Galois' Dream: Group Theory and Differential Equations: Group Theory and Differential Equations

by Michio Kuga, Susan Addington (Translator), Motohico Mulase (Translator)

Overview

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. 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.

Product Details

ISBN-13:	9780817636883
Publisher:	Birkhäuser Boston
Publication date:	02/05/1993
Edition description:	1993
Pages:	150
Product dimensions:	7.01(w) x 10.00(h) x 0.02(d)

Table of Contents

Preface.-Pre-Mathematics.-No Prerequisites.-Sets and Maps.-Equivalence Classes.-The Story of Free Groups.-Heave Ho! (Pull it Tight).-Fundamental Groups of Surfaces.-Fundamental Groups.-Examples of Fundamental Groups.-Examples of Fundamental Groups, Continued.-Men Who Don’t Realize That Their Wives Have Been Interchanged.-Coverings.-Covering surfaces and Fundamental Groups.-Covering Surfaces and Fundamental Groups, Continued.-The Group of Covering Transformations.-Everyone has a Tail.-The Universal Covering Space.-The Correspondence Between Coverings of (D;O) and Subgroups of pi1(D;O).-Seeing Galois Theory.-Continuous Functions of Covering Surfaces.-Solvable or Not?.-Differential Equations.-Elementary methods of Solving Differential Equations.-Regular Singularities.-Differential Equations of Fuchsian Type.-References.-Notation.-Index.

Editorial Reviews

A lively and elementary introduction to some of the advanced ideas in mathematics, for undergraduate mathematics students. Applies Galois groups to the problem of differential equations in such a way as to interest students with a basic understanding of group theory, introductory topology, the theory of functions, and differential equations. First published in Japanese in 1968, where it became "hip" for students to be seen with it, and got Kuga in trouble for its undignified treatment. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"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

From the Publisher