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Galois' Dream: Group Theory and Differential Equations, by Michio Kuga
Download Galois' Dream: Group Theory and Differential Equations, by Michio Kuga
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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.
- Sales Rank: #2391625 in eBooks
- Published on: 2012-10-23
- Released on: 1992-11-30
- Format: Kindle eBook
Review
"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
Language Notes
Text: English (translation)
Original Language: Japanese
From the Back Cover
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.
From elementary ideas to cartoons to funny examples (considered "undignified" by many of his colleagues,) the author provided his students with a book that was considered "hip" just to own, to be seen reading, and perhaps to be learning from. Many of his students went on to become good mathematicians, having fallen into the "crevasse" of mathematical curiosity.
English reading students now have the opportunity to enjoy this lively presentation and to follow the mind of an imaginative and creative mathematician into a world---not really so far removed---of enduring mathematical creations.
Most helpful customer reviews
15 of 16 people found the following review helpful.
well-written but limited in scope
By A Customer
Ever since Galois theory has been used to solve polynomial equations, people have been trying to use analogous techniques to solve differential equations. That's what the title alludes to.
The book does not address what is known on the subject, however, and limits itself to Fuchsian differential equations which are historically important but not very general. The applications of group theory to this class is unlike the development of the subject to other ODEs.
The audience for this book seems to change as the book progresses. The first two lectures seem to be aimed at non-math majors. It progressively requires abstract algebra, topology, and complex analysis. The proper audience is probably a beginning mathematics graduate student, but you wouldn't guess by seeing the elementary level of the first few chapters.
For these students, though, I highly recommend it.
5 of 6 people found the following review helpful.
Comment
By Reader
I would like to comment on the first review, which I fully agree with. I'm familiar with quite a few Japanese books, and they all have the same characteristic: The first few chapters can be so elementary, that they give a deceptive impression of the rest of the book, which can suddenly become demanding. I wonder why that is the case.
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