Excursions in the History of Mathematics

  • Israel Kleiner

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Number Theory

    1. Front Matter
      Pages 1-1
    2. Israel Kleiner
      Pages 31-45
  3. Calculus/Analysis

  4. Proof

    1. Front Matter
      Pages 151-151
    2. Israel Kleiner
      Pages 181-196
    3. Israel Kleiner
      Pages 215-236
  5. Courses Inspired by History

    1. Front Matter
      Pages 237-237
    2. Israel Kleiner
      Pages 239-259
    3. Israel Kleiner
      Pages 285-302
  6. Brief Biographies of Selected Mathematicians

    1. Front Matter
      Pages 303-303

About this book

Introduction

This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively.  Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. 

Each of the first three parts—on number theory, calculus/analysis, and proof—begins with a survey of the respective subject and is followed in more depth by specialized themes. Among the specialized themes are:  Fermat as the founder of modern number theory, Fermat’s Last Theorem from Fermat to Wiles, the history of the function concept, paradoxes, the principle of continuity, and an historical perspective on recent debates about proof. 

The fourth part contains essays describing mathematics courses inspired by history. The essays deal with numbers as a source of ideas in teaching, with famous problems, and with the stories behind various "great" quotations. The last part gives an account of five mathematicians—Dedekind, Euler, Gauss, Hilbert, and Weierstrass—whose lives and work we hope readers will find inspiring.

Key features of the work include:

* A preface describing in some detail the author's ideas on teaching mathematics courses, in particular, the role of history in such courses;

* Explicit comments and suggestions for teachers on how history can affect the teaching of mathematics;

* A description of a course in the history of mathematics taught in an In-Service Master's Program for high school teachers;

* Inclusion of issues in the philosophy of mathematics;

* An extensive list of relevant references at the end of each chapter.

Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.

Keywords

Dedekind Euler Fermat's Last Theorem Gauss Hilbert Weierstrass analysis history of mathematics history of the function concept mathematical proof mathematics education number theory paradoxes philosophy of mathematics principle of continuity teaching mathematics

Authors and affiliations

  • Israel Kleiner
    • 1
  1. 1.Department of Mathematics and Statistics, MathematicsYork UniversityTorontoCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8268-2
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8267-5
  • Online ISBN 978-0-8176-8268-2
  • About this book