Peter J. Eccles (University of Manchester)

An Introduction to Mathematical Reasoning

• Broschiertes Buch

Produktbeschreibung

This book introduces 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. Over 250 problems include questions to interest and challenge the most able student and plenty of routine exercises to help familiarize the reader with the basic ideas.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 364
• Erscheinungstermin: 11. Dezember 1997
• Englisch
• Abmessung: 229mm x 152mm x 21mm
• Gewicht: 524g
• ISBN-13: 9780521597180
• ISBN-10: 0521597188
• Artikelnr.: 22413598

Inhaltsangabe

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.