This site is dedicated to mathematical, historical and algorithmic aspects of some classical mathematical constants (like p, e, the Euler constant g, z(3), Â¼). A few results on prime numbers are added. Easy and fast programs are also included and can be downloaded.

<http://numbers.computation.free.fr/Constants/Miscellaneous/seriesacceleration.html>

Mathematics Doctor Matt

Matthew M. Conroy

<http://www.madandmoonly.com/doctormatt/mathematics/mathematics.htm>

PROJETS - PROJECTS

NumbersWithNames

Simon Colton

NumbersWithNames is a program for exploring some of the sequences in the Encylopedia of Integer Sequences

<http://www.machine-creativity.com/programs/nwn/>

PROBLÈMES - PROBLEMS

Goodstein Sequence

Starting this procedure at an integer n gives the Goodstein sequence {G_k(n)}. Amazingly, despite the apparent rapid increase in the terms of the sequence, Goodstein's theorem states that G_k(n) is 0 for any n and any sufficiently large k.

<http://mathworld.wolfram.com/GoodsteinSequence.html>

Friedman numbers

Problem of the Month (August 2000), Math Magic

<http://www.stetson.edu/~efriedma/mathmagic/0800.html>

EXEMPLES - EXAMPLES

An Interesting Family of Iterated Sequences

Dr. Paul A. Loomis homepage

<http://facstaff.bloomu.edu/ploomis/sequences.html>

Suites numÃ©riques

Jean-Paul Davalan

<http://perso.wanadoo.fr/jean-paul.davalan/mots/suites/index.html>

JAVA

Applets Java Edugraphe

JoÃ«l Amblard

Toutes ces applets ont Ã©tÃ© rÃ©alisÃ©es automatiquement avec le grapheur Edugraphe

Edugraphe est un grapheur disponible gratuitement pour tous les systÃ¨mes (macosx, linux, windows ...) et distribuÃ© sous licence GPL. Convivial et simple d'utilisation, il est particuliÃ¨rement adaptÃ© aux programmes de mathÃ©matiques du secondaire et permet de crÃ©er des applets java directement exploitables en cours.

<http://perso.wanadoo.fr/joel.amblard/applets/index.html>

JAVASCRIPT

Suites numÃ©riques linÃ©aires Ã coefficients constants

Jean-Paul Davalan

Suites de Fibonacci, de Lucas, de Perrin, de Padovan. Nombre d'or, nombre plastique.

<http://perso.wanadoo.fr/jean-paul.davalan/mots/suites/edf/index.html>

Suites de Somos

Jean-Paul Davalan

<http://perso.wanadoo.fr/jean-paul.davalan/mots/suites/somos/index.html>

THÈSES - THESIS

Topics in the theory of uniqueness of trigonometrical series

Field medalist Paul J. Cohen's 1958 Ph.D. thesis

This work was previously only available at the University of Chicago library. Though Paul Cohen is best known for his groundbreaking work in set theory, he also had many important contributions in harmonic analysis starting with his thesis which is still relevant to current research in this area. I have included a brief summary and bibliography of subsequent work in this area

edited by Ilan Vardi

<http://www.lix.polytechnique.fr/Labo/Ilan.Vardi/cohen.ps>

Suites rÃ©currentes linÂ´eaires et sÃ©ries formelles en plusieurs variables

Abdelkader Necer Limoges 1998

<http://www.unilim.fr/laco/theses/1998/T1998_05.pdf>

SUJETS - SUBJECTS

Du Triangle de Pascal aux SÂ´eries Formelles

Farouk Boucekkine CultureMATHAccompagnement et Culture MathÃ©matiques

<http://www.dma.ens.fr/culturemath/maths/pdf/combi/seriesFormelles.pdf>

DOCUMENTS - PAPERS

SÃ©ries hypergÃ©omÃ©triques: de Soeur Celine Ã Zeilberger et Petkovsek

par Denis Monasse, LycÃ©e Louis le Grand, Paris 13 mai 1999

(NDLR Cet article de 22 pages en franÃ§ais vous permet d'aborder bien plus facilement la lecture du livre A=B ci-dessous qui est en anglais et qui a 222 pages)

<http://denis.monasse.free.fr/denis/articles/celine.pdf>

Home Page for the Book "A=B"

by Marko Petkovsek, Herbert Wilf and Doron Zeilberger with a Foreword by Donald E. Knuth

"A=B" is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. The book describes a number of algorithms for doing these tasks, and we intend to maintain the latest versions of the programs that carry out these algorithms on this page. So be sure to consult this page from time to time, and help yourself to the latest versions of the programs.

<http://www.math.upenn.edu/~wilf/AeqB.html>

Une mÃ©thode pour obtenir la fonction gÃ©nÃ©ratrice algÃ©brique d'une sÃ©rie.

Simon Plouffe LACIM UniversitÃ© du QuÃ©bec Ã MontrÃ©al Mars 1993

Approximations de sÃ©ries gÃ©nÃ©ratrices et quelques conjectures

<http://lacim.uqam.ca/~plouffe/articles/FlorencealgebraicLLL.pdf>

Hakmem -- Continued Fractions

Beeler, M., Gosper, R.W., and Schroeppel, R. HAKMEM. MIT AI Memo 239, Feb. 29, 1972. Retyped and converted to html ('Web browser format) by Henry Baker, April, 1995.

<http://www.inwap.com/pdp10/hbaker/hakmem/cf.html>

On the periods of generalized Fibonacci recurrences

R. P. Brent

We give a simple condition for a linear recurrence (mod 2w) of degree r to have the maximal possible period 2w-1(2r-1). It follows that the period is maximal in the cases of interest for pseudo-random number generation, i.e. for 3-term linear recurrences defined by trinomials which are primitive (mod 2) and of degree r > 2. We consider the enumeration of certain exceptional polynomials which do not give maximal period, and list all such polynomials of degree less than 15.

<http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub133.html>

Toby Walsh

SFI Research Professor Cork Constraint Computation Centre University Ireland

Automatic Invention of Integer Sequences idem

<http://4c.ucc.ie/~tw/>

TUTORIELS - TUTORIALS - TUTORS

Cours Heuristique 97

Gilles HUNAULT

<http://www.info.univ-angers.fr/pub/gh/cours_gH/euris.html>

Probability and Statistics

<http://www.seanet.com/~ksbrown/iprobabi.htm>

Sequences Realized by Oligomorphic Permutation Groups

Peter J. Cameron

<http://www.research.att.com/~njas/sequences/JIS/VOL3/groups.html>

BIOGRAPHIES

Why Delannoy Numbers?

Cyril Banderier and Sylviane Schwer

<http://www-lipn.univ-paris13.fr/~banderier/Papers/delannoy2004.ps>

ARTS

Per NÃ¸rgÃ¥rd

By JÃ¸rgen Mortensen

Per NÃ¸rgÃ¥rd discovered his infinity series in 1959, and throughout the years it has had a tremendous influence on his compositions.

<http://www.pernoergaard.dk/eng/strukturer/uendelig/uintro.html>

LIENS - LINKS

<liens_math.html>

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Copyright © 1999-2012 Jean-Paul Davalan - Reproduction interdite.

Suites - SÃ©ries - Sequences

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JAVA

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