Galois’ Dream: Group Theory and Differential Equations

Group Theory and Differential Equations

AvMichio Kuga

Häftad, Engelska, 2012

1 416 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2012-10-23
Mått:178 x 254 x 10 mm
Vikt:322 g
Format:Häftad
Språk:Engelska
Antal sidor:150
Förlag:Springer-Verlag New York Inc.
ISBN:9781461267102
Översättare:Susan Addington, Motohico Mulase

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"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

Innehållsförteckning

Pre-Mathematics.- 0th Week No prerequisites.- 1st Week Sets and Maps.- 2nd Week Equivalence Classes.- 3rd Week The Story of Free Groups.- Heave Ho! (Pull it Tight).- 4th Week Fundamental Groups of Surfaces.- 5th Week Fundamental Groups.- 6th Week Examples of Fundamental Groups.- 7th Week Examples of Fundamental Groups, continued.- Men Who Don’t Realize That Their Wives Have Been Interchanged.- 8th Week Coverings.- 9th Week Covering Surfaces and Fundamental Groups.- 10th Week Covering Surfaces and Fundamental Groups, continued.- 11th Week The Group of Covering Transformations.- Everyone Has a Tail.- 12th Week The Universal Covering Space.- 13th Week The Correspondence Between Coverings of (D; O) and Subgroups of ?1 (D; O).- Seeing Galois Theory.- 14th Week Continuous Functions on Covering Surfaces.- 15th Week Function Theory on Covering Surfaces.- Solvable or Not?.- 16th Week Differential Equations.- 17th Week Elementary Methods of Solving Differential Equations.- 18th Week Regular Singularities.- 19th Week Differential Equations of Fuchsian Type.- References.- Notation.