A Concise Introduction to Pure Mathematics, Second Edition

Published:
November 02, 2005 by Chapman and Hall/CRC - 224 Pages
Author(s):
Martin Liebeck, Imperial College, London, UK; Martin Liebeck, Imperial College, London, UK
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ISBN 9781584885474
Cat# C5475
 

Features

  • Expands upon mathematical basics in interesting and stimulating directions
  • Introduces the language of sets and describes methods for writing proofs
  • Proves basic results on prime numbers, and shows how these can be used to devise secret codes
  • Defines and analyzes three basic number systems - real numbers, integers, and rational numbers
  • Discusses complex numbers and reveals the method for solving cubic equations
  • Explores induction, Euler's formula, and Platonic solids
  • Provides an introduction to Analysis via a fundamental fact about real numbers
  • Reviews Binomial and Multinomial Theorems for counting
  • Addresses problems related to infinite sets
  • A Solutions Manual is available for qualified course adoptions

    • Summary

    A Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.

    The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics.

    What's New in the Second Edition:

  • Contains extra material concerning prime numbers, forming the basis for data encryption
  • Explores "Secret Codes" - one of today's most spectacular applications of pure mathematics
  • Discusses Permutations and their importance in many topics in discrete mathematics

    The textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly independent sections related to: an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability.

    • Table of Contents

    Sets and Proofs
    Number Systems
    Decimals
    Inequalities
    nth Roots and Rational Powers
    Complex Numbers
    Polynomial Equations
    Induction
    Euler's Formula and Platonic Solids
    Introduction to Analysis
    The Integers
    Prime Factorization
    More on Prime Numbers
    Congruence of Integers
    More on Congruence
    Secret Codes
    Counting and Choosing
    More on Sets
    Equivalence Relations
    Functions
    Permutations
    Infinity
    Further Reading
    Index of Symbols

    Editorial Reviews

    "A gentle but fascinating introduction into the culture of mathematics…This book will give a student the understanding to go on in further courses in abstract algebra and analysis. The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. At the very least, the student will have an appreciation of mathematics.

    "As usual, Liebeck's writing style is clear and easy to read. This is a book that could be read by a student on his or her own. There is a wide selection of problems ranging from routine to quite challenging."
    Robert Guralnick, Chair of the Mathematics Department, University of Southern California, from the Foreword

    "The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world for good students not planning to go further in the field."

    – Gerald A. Heuer, in Zentralblatt Math, 2009

     

    ". . . a pleasure to read . . . a very welcome and highly accessible book."

    – Michael Ward, in The Mathematical Gazette, March 2007

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