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portada Descargar ficha PDF Título: Life And Times Of The Central Limit Theorem, The.
Autor: Adams William J Precio: $674.16
Editorial: American Mathematical Society Año: 2009
Tema: Matematicas, Historia, Investigacion Edición:
Sinopsis ISBN: 9780821848999
About the First Edition:

The study of any topic becomes more meaningful if one also studies the historical development that resulted in the final theorem. ... This is an excellent book on mathematics in the making.

--Philip Peak, The Mathematics Teacher, May, 1975

I find the book very interesting. It contains valuable information and useful references. It can be recommended not only to historians of science and mathematics but also to students of probability and statistics.

--Wei-Ching Chang, Historica Mathematica, August, 1976

In the months since I wrote ... I have read it from cover to cover at least once and perused it here and there a number of times. I still find it a very interesting and worthwhile contribution to the history of probability and statistics.

--Churchill Eisenhart, past president of the American Statistical Association, in a letter to the author, February 3, 1975

The name Central Limit Theorem covers a wide variety of results involving the determination of necessary and sufficient conditions under which sums of independent random variables, suitably standardized, have cumulative distribution functions close to the Gaussian distribution. As the name Central Limit Theorem suggests, it is a centerpiece of probability theory which also carries over to statistics.

Part One of The Life and Times of the Central Limit Theorem, Second Edition traces its fascinating history from seeds sown by Jacob Bernoulli to use of integrals of \exp (x^2) as an approximation tool, the development of the theory of errors of observation, problems in mathematical astronomy, the emergence of the hypothesis of elementary errors, the fundamental work of Laplace, and the emergence of an abstract Central Limit Theorem through the work of Chebyshev, Markov and Lyapunov. This closes the classical period of the life of the Central Limit Theorem, 1713-1901.

The second part of the book includes papers by Feller and Le Cam, as well as comments by Doob, Trotter, and Pollard, describing the modern history of the Central Limit Theorem (1920-1937), in particular through contributions of Lindeberg, Cramér, Lévy, and Feller.

The Appendix to the book contains four fundamental papers by Lyapunov on the Central Limit Theorem, made available in English for the first time.

Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.

Table of Contents

Early life and middle years
A seed is sown
Approximation by integrals of e^{-x^{2}}
Impetus provided by the theory of errors of observation
Impetus provided by mathematical astronomy
The flowering of the central limit theorem begins
The development of the hypothesis of elementary errors
The emergence of an abstract central limit theorem
Chebyshev's pupils: A. A. Markov and A. M. Lyapunov
Bibliography
The modern era
W. Feller, The fundamental limit theorems in probability
L. Le Cam, The central limit theorem around 1935
H. F. Trotter, J. L. Doob, David Pollard, and L. Le Cam, Comments and rejoinder
Appendix
A. M. Lyapunov, On a theorem in probability theory
A. M. Lyapunov, On a theorem in probability theory
A. M. Lyapunov, A general proposition in probability theory
A. M. Lyapunov, A new form of a theorem on the limit of a probability
Index
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