Abel's theorem in problems and solutions: based on the lectures of Professor V. I. Arnold
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
[2010]
|
| Edition: | [pbk ed.] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 269 S. Ill., graph. Darst. |
| ISBN: | 9048166098 9789048166091 |
Staff View
MARC
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| 245 | 1 | 0 | |a Abel's theorem in problems and solutions |b based on the lectures of Professor V. I. Arnold |c by V. B. Alekseev |
| 250 | |a [pbk ed.] | ||
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c [2010] | |
| 300 | |a XIV, 269 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
| _version_ | 1804148512449888256 |
|---|---|
| adam_text | Contents
Preface
for the English edition by
V.l.
Arnold
ix
Preface
xiii
Introduction
1
1
Groups
9
1.1
Examples
........................... 9
1.2
Groups of transformations
.................. 13
1.3
Groups
............................. 14
1.4
Cyclic groups
......................... 18
1.5
Isomorphisms
......................... 19
1.6
Subgroups
........................... 21
1.7
Direct product
........................ 23
1.8
Cosets. Lagrange s theorem
................. 24
1.9
Internal automorphisms
................... 26
1.10
Normal subgroups
....................... 28
1.11
Quotient groups
........................ 29
1.12
Commutant
.......................... 31
1.13
Homomorphisms
...................... . 33
1.14
Soluble groups
......................... 38
1.15
Permutations
........................ . 40
2
The complex numbers
45
2.1
Fields and polynomials
.................... 46
2.2
The field of complex numbers
................ 51
2.3
Uniqueness of the field of complex
numbers
............................ 55
2.4
Geometrical descriptions of the
complex numbers
....................... 58
2.5
The trigonometric form of the complex numbers
...... 60
2.6
Continuity
........................... 62
2.7
Continuous curves
....................... 65
2.8
Images of curves: the basic theorem
of the algebra of complex numbers
............. 71
2.9
The Riemann surface of the function
w
=
yfz
....... 74
2.10
The Riemann surfaces of more
complicated functions
..................... 83
2.11
Functions representable by radicals
............. 90
2.12
Monodromy groups of multi-valued
functions
........................... 96
2.13
Monodromy groups of functions
representable by radicals
................... 99
2.14
The Abel theorem
....................... 100
3
Hints, Solutions, and Answers
105
3.1
Problems of Chapter
1.................... 105
3.2
Problems of Chapter
2.................... 148
Drawings of Riemann surfaces (F. Aicardi)
............ 209
Appendix by A. Khovanskii: Solvability of equations
by explicit formulae
221
A.I Explicit solvability of equations
............... 222
A.2 Liouville s theory
....................... 224
A.3
Picard
Vessiot s theory
.................... 228
A.4 Topological obstructions for
the representation of functions
by quadratures
........................ 230
A.5 S-functkms
........................... 231
A.
6
Monodromy group
...................... 232
A.7 Obstructions for the representability
of functions by quadratures
................. 233
A.
8
Solvability of algebraic equations
.............. 234
A.
9
The monodromy pair
..................... 235
A.
10
Mapping of the semi-plane to a
polygon bounded by arcs of circles
............. 237
A.
10.1
Application of the symmetry principle
....... 237
A.
10.2
Almost soluble groups of
homographie
and
conformai
mappings
............... 238
A.10.3
The integrable
case
..................242
Α.
11
Topological obstructions for the
solvability of differential equations
.............244
A.
11.1
The monodromy group of a linear
differential equation and its relation
with the Galois group
................244
A.11.2 Systems of differential equations of
Fuchs
type with small coefficients
..............246
A.
12
Algebraic functions of several
variables
............................ 247
A.
13
Functions of several complex variables
representable by quadratures and
generalized quadratures
....................250
A.MSe-germs
............................ 252
A.
15
Topological obstructions for the
representability by quadratures
of functions of several variables
...............256
A.
16
Topological obstruction for the
solvability of the holonomic systems
of linear differential equations
................257
A.
16.1
The monodromy group of a holonomic
system of linear differential equations
.......257
A.
16.2
Holonomic systems of equations of linear
differential equations with small coefficients
.... 258
Bibliography
............................261
Appendix by
V.l.
Arnold
265
Index
267
|
| any_adam_object | 1 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.25 |
| dewey-search | 512/.25 |
| dewey-sort | 3512 225 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | [pbk ed.] |
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| id | DE-604.BV039652617 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:08:19Z |
| institution | BVB |
| isbn | 9048166098 9789048166091 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024502254 |
| oclc_num | 760140777 |
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| physical | XIV, 269 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| spelling | Alekseev, V. B. Verfasser aut Abel's theorem in problems and solutions based on the lectures of Professor V. I. Arnold by V. B. Alekseev [pbk ed.] Dordrecht [u.a.] Kluwer Acad. Publ. [2010] XIV, 269 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Groupes abéliens ram aAbelian groups Abelsche Gruppe (DE-588)4140988-7 gnd rswk-swf Abelsche Gruppe (DE-588)4140988-7 s DE-604 Arnolʹd, V. I. 1937-2010 Sonstige (DE-588)119540878 oth Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024502254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alekseev, V. B. Abel's theorem in problems and solutions based on the lectures of Professor V. I. Arnold Groupes abéliens ram aAbelian groups Abelsche Gruppe (DE-588)4140988-7 gnd |
| subject_GND | (DE-588)4140988-7 |
| title | Abel's theorem in problems and solutions based on the lectures of Professor V. I. Arnold |
| title_auth | Abel's theorem in problems and solutions based on the lectures of Professor V. I. Arnold |
| title_exact_search | Abel's theorem in problems and solutions based on the lectures of Professor V. I. Arnold |
| title_full | Abel's theorem in problems and solutions based on the lectures of Professor V. I. Arnold by V. B. Alekseev |
| title_fullStr | Abel's theorem in problems and solutions based on the lectures of Professor V. I. Arnold by V. B. Alekseev |
| title_full_unstemmed | Abel's theorem in problems and solutions based on the lectures of Professor V. I. Arnold by V. B. Alekseev |
| title_short | Abel's theorem in problems and solutions |
| title_sort | abel s theorem in problems and solutions based on the lectures of professor v i arnold |
| title_sub | based on the lectures of Professor V. I. Arnold |
| topic | Groupes abéliens ram aAbelian groups Abelsche Gruppe (DE-588)4140988-7 gnd |
| topic_facet | Groupes abéliens aAbelian groups Abelsche Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024502254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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