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

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 algebraica...

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Κύριος συγγραφέας: Alekseev, V.B (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Dordrecht : Springer Netherlands, 2004.
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Alekseev, V.B.  |e author. 
245 1 0 |a Abel’s Theorem in Problems and Solutions  |h [electronic resource] :  |b Based on the lectures of Professor V.I. Arnold /  |c by V.B. Alekseev. 
264 1 |a Dordrecht :  |b Springer Netherlands,  |c 2004. 
300 |a XIV, 270 p.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
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505 0 |a 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. 
520 |a 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. 
650 0 |a Mathematics. 
650 0 |a Algebra. 
650 0 |a Field theory (Physics). 
650 0 |a Group theory. 
650 0 |a Topological groups. 
650 0 |a Lie groups. 
650 0 |a Functions of complex variables. 
650 1 4 |a Mathematics. 
650 2 4 |a Group Theory and Generalizations. 
650 2 4 |a Functions of a Complex Variable. 
650 2 4 |a Field Theory and Polynomials. 
650 2 4 |a Topological Groups, Lie Groups. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9781402021862 
856 4 0 |u http://dx.doi.org/10.1007/1-4020-2187-9  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
912 |a ZDB-2-BAE 
950 |a Mathematics and Statistics (Springer-11649)