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Numbers and Geometry

  • Textbook
  • © 1998

Overview

Authors:
  1. John Stillwell

    1. Department of Mathematics, Monash University, Clayton, Australia

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  • Highly accessible, the book presupposes only high school algebra and therefore can be read by any well prepared student entering university
  • Written by a clear and skillful author who has published several successful books at Springer
  • Contains a highly unique treatment of fundamental topics in algebra, analysis, and geometry, at an elementary level with an historical perspective

Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Arithmetic

    • John Stillwell
    Pages 1-35

  3. Geometry

    • John Stillwell
    Pages 37-67

  4. Coordinates

    • John Stillwell
    Pages 69-109

  5. Rational Points

    • John Stillwell
    Pages 111-142

  6. Trigonometry

    • John Stillwell
    Pages 143-176

  7. Finite Arithmetic

    • John Stillwell
    Pages 177-213

  8. Complex Numbers

    • John Stillwell
    Pages 215-245

  9. Conic Sections

    • John Stillwell
    Pages 247-279

  10. Elementary Functions

    • John Stillwell
    Pages 281-309

  11. Back Matter

    Pages 311-343
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Keywords

About this book

NUMBERS AND GEOMETRY is a beautiful and relatively elementary account of a part of mathematics where three main fields--algebra, analysis and geometry--meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus (or a pre-calculus) book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. The key is algebra, which brings arithmetic and geometry together, and allows them to flourish and branch out in new directions. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He believes that most of mathematics is about numbers, curves and functions, and the links between these concepts can be suggested by a thorough study of simple examples, such as the circle and the square. This book covers the main ideas of Euclid--geometry, arithmetic and the theory of real numbers, but with 2000 years of extra insights attached. NUMBERS AND GEOMETRY presupposes only high school algebra and therefore can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics because it is such an attractive and unusual treatment of fundamental topics. Also, it will serve admirably in courses aimed at giving students from other areas a view of some of the basic ideas in mathematics. There is a set of well-written exercises at the end of each section, so new ideas can be instantly tested and reinforced.

Authors and Affiliations

  • Department of Mathematics, Monash University, Clayton, Australia

    John Stillwell

Bibliographic Information

  • Book Title: Numbers and Geometry

  • Authors: John Stillwell

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0687-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Hardcover ISBN: 978-0-387-98289-2Published: 30 October 1997

  • Softcover ISBN: 978-1-4612-6867-3Published: 28 September 2012

  • eBook ISBN: 978-1-4612-0687-3Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XIV, 343

  • Topics: Number Theory, Geometry

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