Abel’s Theorem in Problems and Solutions - V.B. Alekseev

Abel’s Theorem in Problems and Solutions

Based on the lectures of Professor V.I. Arnold

(Autor)

Buch | Hardcover
270 Seiten
2004
Springer-Verlag New York Inc.
978-1-4020-2186-2 (ISBN)
149,79 inkl. MwSt
Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations?

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.
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.

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.

Erscheint lt. Verlag 31.5.2004
Übersetzer Francesca Aicardi
Zusatzinfo XIV, 270 p.
Verlagsort New York, NY
Sprache englisch
Maße 178 x 254 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
ISBN-10 1-4020-2186-0 / 1402021860
ISBN-13 978-1-4020-2186-2 / 9781402021862
Zustand Neuware
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