Abel’s Theorem in Problems and Solutions

Based on the lectures of Professor V.I. Arnold

Authors: Alekseev, V.B.

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About this book

Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals.

A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable.

This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii.

As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.

Reviews

From the reviews:

"This very special and brilliant text has been written for bright non-specialists in mathematics, but it leads the reader up to topical research problems in the field, and that in a masterly manner. The book is absolutely self-contained, in its own particular fashion, and it is therefore perfectly suited for self-study, ranging from advanced high school to graduate level. No doubt, the thorough and serious working with this outstanding text could turn very beginners into creative almost-experts in the field." (Werner Kleinert, Zentralblatt MATH, Vol. 1065 (16), 2005)


Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-1-4020-2187-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-1-4020-2186-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $109.99
price for USA in USD
  • ISBN 978-90-481-6609-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Abel’s Theorem in Problems and Solutions
Book Subtitle
Based on the lectures of Professor V.I. Arnold
Authors
Translated by
Aicardi, F.
Copyright
2004
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-1-4020-2187-9
DOI
10.1007/1-4020-2187-9
Hardcover ISBN
978-1-4020-2186-2
Softcover ISBN
978-90-481-6609-1
Edition Number
1
Number of Pages
XIV, 270
Additional Information
Originally published in Russian
Topics