Springer Monographs in Mathematics

Topological Galois Theory

Solvability and Unsolvability of Equations in Finite Terms

Authors: Khovanskii, Askold

  • The largest collection of unsolvability results
  • Classical Galois theory and Liouville's explicit integration theory are explained from scratch
  • A gentle introduction to the cutting edge of research
see more benefits

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-3-642-38871-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-642-38870-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 7, 2016
  • ISBN 978-3-662-50602-8
  • Free shipping for individuals worldwide
About this book

This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in explicit form. In particular, it offers a complete exposition of the relatively new area of topological Galois theory, initiated by the author. Applications of Galois theory to solvability of algebraic equations by radicals, basics of Picard–Vessiot theory, and Liouville's results on the class of functions representable by quadratures are also discussed.

A unique feature of this book is that recent results are presented in the same elementary manner as classical Galois theory, which will make the book useful and interesting to readers with varied backgrounds in mathematics, from undergraduate students to researchers.

In this English-language edition, extra material has been added (Appendices A–D), the last two of which were written jointly with Yura Burda.

About the authors

Askold Khovanskii is a Professor of Mathematics at the University of Toronto, and a principal researcher at the RAS Institute for Systems Analysis (Moscow, Russia). He is a founder of topological Galois theory and the author of fundamental results in this area.

Reviews

“This book offers the possibility to learn about the very interesting topological Galois theory, as well as to parallel it with the algebraic and differential Galois theories. It is very well-written and self-contained, making its reading really enjoyable.” (Teresa Crespo, zbMATH 1331.12001, 2016)


Table of contents (7 chapters)

  • Construction of Liouvillian Classes of Functions and Liouville’s Theory

    Khovanskii, Askold

    Pages 1-45

  • Solvability of Algebraic Equations by Radicals and Galois Theory

    Khovanskii, Askold

    Pages 47-83

  • Solvability and Picard–Vessiot Theory

    Khovanskii, Askold

    Pages 85-106

  • Coverings and Galois Theory

    Khovanskii, Askold

    Pages 107-141

  • One-Dimensional Topological Galois Theory

    Khovanskii, Askold

    Pages 143-171

Buy this book

eBook $84.99
price for USA (gross)
  • ISBN 978-3-642-38871-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-642-38870-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 7, 2016
  • ISBN 978-3-662-50602-8
  • Free shipping for individuals worldwide
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Topological Galois Theory
Book Subtitle
Solvability and Unsolvability of Equations in Finite Terms
Authors
Translated by
Kiritchenko, V., Kadets, L., Timorin, V.
Series Title
Springer Monographs in Mathematics
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-38871-2
DOI
10.1007/978-3-642-38871-2
Hardcover ISBN
978-3-642-38870-5
Softcover ISBN
978-3-662-50602-8
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XVIII, 307
Number of Illustrations and Tables
6 b/w illustrations
Topics