Overview
- 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
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
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.
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)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Topological Galois Theory
Book Subtitle: Solvability and Unsolvability of Equations in Finite Terms
Authors: Askold Khovanskii
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-642-38871-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2014
Hardcover ISBN: 978-3-642-38870-5Published: 27 October 2014
Softcover ISBN: 978-3-662-50602-8Published: 23 August 2016
eBook ISBN: 978-3-642-38871-2Published: 10 October 2014
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XVIII, 307
Number of Illustrations: 6 b/w illustrations
Topics: Field Theory and Polynomials, Functions of a Complex Variable, Group Theory and Generalizations, Topological Groups, Lie Groups, Several Complex Variables and Analytic Spaces, Topology