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Title: Abel’s Theorem in Problems and Solutions ([EBook]) : Based on the lectures of Professor V.I. Arnold/ by V.B. Alekseev. Dewey Class: 512.2 Author: Alekseev, Valerij B. Publication: Dordrecht : Springer Netherlands, 2004. Other name(s): SpringerLink (Online service) Physical Details: XIV, 270 pages : online resource. ISBN: 9781402021879 System details note: Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) Summary Note: 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.: Contents note: 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. ------------------------------ *** Es sind keine Exemplare vorhanden *** -----------------------------------------------
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