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Galois’ Dream: Group Theory and Differential Equations

Group Theory and Differential Equations

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  • © 1993

Overview

Authors:
  1. Michio Kuga
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Table of contents (20 chapters)

  1. Front Matter

    Pages i-ix
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  2. Pre-Mathematics

    1. Front Matter

      Pages 1-1
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    2. The 0th Week: No Prerequisites

      • Michio Kuga
      Pages 3-4

    3. The First Week: Sets and Maps

      • Michio Kuga
      Pages 5-18

    4. The Second Week: Equivalence Classes

      • Michio Kuga
      Pages 19-22

    5. The Third Week: The Story of Free Groups

      • Michio Kuga
      Pages 23-29

  3. Heave Ho! (Pull it Tight)

    1. Front Matter

      Pages 31-31
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    2. The Fourth Week: The fundamental group of a surface

      • Michio Kuga
      Pages 33-37

    3. The Fifth Week: Fundamental Groups

      • Michio Kuga
      Pages 38-44

    4. The Sixth Week: Examples of fundamental groups

      • Michio Kuga
      Pages 45-48

    5. The Seventh Week: Examples of fundamental groups, continued

      • Michio Kuga
      Pages 49-50

  4. Men Who Don’t Realize That Their Wives Have Been Interchanged

    1. Front Matter

      Pages 51-51
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    2. The Eighth Week: Coverings

      • Michio Kuga
      Pages 53-58

    3. The Ninth Week: Covering surfaces and fundamental groups

      • Michio Kuga
      Pages 59-60

    4. The Tenth Week: Covering surfaces and fundamental groups, continued

      • Michio Kuga
      Pages 61-69

    5. The Eleventh Week: The Group of Covering Transformations

      • Michio Kuga
      Pages 70-74

  6. Seeing Galois Theory

    1. Front Matter

      Pages 87-87
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Keywords

About this book

First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience---an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world. Michio Kuga’s lectures on Group Theory and Differential Equations are a realization of two dreams---one to see Galois groups used to attack the problems of differential equations---the other to do so in such a manner as to take students from a very basic level to an understanding of the heart of this fascinating mathematical problem. English reading students now have the opportunity to enjoy this lively presentation, from elementary ideas to cartoons to funny examples, and to follow the mind of an imaginative and creative mathematician into a world of enduring mathematical creations.

Reviews

"Galois' theory of equations remains the standard culmination of advanced undergraduate algebra courses...and Kuga makes this the basis for an idiosyncratic geometric exposition of Galois theory... There is nothing like this book in the literature. Highly recommended."

—CHOICE

Bibliographic Information

  • Book Title: Galois’ Dream: Group Theory and Differential Equations

  • Book Subtitle: Group Theory and Differential Equations

  • Authors: Michio Kuga

  • DOI: https://doi.org/10.1007/978-1-4612-0329-2

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1993

  • Hardcover ISBN: 978-0-8176-3688-3Published: 05 February 1993

  • Softcover ISBN: 978-1-4612-6710-2Published: 23 October 2012

  • eBook ISBN: 978-1-4612-0329-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: IX, 150

  • Topics: Group Theory and Generalizations, Field Theory and Polynomials, Ordinary Differential Equations, Algebra

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