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Cubierta del libro
Autor Fischer, Hans. author.

Título A History of the Central Limit Theorem [electronic resource] : From Classical to Modern Probability Theory / by Hans Fischer.

Publicación New York, NY : Springer New York, 2011.
Descripción física XVI, 402 p. online resource.
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Colección Sources and Studies in the History of Mathematics and Physical Sciences
Sources and Studies in the History of Mathematics and Physical Sciences
Springer eBooks. Mathematics and Statistics
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Contiene: Preface -- Introduction -- The central limit theorem from laplace to cauchy: changes in stochastic objectives and in analytical methods -- The hypothesis of elementary errors -- Chebyshev's and markov's contributions -- The way towards modern probability -- General limit problems -- Conclusion: the central limit theorem as a link between classical and modern probability -- Index -- Bibliography.
Resumen: This study aims to embed the history of the central limit theorem within the history of the development of probability theory from its classical to its modern shape, and, more generally, within the corresponding development of mathematics. The history of the central limit theorem is not only expressed in light of "technical" achievement, but is also tied to the intellectual scope of its advancement. The history starts with Laplace's 1810 approximation to distributions of linear combinations of large numbers of independent random variables and its modifications by Poisson, Dirichlet, and Cauchy, and it proceeds up to the discussion of limit theorems in metric spaces by Donsker and Mourier around 1950. This self-contained exposition additionally describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The importance of historical connections between the history of analysis and the history of probability theory is demonstrated in great detail. With a thorough discussion of mathematical concepts and ideas of proofs, the reader will be able to understand the mathematical details in light of contemporary development. Special terminology and notations of probability and statistics are used in a modest way and explained in historical context.
Materia Mathematics.
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History of Mathematical Sciences.
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Probability Theory and Stochastic Processes.
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Statistics, general.
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Autor secundario SpringerLink (Online service)
En Springer eBooks
OTRO SOPORTE Printed edition: 9780387878560
ISBN 9780387878577 978-0-387-87857-7
ISBN/ISSN 10.1007/978-0-387-87857-7 doi