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.
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