{"product_id":"galois-theory-coverings-and-riemann-surfaces-hardcover","title":"Galois Theory, Coverings, and Riemann Surfaces - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eAskold Khovanskii\u003c\/b\u003e (Author), \u003cb\u003eVladlen Timorin\u003c\/b\u003e (Translator), \u003cb\u003eValentina Kiritchenko\u003c\/b\u003e (Translator)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eChapter 1 Galois Theory: 1.1 Action of a Solvable Group and Representability by Radicals.- 1.2 Fixed Points under an Action of a Finite Group and Its Subgroups.- 1.3 Field Automorphisms and Relations between Elements in a Field.- 1.4 Action of a \u003ci\u003ek\u003c\/i\u003e-Solvable Group and Representability by \u003ci\u003ek\u003c\/i\u003e-Radicals.- 1.5 Galois Equations.- 1.6 Automorphisms Connected with a Galois Equation.- 1.7 The Fundamental Theorem of Galois Theory.- 1.8 A Criterion for Solvability of Equations by Radicals.- 1.9 A Criterion for Solvability of Equations by \u003ci\u003ek\u003c\/i\u003e-Radicals.- 1.10 Unsolvability of Complicated Equations by Solving Simpler Equations.- 1.11 Finite Fields.- Chapter 2 Coverings: 2.1 Coverings over Topological Spaces.- 2.2 Completion of Finite Coverings over Punctured Riemann Surfaces.- Chapter 3 Ramified Coverings and Galois Theory: 3.1 Finite Ramified Coverings and Algebraic Extensions of Fields of Meromorphic Functions.- 3.2 Geometry of Galois Theory for Extensions of a Field of Meromorphic Functions.- References.- Index\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to the topological Galois theory developed by the author. \u003c\/p\u003e\u003cp\u003eAll results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003eAskold 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.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 81\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.25 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e November 20, 2013\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52704972603699,"sku":"9783642388408","price":136.58,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/bFNscUVvVXdpRjVveFBSVlF5d1VhUT09.webp?v=1763369896","url":"https:\/\/www.vysn.com\/en-ca\/products\/galois-theory-coverings-and-riemann-surfaces-hardcover","provider":"VYSN","version":"1.0","type":"link"}