LEADER 00000nam a22004695i 4500 001 978-0-387-87857-7 003 DE-He213 005 20151204180957.0 007 cr nn 008mamaa 008 101013s2011 xxu| s |||| 0|eng d 020 9780387878577|9978-0-387-87857-7 024 7 10.1007/978-0-387-87857-7|2doi 040 ES-ZaU 072 7 PBX|2bicssc 072 7 MAT015000|2bisacsh 082 04 510.9|223 100 1 Fischer, Hans.|eauthor. 245 12 A History of the Central Limit Theorem|h[electronic resource] :|bFrom Classical to Modern Probability Theory / |cby Hans Fischer. 260 1 New York, NY :|bSpringer New York,|c2011. 300 XVI, 402 p.|bonline resource. 336 text|btxt|2rdacontent 337 computer|bc|2rdamedia 338 online resource|bcr|2rdacarrier 347 text file|bPDF|2rda 490 1 Sources and Studies in the History of Mathematics and Physical Sciences 490 0 Springer eBooks.|aMathematics and Statistics 505 0 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. 520 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. 650 0 Mathematics. 650 0 History. 650 0 Probabilities. 650 0 Statistics. 650 14 Mathematics. 650 24 History of Mathematical Sciences. 650 24 Probability Theory and Stochastic Processes. 650 24 Statistics, general. 710 2 SpringerLink (Online service) 773 0 |tSpringer eBooks 776 08 |iPrinted edition:|z9780387878560 830 0 Sources and Studies in the History of Mathematics and Physical Sciences 856 40 |zAcceso al texto completo|uhttp://dx.doi.org/10.1007/978- 0-387-87857-7

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