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＜電子ブック＞
Abel’s Theorem in Problems and Solutions : Based on the lectures of Professor V.I. Arnold / by V.B. Alekseev

版	1st ed. 2004.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2004
大きさ	XIV, 270 p : online resource
著者標目	*Alekseev, V.B author SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Functions of complex variables LCSH:Algebraic fields LCSH:Polynomials LCSH:Topological groups LCSH:Lie groups FREE:Group Theory and Generalizations FREE:Functions of a Complex Variable FREE:Field Theory and Polynomials FREE:Topological Groups and Lie Groups
一般注記	From the contents: Preface for the English edition; V.I. Arnold -- Preface -- Introduction -- 1: Groups -- 2: The complex numbers -- 3: Hints, Solutions and Answers -- Appendix. Solvability of equations by explicit formulae; A. Khovanskii -- Bibliography -- Appendix; V.I. Arnold -- Index Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate HTTP:URL=https://doi.org/10.1007/1-4020-2187-9

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