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83,98 ۥThe 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
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.
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.
Table of contents (7 chapters)
1.Construction of Liouvillian Classes of Functions and Liouville’s Theory
2.Solvability of Algebraic Equations by Radicals and Galois Theory
3.Solvability and Picard–Vessiot Theory
4.Coverings and Galois Theory
5.One-Dimensional Topological Galois Theory
6.Solvability of Fuchsian Equations
7.Multidimensional Topological Galois Theory
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