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Topological Galois theory [electronic resource] : solvability and unsolvability of equations in finite terms

Topological Galois theory [electronic resource] : solvability and unsolvability of equations in finite terms

Material type
E-Book(소장)
Personal Author
Khovanskiĭ, A. G.
Title Statement
Topological Galois theory [electronic resource] : solvability and unsolvability of equations in finite terms / Askold Khovanskii.
Publication, Distribution, etc
Berlin ;   Heidelberg :   Springer Berlin Heidelberg :   Imprint: Springer,   2014.  
Physical Medium
1 online resource (xviii, 307 p.).
Series Statement
Springer monographs in mathematics,1439-7382
ISBN
9783642388712
요약
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.
General Note
Title from e-Book title page.  
Content Notes
Preface -- 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 -- Appendix A: Straightedge and Compass Constructions -- Appendix B: Chebyshev Polynomials and Their Inverses -- Appendix C: Signatures of Branched Coverings and Solvability in Quadratures -- Appendix D: On an Algebraic Version of Hilbert’s 13th Problem -- References.
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Galois theory.
Short cut
URL
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008 200916s2014 gw ob 001 0 eng d
020 ▼a 9783642388712
040 ▼a 211009 ▼c 211009 ▼d 211009
050 4 ▼a QA161.A-161.Z
082 0 4 ▼a 512/.32 ▼2 23
084 ▼a 512.32 ▼2 DDCK
090 ▼a 512.32
100 1 ▼a Khovanskiĭ, A. G.
245 1 0 ▼a Topological Galois theory ▼h [electronic resource] : ▼b solvability and unsolvability of equations in finite terms / ▼c Askold Khovanskii.
260 ▼a Berlin ; ▼a Heidelberg : ▼b Springer Berlin Heidelberg : ▼b Imprint: Springer, ▼c 2014.
300 ▼a 1 online resource (xviii, 307 p.).
490 1 ▼a Springer monographs in mathematics, ▼x 1439-7382
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
505 0 ▼a Preface -- 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 -- Appendix A: Straightedge and Compass Constructions -- Appendix B: Chebyshev Polynomials and Their Inverses -- Appendix C: Signatures of Branched Coverings and Solvability in Quadratures -- Appendix D: On an Algebraic Version of Hilbert’s 13th Problem -- References.
520 ▼a 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Galois theory.
830 0 ▼a Springer monographs in mathematics.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-3-642-38871-2
945 ▼a KLPA
991 ▼a E-Book(소장)

Holdings Information

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No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.32 Accession No. E14032339 Availability Loan can not(reference room) Due Date Make a Reservation Service M

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