Source and Reference Materials

Aguiar, Marcelo, Nantel Bergeron, and Kathryn Nyman.  The peak algebra and the descent algebras of types B and D  (http://arxiv.org/abs/math/0302278, October 2004).

Berlinski, David.  The Advent of the Algorithm:  The Idea that Rules the World  (Harcourt, Inc., New York, 2000).

Edwards, A.W.F.  Pascal's Arithmetical Triangle:  The Story of a Mathematical Idea (The Johns Hopkins University Press, Baltimore, MD, 2002).  He cites:

[33] page 85 of Smith, D.E.  (1929).  A Source Book in Mathematics.  New York and London:  McGraw-Hill.

[34] page 97 of Bernoulli, James (1713).  Ars conjectandi.  Basilea.  Facsimile reprint:  Bruxelles:  Culture et Civilisation (1968).  Reprinted in Die Werke von Jakob Bernoulli, III, 107-286, Basel:  Birkhauser (1975).

Gleick, James.  Chaos:  Making a New Science (Penguin Books, New York, 1988).

Kaplan, Robert.  The Nothing That Is:  A Natural History of Zero (Oxford University Press, Oxford, 1999).

Peterson, Ivars.  Islands of Truth:  A Mathematical Mystery Cruise (W. H. Freeman and Company, New York, 1990).

Pengelley, David J.  The bridge between the continuous and the discrete via original sources in Study the Masters:  The Abel-Fauvel Conference, Kristiansand, 2002, (ed. Otto Bekken et al), National Center for Mathematics Education, University of Gothenburg, Sweden, in press.  See the paper.  He cites:

Boyer, C. (1943).  Pascal's formula for the sums of powers of the integers.  Scripta Mathematica, 9, 237-244.

Katz, V.  (1998).  A History of Mathematics, 2nd edition.  Reading, Mass:  Addison-Wesley.

Pascal, Blaise.  (1976).  Oeuvres.  Paris:  L. Brunschvieg (ed.) (1908-14); Vaduz, Liechtenstein:  Kraus Reprint.

Santayana, George.  The Sense of Beauty:  Being the Outlines of Aesthetic Theory (Charles Scribner's Sons, New York, 1936).

Singh, Simon.  Fermat's Enigma (Walker and Co., New York, 1997).

Wells, David.  The Penguin Dictionary of Curious and Interesting Numbers:  Revised Edition (Penguin Books, London, 1997).

Wittgenstein, Ludwig. Philosophical Investigations, ed. G.E.M. Anscombe and R. Rhees, tr. G.E.M. Anscombe, 2nd edn. (Blackwell, Oxford, 1958).

Zeilberger, Doron.   '"Real" Analysis is a Degenerate Case of Discrete Analysis'; written: Nov. 26, 2001; Appeared in "New Progress in Difference Equations", edited by Bernd Aulbach, Saber Elaydi, and Gerry Ladas, (Proc. ICDEA 2001), Bernd Aulbach, ed., Taylor and Frances, London.

Web Links

Eric Weisstein's World of Mathematics -- Definitions, explanations and illustrations on a site supported by Wolfram Research

Pascal's Traité du triangle arithmétique, 1654  --  images from the 1654 publication thanks to the Cambridge University Library, UK.

Sloane's On-Line Encyclopedia of Integer Sequences -- "Most people use this web site to get information about a particular number sequence. If you are a new visitor, then you might ask the database if it can recognize your favorite sequence, if you have one." "Since the mid-1960's Neil Sloane has been collecting integer sequences from every possible source. His goal is to have all interesting number sequences in the table. At the present time the table contains over 80000 sequences." [Quoted from the website.]

Photographs

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