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An Introduction to Mathematical Reasoning : Numbers, Sets and Functions - Peter J. Eccles

An Introduction to Mathematical Reasoning

Numbers, Sets and Functions

Paperback Published: 11th December 1997
ISBN: 9780521597180
Number Of Pages: 361

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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.

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'The book is written with understanding of the needs of students ...' European Mathematical Society

Mathematical Statements and Proofs
The language of mathematics
Proof by contradiction
The induction principle
Sets and Functions
The language of set theory
Injections, surjections and bijections
Numbers and Counting
Properties of finite sets
Counting functions and subsets
Number systems
Counting infinite sets
The division theorem
The Euclidean algorithm
Consequences of the Euclidean algorithm
Linear diophantine equations
Modular Arithmetic
Congruences of integers
Linear congruences
Congruence classes and the arithmetic of remainders
Partitions and equivalence relations
Prime Numbers
The sequence of prime numbers
Congruence modulo a prime
Solutions to exercises
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521597180
ISBN-10: 0521597188
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 361
Published: 11th December 1997
Country of Publication: GB
Dimensions (cm): 22.61 x 14.99  x 1.78
Weight (kg): 0.52