Mathematical thought from ancient to modern times: Volume 3
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; Oxford
Oxford University Press
1990
|
| Ausgabe: | First issued as an Oxford University Press paperback |
| Schriftenreihe: | Oxford paperbacks
Oxford paperbacks |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiii Seiten, Seite 813-1211, xxii Seiten Diagramme |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents 34. The Theory of Numbers in the Nineteenth Century, 813 1. Introduction, 813 2. The Theory of Congruences, 813 3. Algebraic Numbers, 818 4. The Ideals of Dedekind, 822 5. The Theory of Forms, 826 6. Analytic Number Theory, 829 35. The Revival of Projective Geometry, 834 1. The Renewal of Interest in Geometry, 834 2. Synthetic Euclidean Geometry, 837 3. The Revival of Synthetic Projective Geometry, 840 4. Algebraic Projective Geometry, 852 5. Higher Plane Curves and Surfaces, 855 36. Non-Euclidean Geometry, 861 1. Introduction, 861 2. The Status of Euclidean Geometry About 1800,861 3. The Research on the Parallel Axiom, 863 4. Foreshadowings of Non-Euclidean Geometry, 867 5. The Creation of Non-Euclidean Geometry, 869 6. The Technical Content of Non-Euclidian Geometry, 874 7. The Claims of Lobatchevsky and Bolyai to Priority, 877 8. The Implications of Non-Euclidean Geometry, 879 37. The Differential Geometry of Gauss and Riemann, 882 1. Introduction, 882 2. Gauss’s Differential Geometry, 882 3. Riemann’s Approach to Geometry, 889 4. The Successors of Riemann, 896 5. Invariants of Differential Forms, 899 38. Projective and Metric Geometry, 904 1. Introduction, 904 2. Surfaces as Models of Non-Euclidean Geometry, 904 3. Projective and Metric Geometry, 906 4. Models and the Consistency Problem, 913 5. Geometry from the Transformation Viewpoint, 917 6. The Reality of Non-Euclidean Geometry, 921 39. Algebraic Geometry, 924 1. Background, 924 2. The Theory of Algebraic Invariants, 925 3. The Concept of Birational Transformations, 932 4. The Function-Theoretic Approach
to Algebraic Geometry, 934 5. The Uniformization Problem, 937 6. The Algebraic-Geometric Approach, 939 7. The Arithmetic Approach, 942 8. The Algebraic Geometry of Surfaces, 943
xii CONTENTS 40. The Instillation of Rigor in Analysis, 947 1. Introduction, 947 2. Functions and Their Properties, 949 3. The Derivative, 954 4. The Integral, 956 5. Infinite Series, 961 6. Fourier Series, 966 7. The Status of Analysis, 972 41. The Foundations of the Real and Transfinite Numbers, 979 1. Introduction, 979 2. Algebraic and Transcendental Numbers, 980 3. The Theory ofirrational Numbers, 982 4. The Theory of Rational Numbers, 987 5. Other Approaches to the Real Number System, 990 6. TheConcept of an Infinite Set, 992 7. The Foundation of the Theory of Sets, 994 8. Transfinite Cardinals and Ordinals, 998 9. The Status of Set Theory by 1900,1002 42. The Foundations of Geometry, 1005 1. The Defects in Euclid, 1005 2. Contributions to the Foundations of Projective Geometry, 1007 3. The Foundations of Euclidean Geometry, 1010 4. Some Related Foundational Work, 1015 5. Some Open Questions, 1017 43. Mathematics as of 1900,1023 1. The Chief Features of the Nineteenth-Century Developments, 1023 2. TheAxiomatic Movement, 1026 3. Mathematics as Man’s Creation, 1028 4. The Loss of Truth, 1032 5. Mathematics as the Study of Arbitrary Structures, 1036 6. The Problem of Consistency, 1038 7. A Glance Ahead, 1039 44. The Theory of Functions of Real Variables, 1040 1. TheOrigins, 1040 2. The Stieltjes Integral, 1041 3. Early Work on Content and Measure, 1041 4. The Lebesgue Integral, 1044 5. Generalizations, 1050 45. Integral Equations, 1052 1. Introduction, 1052 2. The Beginning of a General Theory, 1056 3. TheWorkof Hilbert, 1060 4. The Immediate Successors of Hilbert, 1070
5. Extensions of the Theory, 1073 46. Functional Analysis, 1076 1. The Nature of Functional Analysis, 1076 2. The Theory of Functionals, 1077 3. Linear Functional Analysis, 1081 4. The Axiomatization of Hilbert Space, 1091 47. Divergent Series, 1096 1. Introduction, 1096 2. The InformalUses of Divergent Series, 1098 3. The Formal Theory of Asymptotic Series, 1103 4. Summability, 1109 48. Tensor Analysis and Differential Geometry, 1122 1. The Origins of Tensor Analysis, 1122 2. The Notion of a Tensor, 1123 3. Covariant Differentiation, 1127 4. Parallel Displacement, 1130 5. Generalizations of Riemannian Geometry, 1133
CONTENTS xiii 49. The Emergence of Abstract Algebra, 1136 1. The Nineteenth-Century Background, 1136 2. Abstract Group Theory, 1137 3. The Abstract Theory of Fields, 1146 4. Rings, 1150 5. Non-Associative Algebras, 1153 6. The Range of Abstract Algebra, 1156 50. The Beginnings of Topology, 1158 1. The Nature of Topology, 1158 2. Point Set Topology, 1159 3. The Beginnings of Combinational Topology, 1163 4. The Combinational Work of Poincaré, 1170 5. Combinatorial Invariants, 1176 6. Fixed Point Theorems, 1177 7. Generalizations and Extensions, 1179 51. The Foundations of Mathematics, 1182 1. Introduction, 1182 2. The Paradoxes of Set Theory, 1183 3. The Axiomatization of Set Theory, 1185 4. The Rise of Mathematical Logic, 1187 5. The Logistic School, 1192 6. The Intuitionist School, 1197 7. The Formalist School, 1203 8. Some Recent Developments, 1208 List ofAbbreviations Index
|
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| indexdate | 2024-07-09T21:57:35Z |
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| language | English |
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| physical | xiii Seiten, Seite 813-1211, xxii Seiten Diagramme |
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| spelling | Kline, Morris 1908-1992 Verfasser (DE-588)131716271 aut Mathematical thought from ancient to modern times Volume 3 Morris Kline First issued as an Oxford University Press paperback New York ; Oxford Oxford University Press 1990 xiii Seiten, Seite 813-1211, xxii Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Oxford paperbacks (DE-604)BV010769255 3 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018317957&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kline, Morris 1908-1992 Mathematical thought from ancient to modern times |
| title | Mathematical thought from ancient to modern times |
| title_auth | Mathematical thought from ancient to modern times |
| title_exact_search | Mathematical thought from ancient to modern times |
| title_full | Mathematical thought from ancient to modern times Volume 3 Morris Kline |
| title_fullStr | Mathematical thought from ancient to modern times Volume 3 Morris Kline |
| title_full_unstemmed | Mathematical thought from ancient to modern times Volume 3 Morris Kline |
| title_short | Mathematical thought from ancient to modern times |
| title_sort | mathematical thought from ancient to modern times |
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