 13 Proofs in Group Theory

Chapter 14 Proofs in Ring Theory (Online)

Chapter 15 Proofs in Linear Algebra (Online)

Chapter 16 Proofs in Topology (Online)

## Book Details

- Title: Mathematical Proofs: A Transition to Advanced Mathematics, 3rd Edition
- Author: Albert D. Polimeni, Gary Chartrand, Ping Zhang
- Length: 416 pages
- Edition: 3
- Language: English
- Publisher: Pearson
- Publication Date: 2012-09-27
- ISBN-10: 0321797094
- ISBN-13: 9780321797094

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