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9780521597180

An Introduction to Mathematical Reasoning: Numbers, Sets and Functions

by
  • ISBN13:

    9780521597180

  • ISBN10:

    0521597188

  • Format: Paperback
  • Copyright: 1998-01-28
  • Publisher: Cambridge University Press

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Supplemental Materials

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Summary

This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

Table of Contents

Part I. Mathematical Statements and Proofs: 1. The language of mathematics
2. Implications
3. Proofs
4. Proof by contradiction
5. The induction principle
Part II. Sets and Functions: 6. The language of set theory
7. Quantifiers
8. Functions
9. Injections, surjections and bijections
Part III. Numbers and Counting: 10. Counting
11. Properties of finite sets
12. Counting functions and subsets
13. Number systems
14. Counting infinite sets
Part IV. Arithmetic: 15. The division theorem
16. The Euclidean algorithm
17. Consequences of the Euclidean algorithm
18. Linear diophantine equations
Part V. Modular Arithmetic: 19. Congruences of integers
20. Linear congruences
21. Congruence classes and the arithmetic of remainders
22. Partitions and equivalence relations
Part VI. Prime Numbers: 23. The sequence of prime numbers
24. Congruence modulo a prime
Solutions to exercises.

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

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