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SUMMARY:On reading Bernoulli’s Ars conjectandi 1713 - Anthony Edwards\, 
 Gonville and Caius
DTSTART:20150202T191500Z
DTEND:20150202T213000Z
UID:TALK51089@talks.cam.ac.uk
CONTACT:Peter Watson
DESCRIPTION:James Bernoulli’s posthumous book is famous among statistici
 ans for the binomial distribution in Part I\, the Bernoulli numbers in Par
 t II and the limit theorem in Part IV\, but it contains much else of inter
 est besides. It is full of Pascal triangles\, and Bernoulli’s treatment 
 of the polynomials for the sums of the powers of the integers leads to the
  discovery that the Bernoulli numbers had already been published by Johann
  Faulhaber in 1631. We can now see how Bernoulli derived the polynomials\;
  the simple algorithm reveals an error in his table of the coefficients. A
 n alternative and elegant procedure involves the inversion of Pascal matri
 ces of binomial coefficients.
LOCATION:Statistical Laboratory\, University of Cambridge
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