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Introduction to Mathematical Reasoning : Numbers, Sets and Functions by Peter J. Eccles (1997, Trade Paperback)
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Introduction to Mathematical Reasoning : Numbers, Sets and Functions, Paperback by Eccles, Peter J., ISBN 0521597188, ISBN-13 9780521597180, Brand New, Free shipping in the US The purpose of this book is to introduce the basic ideas of mathematical proof and reasoning to students starting university mathematics.
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-100521597188
ISBN-139780521597180
eBay Product ID (ePID)943131
Product Key Features
Number of Pages361 Pages
Publication NameIntroduction to Mathematical Reasoning : Numbers, Sets and Functions
LanguageEnglish
Publication Year1997
SubjectLogic
TypeTextbook
AuthorPeter J. Eccles
Subject AreaMathematics
FormatTrade Paperback
Dimensions
Item Height0.8 in
Item Weight16.2 Oz
Item Length9 in
Item Width6 in
Additional Product Features
Intended AudienceCollege Audience
LCCN97-011977
Reviews"A student planning to study advanced mathematics would be well served by first mastering the material in this book...a rigorous study of sevearl fundamental topics pervasive in mathematics, including sets, functions, cardinality, combinatorics, and modular arithmetic." D.S. Larson, Choice
Dewey Edition21
TitleLeadingAn
IllustratedYes
Dewey Decimal511.3
Table Of ContentPart 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.
SynopsisThis 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., 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., 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.
LC Classification NumberQA9.54 .E23 1997
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