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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

Hardcover

Published: 11th December 1997
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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.

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

Mathematical Statements and Proofs
The language of mathematics
Implications
Proofs
Proof by contradiction
The induction principle
Sets and Functions
The language of set theory
Quantifiers
Functions
Injections, surjections and bijections
Numbers and Counting
Counting
Properties of finite sets
Counting functions and subsets
Number systems
Counting infinite sets
Arithmetic
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: 9780521592697
ISBN-10: 0521592690
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 364
Published: 11th December 1997
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.72 x 16.2  x 2.92
Weight (kg): 0.69