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An Introduction to Mathematical Reasoning

An Introduction to Mathematical Reasoning
Numbers, Sets and Functions

  • Date Published: February 1998
  • availability: Available
  • format: Paperback
  • isbn: 9780521597180
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About the Authors
  • 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.

    • Provides an introduction to the key notion of mathematical proof
    • Fully class-tested by the author
    • Makes use of a large number of fully worked examples
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    Reviews & endorsements

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

    Customer reviews

    02nd Oct 2016 by KarenSinM

    It is recommended by our teacher.In this case,i think it is an essensial reference for the student.

    09th Oct 2016 by BENDEWDEW

    it is a good way to learn maths. so it is very useful

    11th Jan 2017 by Linhnguyen97

    This book is highly recommended as a very helpful resource for learning and revising.

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    Product details

    • Date Published: February 1998
    • format: Paperback
    • isbn: 9780521597180
    • length: 361 pages
    • dimensions: 228 x 153 x 21 mm
    • weight: 0.495kg
    • availability: Available
  • 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.

  • Author

    Peter J. Eccles, University of Manchester

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