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    An Introduction to Mathematical Reasoning: Numbers, Sets and Functions (Paperback) By (author) Peter J. Eccles

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    DescriptionThe 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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  • Full bibliographic data for An Introduction to Mathematical Reasoning

    Title
    An Introduction to Mathematical Reasoning
    Subtitle
    Numbers, Sets and Functions
    Authors and contributors
    By (author) Peter J. Eccles
    Physical properties
    Format: Paperback
    Number of pages: 361
    Width: 152 mm
    Height: 226 mm
    Thickness: 20 mm
    Weight: 581 g
    Language
    English
    ISBN
    ISBN 13: 9780521597180
    ISBN 10: 0521597188
    Classifications

    BIC E4L: MAT
    B&T Book Type: NF
    DC21: 510
    Nielsen BookScan Product Class 3: S7.9T
    B&T Modifier: Region of Publication: 03
    B&T Modifier: Academic Level: 01
    B&T General Subject: 710
    Warengruppen-Systematik des deutschen Buchhandels: 16200
    Ingram Subject Code: MA
    Libri: I-MA
    B&T Modifier: Text Format: 06
    B&T Merchandise Category: STX
    DC22: 511.3
    LC subject heading:
    BIC subject category V2: PBC
    BISAC V2.8: MAT028000, MAT018000
    B&T Approval Code: A10603000
    LC subject heading:
    BISAC V2.8: MAT022000, MAT036000
    B&T Approval Code: A51090000
    BISAC V2.8: MAT021000
    LC classification: QA9.54 .E23 1997
    LC subject heading:
    Thema V1.0: PBCD, PBH, PBV, PBC
    Edition statement
    New ed.
    Publisher
    CAMBRIDGE UNIVERSITY PRESS
    Imprint name
    CAMBRIDGE UNIVERSITY PRESS
    Publication date
    28 January 1998
    Publication City/Country
    Cambridge
    Author Information
    fm.author_biographical_note1
    Review quote
    'The book is written with understanding of the needs of students ...' European Mathematical Society
    Table of contents
    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.