Elements of the History of Mathematics
Springer Science & Business Media, 1998 M11 18 - 301 páginas
This work gathers together, without substantial modification, the major ity of the historical Notes which have appeared to date in my Elements de M atMmatique. Only the flow has been made independent of the Elements to which these Notes were attached; they are therefore, in principle, accessible to every reader who possesses a sound classical mathematical background, of undergraduate standard. Of course, the separate studies which make up this volume could not in any way pretend to sketch, even in a summary manner, a complete and con nected history of the development of Mathematics up to our day. Entire parts of classical mathematics such as differential Geometry, algebraic Geometry, the Calculus of variations, are only mentioned in passing; others, such as the theory of analytic functions, that of differential equations or partial differ ential equations, are hardly touched on; all the more do these gaps become more numerous and more important as the modern era is reached. It goes without saying that this is not a case of intentional omission; it is simply due to the fact that the corresponding chapters of the Elements have not yet been published. Finally the reader will find in these Notes practically no bibliographic or anecdotal information about the mathematicians in question; what has been attempted above all, for each theory, is to bring out as clearly as possible what were the guiding ideas, and how these ideas developed and reacted the ones on the others.
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abelian groups Algebraic Geometry algebraic numbers already analogous Analysis analytic appears arbitrary Archimedes arithmetic axiomatic axioms Borel Cantor Cartan Cauchy classical coefficients commutative complete complex numbers conception considered continuous functions convergence curve decomposition Dedekind defined definition Descartes developed Euclid Euclidean Euler example existence Fermat field formula fundamental Galois Gauss generalisation geometry gives Greek Hilbert Hilbert space idea ideal infinite infinitesimal calculus integral introduced intuition invariant irreducible isomorphism Kronecker Lagrange later Lebesgue Leibniz Lie algebra Lie groups linear linked mathematicians mathematics measure memoir method metric metric spaces modern multiplication notation notion obtained p-adic particular plane Poincare point of view polynomial precise prime ideal prime numbers principle problem proof properties proves quadratic forms quadrics quantities real numbers representation Riemann ring roots roots of unity semisimple Lie algebras sequence solution space straight line theorem tion topology transformations variables Weierstrass whole numbers XlXth century XVIIth century
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