Beschreibung
xiii, 813-1211, xxii p. Das Exemplar ist in tadellosem Zustand und neuwertig. / The copy is in mint condition and as good as new. -- 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 -- 40. The Instillation of Rigor in Analysis, 947 -- CONTENTS -- 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, 980 982 4. The Theory of Rational Numbers, 987 -- 3. The Theory -- of Irrational Numbers, -- 5. Other -- Approaches to the Real Number System, 990 7. The Foundation of the Theory of Sets, 994 -- 6. The Concept of an Infinite Set, 992 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 Foundations of Euclidean Geometry, 1010 -- Geometry, 1007 3. The Foundational Work, 1015 -- 4. Some Related -- 5. Some Open Questions, 1017 -- 43. Mathematics as of 1900, 1023 -- 1. The Chief Features of the Nineteenth-Century Developments, 1023 -- 2. The Axiomatic -- Movement, 1026 -- 3. Mathematics as Man's Creation, 1028 -- 4. The Loss of Truth, 1032 -- 5. Mathematics as -- the Study of Arbitrary Structures, 1036 7. A Glance Ahead, 1039 -- 6. The Problem of -- Consistency, 1038 -- 44. The Theory of Functions of Real Variables, 1040 -- 1. The Origins, 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. The Work of -- 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.
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