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CATEGORIES:Cambridge Statistics Discussion Group (CSDG)
SUMMARY:On reading Bernoulli’s Ars conjectandi 1713 - Anth
ony Edwards\, Gonville and Caius
DTSTART;TZID=Europe/London:20150202T191500
DTEND;TZID=Europe/London:20150202T213000
UID:TALK51089AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/51089
DESCRIPTION:James Bernoulli’s posthumous book is famous among
statisticians for the binomial distribution in Par
t I\, the Bernoulli numbers in Part II and the lim
it theorem in Part IV\, but it contains much else
of interest besides. It is full of Pascal triangle
s\, and Bernoulli’s treatment of the polynomials f
or the sums of the powers of the integers leads to
the discovery that the Bernoulli numbers had alre
ady been published by Johann Faulhaber in 1631. We
can now see how Bernoulli derived the polynomials
\; the simple algorithm reveals an error in his ta
ble of the coefficients. An alternative and elegan
t procedure involves the inversion of Pascal matri
ces of binomial coefficients.
LOCATION:Statistical Laboratory\, University of Cambridge
CONTACT:Peter Watson
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