Topological Galois Theory: Solvability And Unsolvability Of Equations In Finite Terms (springer Monographs In Mathematics)
by Askold Khovanskii /
2014 / English / EPUB
2.6 MB Download
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.
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.
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.
In this English-language edition, extra material has been added
(Appendices A–D), the last two of which were written jointly with
Yura Burda.