Mathematics of the 19th century: mathematical logic, algebra, number theory, probability theory
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1992
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 289 - 301 |
| Beschreibung: | 308 S. Ill. |
| ISBN: | 3764325526 0817625526 |
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Datensatz im Suchindex
| _version_ | 1817318867817463808 |
|---|---|
| adam_text |
MATHEMATICS OF
THE 19TH
CENTURY
MATHEMATICAL
LOGIC
ALGEBRA
NUMBER
THEORY
PROBABILITY
THEORY
EDITED BY
A.N.
KOLMOGOROV
A.P.
YUSHKEVICH
1992
BIRKHAEUSER
VERLAG
BASEL
YY
BOSTON
YY
BERLIN
CONTENTS
PREFACE IX
INTRODUCTION TO THE ENGLISH TRANSLATION
XIII
CHAPTER ONE
MATHEMATICAL
LOGIC (BY Z.A. KUZICHEVA)
1
THE PREHISTORY OF MATHEMATICAL LOGIC 1
LEIBNIZ'S SYMBOLIC LOGIC 2
THE QUANTIFICATION OF A PREDICATE 9
THE "FORMAL LOGIC" OF A. DE MORGAN 10
BOOLE'S ALGEBRA OF LOGIC 14
JEVONS' ALGEBRA OF LOGIC 20
VENN'S SYMBOLIC LOGIC 24
SCHROEDER'S AND PORETSKII'S LOGICAL ALGEBRA 27
CONCLUSION 33
CHAPTER TWO
ALGEBRA
AND ALGEBRAIC NUMBER THEORY
(BY
I.G. BASHMAKOVA AND A.N. RUDAKOV WITH THE
ASSISTANCE
OF A.N. PARSHIN AND E.I. SLAVUTIN)
35
1
SURVEY OF THE EVOLUTION OF ALGEBRA AND OF THE THEORY
OF
ALGEBRAIC NUMBERS DURING THE PERIOD OF 1800-1870 35
2 THE EVOLUTION OF ALGEBRA 41
ALGEBRAIC PROOFS OF THE FUNDAMENTAL THEOREM
OF
ALGEBRA IN THE 18TH CENTURY 41
C.F. GAUSS' FIRST PROOF 43
C.F. GAUSS' SECOND PROOF 44
THE KRONECKER CONSTRUCTION 47
THE THEORY OF EQUATIONS 50
CARL FRIEDRICH GAUSS 50
SOLUTION OF THE CYCLOTOMIC EQUATION 52
NIELS HENRIK ABEL 55
EVARISTE GALOIS 57
THE ALGEBRAIC WORK OF EVARISTE GALOIS 58
THE FIRST STEPS IN THE EVOLUTION OF GROUP THEORY 63
THE EVOLUTION OF LINEAR ALGEBRA 68
HYPERCOMPLEX NUMBERS 72
WILLIAM ROWAN HAMILTON 74
MATRIX ALGEBRA 77
THE ALGEBRAS OF GRASSMANN AND CLIFFORD 78
ASSOCIATIVE ALGEBRAS 79
THE THEORY OF INVARIANTS 80
3 THE THEORY OF ALGEBRAIC NUMBERS AND THE
BEGINNINGS
OF COMMUTATIVE ALGEBRA 86
DISQUISITIONES ARITHMETICAE
OF C.F. GAUSS 86
INVESTIGATION OF THE NUMBER OF CLASSES OF QUADRATIC FORMS .
.
.
. 92
GAUSSIAN
INTEGERS AND THEIR ARITHMETIC 94
FERMAT'S LAST THEOREM. THE DISCOVERY OF E. KUMMER 99
KUMMER'S THEORY 102
DIFNCULTIES. THE NOTION OF AN INTEGER 106
THE ZOLOTAREV THEORY. INTEGRAL AND P-INTEGRAL NUMBERS 108
DEDEKIND'S
IDEAL THEORY 116
ON DEDEKIND'S METHOD. IDEALS AND CUTS 123
CONSTRUCTION OF IDEAL THEORY IN ALGEBRAIC FUNCTION FIELDS .
.
.
. 125
L.
KRONECKER'S DIVISOR THEORY 131
CONCLUSION 133
CHAPTER THREE
PROBLEMS
OF NUMBER THEORY (BY E.P. OZHIGOVA WITH
THE
ASSISTANCE OF A.P. YUSHKEVICH)
137
1
THE ARITHMETIC THEORY OF QUADRATIC FORMS 137
THE GENERAL THEORY OF FORMS; CH. HERMITE 137
KORKIN'S AND ZOLOTAREV'S WORKS ON
THE
THEORY OF QUADRATIC FORMS 144
THE INVESTIGATIONS OF A.A. MARKOV 151
2 GEOMETRY OF NUMBERS 154
ORIGIN OF THE THEORY 154
THE WORK OF H.J.S. SMITH 159
GEOMETRY OF NUMBERS: HERMANN MINKOWSKI 161
THE WORKS OF G.F. VORONOI 166
3 ANALYTIC METHODS IN NUMBER THEORY 171
LEJEUNE-DIRICHLET AND THE THEOREM ON ARITHMETIC PROGRESSIONS 171
ASYMPTOTIC
LAWS OF NUMBER THEORY 177
CHEBYSHEV AND THE THEORY OF DISTRIBUTION OF PRIMES 182
THE IDEAS OF BERNHARD RIEMANN 189
PROOF OF THE ASYMPTOTIC LAW OF DISTRIBUTION
OF
PRIME NUMBERS 192
SOME APPLICATIONS OF ANALYTIC NUMBER THEORY 194
ARITHMETIC FUNCTIONS AND IDENTITIES.
THE
WORKS OF N.V. BUGAEV 196
4 TRANSCENDENTAL NUMBERS 201
THE WORKS OF JOSEPH LIOUVILLE 201
CHARLES HERMITE AND THE PROOF OF THE TRANSCENDENCE OF
THE
NUMBER E; THE THEOREM
V
OF
FERDINAND LINDEMANN 205
CONCLUSION 209
CHAPTER FOUR
THE
THEORY OF PROBABIUTY (BY B.V. GNEDENKO AND O.B. SHEININ)
. 211
INTRODUCTION 211
LAPLACE'S THEORY OF PROBABILITY 212
LAPLACE'S THEORY OF ERRORS 222
GAUSS' CONTRIBUTION TO THE THEORY OF PROBABILITY 226
THE CONTRIBUTIONS OF POISSON AND CAUCHY 230
SOCIAL AND ANTHROPOMETRIC STATISTICS 242
THE RUSSIAN SCHOOL OF THE THEORY
OF
PROBABILITY, P.L. CHEBYSHEV 247
NEW FIELDS OF APPLICATION OF THE THEORY OF PROBABILITY.
THE
RISE OF MATHEMATICAL STATISTICS 268
WORKS OF THE SECOND HALF OF THE 19TH CENTURY
IN
WESTERN EUROPE 276
CONCLUSION 280
ADDENDUM (BY O.B. SHEININ) 283
1.
FRENCH AND GERMAN QUOTATIONS 283
2.
NOTES 285
3.
ADDITIONAL BIBLIOGRAPHY 286
BIBLIOGRAPHY (BY F.A. MEDVEDEV) 289
ABBREVIATIONS 302
INDEX OF NAMES 304 |
| any_adam_object | 1 |
| author2 | Kolmogorov, Andrej Nikolaevič 1903-1987 |
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| author2_variant | a n k an ank |
| author_GND | (DE-588)119056399 |
| author_facet | Kolmogorov, Andrej Nikolaevič 1903-1987 |
| building | Verbundindex |
| bvnumber | BV025860472 |
| classification_rvk | SG 570 SG 575 |
| ctrlnum | (OCoLC)243721622 (DE-599)BVBBV025860472 |
| discipline | Mathematik |
| era | Geschichte 1801-1900 gnd Geschichte 1801-1990 gnd Geschichte 1801-1930 gnd |
| era_facet | Geschichte 1801-1900 Geschichte 1801-1990 Geschichte 1801-1930 |
| format | Book |
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| publisher | Birkhäuser |
| record_format | marc |
| spelling | Matematika XIX veka Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory ed. by A. N. Kolmogorov ... Matematika XIX veka <engl.> Basel [u.a.] Birkhäuser 1992 308 S. Ill. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 289 - 301 Geschichte 1801-1900 gnd rswk-swf Geschichte 1801-1990 gnd rswk-swf Geschichte 1801-1930 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Mathematische Logik (DE-588)4037951-6 s Geschichte 1801-1930 z DE-604 Algebra (DE-588)4001156-2 s Zahlentheorie (DE-588)4067277-3 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Mathematik (DE-588)4037944-9 s Geschichte 1801-1900 z Geschichte 1801-1990 z Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 1\p DE-604 Kolmogorov, Andrej Nikolaevič 1903-1987 (DE-588)119056399 edt DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019108193&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Logik (DE-588)4037951-6 gnd Algebra (DE-588)4001156-2 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4064324-4 (DE-588)4037944-9 (DE-588)4037951-6 (DE-588)4001156-2 (DE-588)4067277-3 (DE-588)4143413-4 |
| title | Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory |
| title_alt | Matematika XIX veka Matematika XIX veka <engl.> |
| title_auth | Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory |
| title_exact_search | Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory |
| title_full | Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory ed. by A. N. Kolmogorov ... |
| title_fullStr | Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory ed. by A. N. Kolmogorov ... |
| title_full_unstemmed | Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory ed. by A. N. Kolmogorov ... |
| title_short | Mathematics of the 19th century |
| title_sort | mathematics of the 19th century mathematical logic algebra number theory probability theory |
| title_sub | mathematical logic, algebra, number theory, probability theory |
| topic | Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Logik (DE-588)4037951-6 gnd Algebra (DE-588)4001156-2 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Wahrscheinlichkeitstheorie Wahrscheinlichkeitsrechnung Mathematik Mathematische Logik Algebra Zahlentheorie Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019108193&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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