Mathematics of the 19th Century

Mathematical Logic Algebra Number Theory Probability Theory

Häftad, Engelska, 2001

AvA.N. Kolmogorov,A.P. Yushkevich,A. N. Kolmogorov,A. P. Yushkevich

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New Editional New in Paperback! This is the second revised edition of the first volume of the outstanding collection of historical studies of mathematics in the nineteenth century compiled in three volumes by A. N. Kolmogorov and A. P. Yushkevich. This second edition was carefully revised by Abe Shenitzer, York University, Ontario, Canada. The historical period covered in this book extends from the early nineteenth century up to the end of the 1930s, as neither 1801 nor 1900 are, in themselves, turning points in the history of mathematics, although each date is notable fo a remarkable event: the first for the publication of Gauss' "Disquisitiones arithmeticae", the second for Hilbert's "Mathematical Problems." Beginning in the second quarter of the nineteenth century mathematics underwent a revolution as crucial and profound in its consequences for the general world outlook as the mathematical revolution in the beginning of the modern era. The main changes included a new statement of the problem of the existence of mathematical objects, particulary in the calculus, and soon thereafter the formation of non-standard structures in geometry, arithmetic and algebra.The primary objective of the work has been to treat the evolution of mathematics in the nineteenth century as a whole; the discussion is concentrated on the essential concepts, methods, and algorithms.

Produktinformation

Utgivningsdatum2001-03-01
Mått155 x 235 x 18 mm
Vikt619 g
FormatHäftad
SpråkEngelska
Antal sidor308
Upplaga2
FörlagBirkhauser Verlag AG
ISBN9783764364427
ÖversättareShenitzer, A., Grant, H., Sheinin, O.B., Sheinin, O. B.

Tillhör följande kategorier

Matematikens historia inom Naturvetenskap och teknik

One Mathematical Logic.- The Prehistory of Mathematical Logic.- Leibniz’s Symbolic Logic.- The Quantification of a Predicate.- The “Formal Logic” of A. De Morgan.- Boole’s Algebra of Logic.- Jevons’ Algebra of Logic.- Venn’s Symbolic Logic.- Schröder’s and Poretski-’s Logical Algebra.- Conclusion.- Two Algebra and Algebraic Number Theory.- 1 Survey of the Evolution of Algebra and of the Theory of Algebraic Numbers During the Period of 1800-1870.- 2 The Evolution of Algebra.- 3 The Theory of Algebraic Numbers and the Beginnings of Commutative Algebra.- Three Problems of Number Theory.- 1 The Arithmetic Theory of Quadratic Forms.- 2 Geometry of Numbers.- 3 Analytic Methods in Number Theory.- 4 Transcendental Numbers.- Four The Theory of Probability.- Laplace’s Theory of Probability.- Laplace’s Theory of Errors.- Gauss’ Contribution to the Theory of Probability.- The contributions of Poisson and Cauchy.- Social and Anthropometric Statistics.- The Russian School of the Theory of Probability. P.L. Chebyshev.- New Fields of Application of the Theory of Probability. The Rise of Mathematical Statistics.- Works of the Second Half of the 19th Century in Western Europe.- Conclusion.- Addendum.- 1. French and German Quotations.- 2. Notes.- 3. Additional Bibliography.- Bibliography (by F.A. Medvedev).- Abbreviations.- Index of Names.