Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Image from Google Jackets

Topological Galois theory : solvability and unsolvability of equations in finite terms / Askold Khovanskii.

By: Series: Springer monographs in mathematicsPublication details: Berlin : Springer-Verlag, 2014.Description: xviii, 307 p. ; 24 cmISBN:
  • 9783642388705
Subject(s): DDC classification:
  • 512.32 23 K45
Contents:
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 Gaolis theory -- 5. One-dimensional topological Galois theory -- 6. Solvability of Fuchsian equations -- 7. Multidimensional topological Galois theory -- A. Straightedge and compass constructions -- B. Chebyshev polynominals and their inverses -- C. Signatures of branched coverings and solvability in quadratures -- D. On an algebraic version of Hilbert's 13th problem-- References-- Index.
Summary: 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.
Tags from this library: No tags from this library for this title. Log in to add tags.

Includes bibliographical references and index.

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 Gaolis theory --
5. One-dimensional topological Galois theory --
6. Solvability of Fuchsian equations --
7. Multidimensional topological Galois theory --
A. Straightedge and compass constructions --
B. Chebyshev polynominals and their inverses --
C. Signatures of branched coverings and solvability in quadratures --
D. On an algebraic version of Hilbert's 13th problem--
References--
Index.

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.

There are no comments on this title.

to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in