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

V B Alekseev

ISBN 10: 1402021860 / ISBN 13: 9781402021862

Edité par Springer Mai 2004, 2004

A propos de cet article

Neuware - 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.

N° de réf. du vendeur 9781402021862

Détails bibliographiques

• Titre: Abel's Theorem in Problems and Solutions : Based on the Lectures of Professor V.I. Arnold
• Éditeur: Springer Mai 2004
• Date de parution: 2004
• Langue: anglais
• ISBN à 10 chiffres: 1402021860
• ISBN à 13 chiffres: 9781402021862
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 261 L x 182 H x 22 P (en millimètres) 261 millimètres de largeur par 182 millimètres de hauteur par 22 millimètres de profondeur
• Poids: 691 grammes

A propos de ce titre

Synopsis

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.