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04910nam a22004575i 4500 |
| 001 - CONTROL NUMBER |
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978-1-84628-633-9 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20161121231126.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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100301s2007 xxk| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781846286339 |
| -- |
978-1-84628-633-9 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-1-84628-633-9 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA21-27 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBX |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT015000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510.9 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Gray, Jeremy. |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
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| Title |
Worlds Out of Nothing |
| Medium |
[electronic resource] : |
| Remainder of title |
A Course in the History of Geometry in the 19th Century / |
| Statement of responsibility, etc. |
by Jeremy Gray. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
London : |
| Name of producer, publisher, distributor, manufacturer |
Springer London, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2007. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XXIV, 376 p. 68 illus. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Springer Undergraduate Mathematics Series, |
| International Standard Serial Number |
1615-2085 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Mathematics in the French Revolution -- Poncelet (and Pole and Polar) -- Theorems in Projective Geometry -- Poncelet’s Traité -- Duality and the Duality Controversy -- Poncelet, Chasles, and the Early Years of Projective Geometry -- Euclidean Geometry, the Parallel Postulate, and the Work of Lambert and Legendre -- Gauss (Schweikart and Taurinus) and Gauss’s Differential Geometry -- János Bolyai -- Lobachevskii -- Publication and Non-Reception up to 1855 -- On Writing the History of Geometry — 1 -- Across the Rhine — Möbius’s Algebraic Version of Projective Geometry -- Plücker, Hesse, Higher Plane Curves, and the Resolution of the Duality Paradox -- The Plücker Formulae -- The Mathematical Theory of Plane Curves -- Complex Curves -- Riemann: Geometry and Physics -- Differential Geometry of Surfaces -- Beltrami, Klein, and the Acceptance of Non-Euclidean Geometry -- On Writing the History of Geometry — 2 -- Projective Geometry as the Fundamental Geometry -- Hilbert and his Grundlagen der Geometrie -- The Foundations of Projective Geometry in Italy -- Henri Poincaré and the Disc Model of non-Euclidean Geometry -- Is the Geometry of Space Euclidean or Non-Euclidean? -- Summary: Geometry to 1900 -- What is Geometry? The Formal Side -- What is Geometry? The Physical Side -- What is Geometry? Is it True? Why is it Important? -- On Writing the History of Geometry — 3. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students in mathematics but will also appeal to the reader with a general interest in the history of mathematics. Emphasis is placed on understanding the historical significance of the new mathematics: Why was it done? How - if at all - was it appreciated? What new questions did it generate? Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry, as exemplified by Klein’s Erlangen Program, rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance. It then concludes with discussions on geometry and formalism, examining the Italian contribution and Hilbert’s Foundations of Geometry; geometry and physics, with a look at some of Einstein’s ideas; and geometry and truth. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for. The Springer Undergraduate Mathematics Series (SUMS) is designed for undergraduates in the mathematical sciences. From core foundational material to final year topics, SUMS books take a fresh and modern approach and are ideal for self-study or for a one- or two-semester course. Each book includes numerous examples, problems and fully-worked examples. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Geometry. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
History. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
History of Mathematical Sciences. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Geometry. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Printed edition: |
| International Standard Book Number |
9781846286322 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Springer Undergraduate Mathematics Series, |
| International Standard Serial Number |
1615-2085 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-1-84628-633-9 |
| 912 ## - |
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| -- |
ZDB-2-SMA |
