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Abel's Theorem in Problems and Solutions

Based on the Lectures of Professor V.I. Arnold. the Kluwer International Series in Engineering & Computer Science

By (author) V.B. Alekseev
Genres: Algebra
Format: Other digital
Publisher: Springer-Verlag New York Inc., New York, NY, United States
Published: 1st May 2004
ISBN-10: 1402021879
ISBN-13: 9781402021879
Barcode No: 9781402021879
Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? Formally, the main aim of this book is to give new geometrical prove, proposed by Professor V.I. Arnold, of Abel's theorem, stating that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients only with arithmetic operations and radicals. But the more important aim of this book is to acquaint the reader with two very important branches of modern mathematics, different in spirit: group theory and theory of functions of a complex variable. And no special preliminary knowledge is required for reading this book. Because the book is composed as definitions, examples, problems and solutions, it is suitable for teachers or self-education and can be used by any reader (starting from high school students) for checking their ability to design the whole mathematical theory. As added bonus the book has an extensive appendix written by Professor A.G. Khovanskii,devoted to the differential Galois theory.

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