The history of the theory of errors:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Egelsbach ; Frankfurt [Main] ; St. Peter Port
Hänsel-Hohenhausen
1996
|
| Schriftenreihe: | Deutsche Hochschulschriften
1118 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 153 - 176 |
| Beschreibung: | 180 S. |
| ISBN: | 3826711181 |
Internformat
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| 650 | 4 | |a Error analysis (Mathematics) -- History | |
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Datensatz im Suchindex
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| adam_text | OSCAR SHEYNIN THE HISTORY OF THE THEORY OF ERRORS .HANSEL^HOHENHAUSEN
EGELSBACH | FRANKFURT | ST. PETER PORT CONTENTS 0. INTRODUCTION
............................................ 8 0.1. THE GOALS OF THE
THEORY OF ERRORS 8 0.2. INTERRELATION WITH STATISTICS 9 0.3. ASTRONOMY
AND GEODESY 10 0.4. WHY AND WHEN DID THE THEORY OF ERRORS EMERGE? ......
11 0.5. THE SCOPE OF THIS BOOK 13 0.6. SOME TERMINOLOGY AND NOTATION 13
1. THE EARLY HISTORY 17 1.1. BOUNDS AND ESTIMATORS 17 1.2. REGULAR
OBSERVATIONS 18 1.3. OPTIMAL CIRCUMSTANCES OF OBSERVATION
............... 18 1.4. PTOLEMY 19 1.3. SOME EXPLANATION 21 1.6.
AL=BIRUNI 21 1.7. GALILEO 23 1.8. TYCHO BRAHE 24 1.9. KEPLER 25 NOTES 28
MAIN LITERATURE . 29 2. THE EIGHTEENTH CENTURY 31 2.1. THE ARITHMETIC
MEAN ................................ 31 2.2. MAYER 31 2.3. LAMBERT 32
2.4. BOSCOVICH 36 2.5. SIMPSON 39 2.6. LAGRANGE . 42 2.7. DANIEL
BERNOULLI I 42 2.8. EULER ; 45 NOTES 47 MAIN LITERATURE 50 3. LAPLACE
51 3.1. INTRODUCTION 51 3.2. EARLY MEMOIRS 52 3.3. LATER WORK (1810 *
1811) 56 3.4. THE THEORIE ANALYTIQUE DES PROBABILITES 58 3.5. SUPPLEMENT
1 (1616) 61 3.6. SUPPLEMENT 2 (1818) 62 3.7. SUPPLEMENT 3 (CA. 1819) 67
3.8. A FAULTY DISCUSSION OF DEPENDENT OBSERVATIONS ...... 69 NOTES 70
MAIN LITERATURE 73 4. THE NINETEENTH CENTURY BEFORE 1809 75 4.1. SOLVING
REDUNDANT SYSTEMS OF EQUATIONS ............. 75 4.2. A VENERABLE PROBLEM
IN LAND SURVEYING 76 4.3. HUBER 76 4.4. LEGENDRE 77 4.5. ADRAIN 78 4.6.
GAUSS 82 NOTES 84 MAIN LITERATURE 84 5. GAUSS 85 5.1. THEORIA MOTUS
,,,.*,,, 85 5.2. DETERMINING THE PRECISION OF OBSERVATIONS .......... 88
5.3* THEORIA COMBINATIONIS 90 5.4. PRACTICAL CONSIDERATIONS. THE ERROR
THEORY SURVEYED 97 NOTES 101 MAIN LITERATURE 103 6. FROM GAUSS TO
HELMERT AND BEYOND 105 6.1. SOME NEW WORK 105 6.2. PHYSICS, CHEMISTRY,
METEOROLOGY ................... 108 6.3. THE NORMAL LAW 111 6.4. THE
NORMAL LAW MODIFIED 114 6.5. THE THEORY OF ERRORS AND STATISTICS
............... 118 NOTES 121 MAIN LITERATURE 125 7. HELMERT 127 7.1.
REJECTION OF OUTLYING OBSERVATIONS 127 7.2. REVEALING SYSTEMATIC ERRORS
....................... 127 7.3. REVEALING SYSTEMATIC ERRORS: THE ABBE
CRITERION ... 129 7.4. THE SUMS OF NATURAL POWERS OF ERRORS 130 7.5. THE
CHISQUARED DISTRIBUTION 131 7.6. THE PETERS FORMULA 132 7.7. THE GAUSS
FORMULA 134 7.8. ANTICIPATING THE STUDENT * FISHER THEOREM 135 7.9. THE
PRECISION OF THE MEAN SQUARE ERROR 135 7.10. IS UNBIASEDNESS NECESSARY?
136 NOTES 137 MAIN LITERATURE ..........................................
138 8. STABLE LAWS (LEVY) 139 8.1. RANDOM ERRORS 139 8.2. THE PRECISION
OF OBSERVATIONS ....................... 139 8.3. THE MEAN SQUARE ERROR
............................... 140 8.4. A NEW CONCEPT OF PRECISION 141
8.5. STABLE LAWS. 141 NOTES 143 MAIN LITERATURE 143 9. THE DETERMINATE
THEORY OF ERRORS ......................... 145 9.1. EXPERIMENTAL DESIGN
AND PRELIMINARY DATA ANALYSIS ... 145 9.2. THE EIGHTEENTH CENTURY 14.5
9.3. LAPLACE 14.7 9.4. GAUSS AND BESSEL 148 9.5. HELMERT 151 NOTES 152
BIBLIOGRAPHY 153 / IKDERS. * JSTAAT5- U.T.J. RV.-| V GOTTINGEN
|
| any_adam_object | 1 |
| author | Šejnin, Oskar B. 1925- |
| author_GND | (DE-588)128703350 |
| author_facet | Šejnin, Oskar B. 1925- |
| author_role | aut |
| author_sort | Šejnin, Oskar B. 1925- |
| author_variant | o b š ob obš |
| building | Verbundindex |
| bvnumber | BV010926235 |
| callnumber-first | Q - Science |
| callnumber-label | QA275 |
| callnumber-raw | QA275.S458 1996 |
| callnumber-search | QA275.S458 1996 |
| callnumber-sort | QA 3275 S458 41996 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SG 500 SG 590 |
| ctrlnum | (OCoLC)645602732 (DE-599)BVBBV010926235 |
| dewey-full | 511/.4321 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.43 21 |
| dewey-search | 511/.43 21 |
| dewey-sort | 3511 243 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010926235 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:01:14Z |
| institution | BVB |
| isbn | 3826711181 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007309184 |
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| physical | 180 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Hänsel-Hohenhausen |
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| series | Deutsche Hochschulschriften |
| series2 | Deutsche Hochschulschriften |
| spelling | Šejnin, Oskar B. 1925- Verfasser (DE-588)128703350 aut The history of the theory of errors Oscar Sheynin Egelsbach ; Frankfurt [Main] ; St. Peter Port Hänsel-Hohenhausen 1996 180 S. txt rdacontent n rdamedia nc rdacarrier Deutsche Hochschulschriften 1118 Literaturverz. S. 153 - 176 Error analysis (Mathematics) - History Geschichte Error analysis (Mathematics) -- History Fehlerrechnung (DE-588)4153837-7 gnd rswk-swf Irrtum (DE-588)4140092-6 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Fehlerrechnung (DE-588)4153837-7 s Geschichte (DE-588)4020517-4 s DE-604 Mathematik (DE-588)4037944-9 s Irrtum (DE-588)4140092-6 s Deutsche Hochschulschriften 1118 (DE-604)BV004679961 1118 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007309184&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Šejnin, Oskar B. 1925- The history of the theory of errors Deutsche Hochschulschriften Error analysis (Mathematics) - History Geschichte Error analysis (Mathematics) -- History Fehlerrechnung (DE-588)4153837-7 gnd Irrtum (DE-588)4140092-6 gnd Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4153837-7 (DE-588)4140092-6 (DE-588)4020517-4 (DE-588)4037944-9 |
| title | The history of the theory of errors |
| title_auth | The history of the theory of errors |
| title_exact_search | The history of the theory of errors |
| title_full | The history of the theory of errors Oscar Sheynin |
| title_fullStr | The history of the theory of errors Oscar Sheynin |
| title_full_unstemmed | The history of the theory of errors Oscar Sheynin |
| title_short | The history of the theory of errors |
| title_sort | the history of the theory of errors |
| topic | Error analysis (Mathematics) - History Geschichte Error analysis (Mathematics) -- History Fehlerrechnung (DE-588)4153837-7 gnd Irrtum (DE-588)4140092-6 gnd Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Error analysis (Mathematics) - History Geschichte Error analysis (Mathematics) -- History Fehlerrechnung Irrtum Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007309184&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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