Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

Within this two-volume edition, Professor Smith covers the entire history of mathematics in the Near and Far East and the West, from primitive number concepts to the calculus. His account is distinguished by impeccable scholarship combined with unusual clarity and readability. Footnotes add many technical points outside the book's actual line of development and direct the reader to disputed matters and source readings. Hundreds of illustrations from Egyptian papyri, Hindu, Chinese, and Japanese manuscripts, Greek and Roman texts, Medieval treatises, maps, portraits, etc. are used along with modern graphs and diagrams. Every major figure from Euclid to Descartes, Gauss, and Riemann and hundreds of lesser-known figures — Theon of Smyrna, Rabbi ben Ezra, Radulph of Laon, Mersenns, Benedetti, and more — are considered both with respect to specific problems and with an awareness of their overall influence on mathematics. Volume II: Special Topics, considering mathematics in terms of arithmetic geometry, algebra, trig, calculus, calculating machines, and other specific fields and problems. 192 Topics for Discussion. 195 illustrations. Index.

Deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables.

V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.

Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.