MARC Record from harvard_bibliographic_metadata

LEADER: 02993cam a22003738a 4500
001 012620757-7
005 20140910154240.0
008 100520s2011 nyua b 001 0 eng
015 $aGBB064827$2bnb
016 7 $a015562048$2Uk
020 $a9780387878560 (hbk.)
020 $a0387878564 (hbk.)
035 0 $aocn567148466
040 $aUKM$cUKM$dBTCTA$dYDXCP
050 4 $aQA273.67$b.F57 2011
082 04 $a519.2$222
100 1 $aFischer, Hans.
245 10 $aHistory of the central limit theorem :$bfrom classical to modern probability theory /$cHans Fischer.
260 $aNew York ;$aLondon :$bSpringer,$cc2011.
300 $axvi, 402 p. :$bill. ;$c24 cm.
490 1 $aSources and studies in the history of mathematics and the physical sciences
504 $aIncludes bibliographical references (p. 363-391) and indexes.
505 0 $aIntroduction -- The cental 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 toward modern probability -- Lévy and Feller on normal limit distributions around 1935 -- Generalizations -- Conclusion: the central limit theorem as a link between classical and modern probability theory.
520 $aThis 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 $aCentral limit theorem.
650 0 $aCentral limit theorem$xHistory.
650 0 $aDistribution (Probability theory).
650 0 $aMathematics.
650 0 $aMathematics_$xHistory.
650 0 $aStatistics.
830 0 $aSources and studies in the history of mathematics and physical sciences.
899 $a415_565807
988 $a20101123
906 $0OCLC