Author	Alekseev, V.B. author
Title	Abel's Theorem in Problems and Solutions [electronic resource] : Based on the lectures of Professor V.I. Arnold / by V.B. Alekseev
Imprint	Dordrecht : Springer Netherlands, 2004
Connect to	http://dx.doi.org/10.1007/1-4020-2187-9
Descript	XIV, 270 p. online resource

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

1. Mathematics
2. Algebra
3. Field theory (Physics)
4. Group theory
5. Topological groups
6. Lie groups
7. Functions of complex variables
8. Mathematics
9. Group Theory and Generalizations
10. Functions of a Complex Variable
11. Field Theory and Polynomials
12. Topological Groups
13. Lie Groups