Mathematical Thought From Ancient to Modern Times, Volume 3, Volume 3This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study. |
Contents
| 813 | |
| 834 | |
36 NonEuclidean Geometry | 861 |
37 The Differential Geometry of Gauss and Riemann | 882 |
38 Projective and Metric Geometry | 904 |
39 Algebraic Geometry | 924 |
40 The Instillation of Rigor in Analysis | 947 |
41 The Foundations of the Real and Transfinite Numbers | 979 |
45 Integral Equations | 1052 |
46 Functional Analysis | 1076 |
47 Divergent Series | 1096 |
48 Tensor Analysis and Differential Geometry | 1122 |
49 The Emergence of Abstract Algebra | 1136 |
50 The Beginnings of Topology | 1158 |
51 The Foundations of Mathematics | 1182 |
List of Abbreviations | i |
Other editions - View all
Mathematical Thought From Ancient to Modern Times, Volume 3, Volume 3 Morris Kline Limited preview - 1990 |
Common terms and phrases
abstract algebraic integers algebraic numbers Amer analysis analytic angle arithmetic asymptotic asymptotic series axiomatic Betti number calculus calculus of variations called Cantor cardinal number Cauchy Chap coefficients concept continuous continuous functions convergence coordinates covariant curvature curve defined definition derived differential equations divergent series elements elliptic geometry Euclid's Euclidean geometry existence field figures finite number formulas Fourier Fourier series functions Gauss geodesics given Hilbert hyperbolic geometry infinite sets integral equations interval introduced invariants irrational numbers Jour Lebesgue Lebesgue integrable linear Lobatchevsky logic manifold Math mathematicians mathematics metric n-dimensional non-Euclidean geometry notion number system number theory operator paper parallel axiom plane Poincaré points polynomials problem projective geometry proof properties proved rational numbers real numbers Riemann Riemannian sequence solution space summable surface tensor theorem topology transformation triangle variables vector Werke Wiss zero