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Numbers

  • Textbook
  • © 1991

Overview

Authors:
  1. Heinz-Dieter Ebbinghaus

    1. Mathematisches Institut, Universität Freiburg, Freiburg, Germany

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  2. Hans Hermes

    1. Mathematisches Institut, Universität Freiburg, Freiburg, Germany

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  3. Friedrich Hirzebruch

    1. Man-Planck-Institut für Mathematik, Bonn, Germany

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  4. Max Koecher

    1. Mathematisches Institut, Universität Münster, Münster, Germany

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  5. Klaus Mainzer

    1. Lehrstuhl für Philosophie und Wissenschaftstheorie, Universität Augsburg, Augsburg, Germany

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  6. Jürgen Neukirch

    1. Fachbereich Mathematik, Regensburg, Germany

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  7. Alexander Prestel

    1. Fakultät für Mathematik, Universität Konstanz, Konstanz, Germany

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  8. Reinhold Remmert

    1. Mathematisches Institut, Universität Münster, Münster, Germany

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 123)

Part of the book sub series: Readings in Mathematics (READMATH)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Introduction

    1. Introduction

      • K. Lamotke
      Pages 1-6

  3. From the Natural Numbers, to the Complex Numbers, to the p-adics

    1. Front Matter

      Pages 7-7
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    2. Natural Numbers, Integers, and Rational Numbers

      • K. Mainzer
      Pages 9-26

    3. Real Numbers

      • K. Mainzer
      Pages 27-53

    4. Complex Numbers

      • R. Remmert
      Pages 55-96

    5. The Fundamental Theorem of Algebra

      • R. Remmert
      Pages 97-122

    6. What is π?

      • R. Remmert
      Pages 123-153

    7. The p-Adic Numbers

      • J. Neukirch
      Pages 155-178

  4. Real Division Algebras

    1. Front Matter

      Pages 179-179
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    2. Introduction

      • M. Koecher, R. Remmert
      Pages 181-182

    3. Repertory. Basic Concepts from the Theory of Algebras

      • M. Koecher, R. Remmert
      Pages 183-187

    4. Hamilton’s Quaternions

      • M. Koecher, R. Remmert
      Pages 189-220

    5. The Isomorphism Theorems of Frobenius, Hopf and Gelfand—Mazur

      • M. Koecher, R. Remmert
      Pages 221-247

    6. Cayley Numbers or Alternative Division Algebras

      • M. Koecher, R. Remmert
      Pages 249-264

    7. Composition Algebras. Hurwitz’s Theorem—Vector-Product Algebras

      • M. Koecher, R. Remmert
      Pages 265-280

    8. Division Algebras and Topology

      • F. Hirzebruch
      Pages 281-302

  5. Infinitesimals, Games, and Sets

    1. Front Matter

      Pages 303-303
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    2. Nonstandard Analysis

      • A. Prestel
      Pages 305-327

    3. Numbers and Games

      • H. Hermes
      Pages 329-353
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Keywords

About this book

A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number"­ told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi­ cult to develop broad perspective about their subject. While we each view our specialty as having roots in the past, and sometimes having connec­ tions to other specialties in the present, we seldom see the panorama of mathematical development over thousands of years. Numbers attempts to give that broad perspective, from hieroglyphs to K-theory, from Dedekind cuts to nonstandard analysis.

Authors and Affiliations

  • Mathematisches Institut, Universität Freiburg, Freiburg, Germany

    Heinz-Dieter Ebbinghaus, Hans Hermes

  • Man-Planck-Institut für Mathematik, Bonn, Germany

    Friedrich Hirzebruch

  • Mathematisches Institut, Universität Münster, Münster, Germany

    Max Koecher, Reinhold Remmert

  • Lehrstuhl für Philosophie und Wissenschaftstheorie, Universität Augsburg, Augsburg, Germany

    Klaus Mainzer

  • Fachbereich Mathematik, Regensburg, Germany

    Jürgen Neukirch

  • Fakultät für Mathematik, Universität Konstanz, Konstanz, Germany

    Alexander Prestel

Bibliographic Information

  • Book Title: Numbers

  • Authors: Heinz-Dieter Ebbinghaus, Hans Hermes, Friedrich Hirzebruch, Max Koecher, Klaus Mainzer, Jürgen Neukirch, Alexander Prestel, … Reinhold Remmert

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1005-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1991

  • Softcover ISBN: 978-0-387-97497-2Published: 19 December 1990

  • eBook ISBN: 978-1-4612-1005-4Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XVIII, 398

  • Topics: Number Theory

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