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

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Springer Science & Business Media, May 31, 2004 - Mathematics - 269 pages
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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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Contents

IV
9
V
13
VI
14
VII
18
VIII
19
IX
21
X
23
XI
24
XXXIII
100
XXXIV
105
XXXV
148
XXXVI
209
XXXVII
221
XXXVIII
222
XXXIX
224
XL
228

XII
26
XIII
28
XIV
29
XV
31
XVI
33
XVII
38
XVIII
40
XIX
45
XX
46
XXI
51
XXII
55
XXIII
58
XXIV
60
XXV
62
XXVI
65
XXVII
71
XXVIII
74
XXIX
83
XXX
90
XXXI
96
XXXII
99
XLI
230
XLII
231
XLIII
232
XLIV
233
XLV
234
XLVI
235
XLVII
237
XLVIII
238
XLIX
242
L
244
LI
246
LII
247
LIII
250
LIV
252
LV
256
LVI
257
LVII
258
LVIII
261
LIX
265
LX
267
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