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Catalogue Information
Field name	Details
Dewey Class	512.2
Title	Abel’s Theorem in Problems and Solutions ([EBook]) : Based on the lectures of Professor V.I. Arnold / by V.B. Alekseev.
Author	Alekseev, Valerij B.
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : Springer Netherlands , 2004.
Physical Details	XIV, 270 pages : online resource.
ISBN	9781402021879
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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/1-4020-2187-9
Links to Related Works	Subject References: Abelian groups . Field Theory and Polynomials . Field theory (Physics) . Functions of a Complex Variable . Functions of complex variables . Group theory . Lie groups . Topological groups . Topological groups, Lie groups . Authors: Alekseev, Valerij B. . Corporate Authors: SpringerLink (Online service) . Classification: 512.2 .

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Abel’s Theorem in Problems and Solutions: Based on the lectures of Professor V.I. Arnold

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