000			03396nam a22004815i 4500
001			978-0-387-87857-7
003			DE-He213
005			20140220083710.0
007			cr nn 008mamaa
008			101013s2011 xxu| s |||| 0|eng d
020			_a9780387878577 _9978-0-387-87857-7
024	7		_a10.1007/978-0-387-87857-7 _2doi
050		4	_aQA21-27
072		7	_aPBX _2bicssc
072		7	_aMAT015000 _2bisacsh
082	0	4	_a510.9 _223
100	1		_aFischer, Hans. _eauthor.
245	1	2	_aA History of the Central Limit Theorem _h[electronic resource] : _bFrom Classical to Modern Probability Theory / _cby Hans Fischer.
264		1	_aNew York, NY : _bSpringer New York, _c2011.
300			_aXVI, 402 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSources and Studies in the History of Mathematics and Physical Sciences
505	0		_aPreface -- 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			_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	_aMathematics.
650		0	_aMathematics_$xHistory.
650		0	_aDistribution (Probability theory).
650		0	_aStatistics.
650	1	4	_aMathematics.
650	2	4	_aHistory of Mathematics.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aStatistics, general.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387878560
830		0	_aSources and Studies in the History of Mathematics and Physical Sciences
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-87857-7
912			_aZDB-2-SMA
999			_c105054 _d105054