An Introduction to Mathematical Reasoning

Numbers, sets and functions

Peter J. Eccles

362 pages, parution le 11/12/1997

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Résumé

The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. 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 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. Over 250 problems include questions to interest and challenge the most able student as well as plenty of routine exercises to help familiarize the reader with the basic ideas.

Provides an introduction to the key notion of mathematical proof
Fully class tested by the author
Makes use of a large number of fully worked examples

Sommaire

Mathematical Statements and Proofs:
- 1. The language of mathematics
- 2. Implications
- 3. Proofs
- 4. Proof by contradiction
- 5. The induction principle
Sets and Functions:
- 6. The language of set theory
- 7. Quantifiers
- 8. Functions
- 9. Injections, surjections and bijections
Numbers and Counting:
- 10. Counting
- 11. Properties of finite sets
- 12. Counting functions and subsets
- 13. Number systems
- 14. Counting infinite sets
Arithmetic:
- 15. The division theorem
- 16. The Euclidean algorithm
- 17. Consequences of the Euclidean algorithm
- 18. Linear diophantine equations
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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Peter J. Eccles
Parution	11/12/1997
Nb. de pages	362
Format	15,5 x 23
Couverture	Broché
Poids	510g
Intérieur	Noir et Blanc
EAN13	9780521597180
ISBN13	978-0-521-59718-0