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[math-fun] Spam-blocking, Bayesian methods
by Guy Haworth 18 Sep '03

18 Sep '03

I would appreciate a pointer to a readily accessible article or three on how Bayesian methods can be used to block Spam. Pointers to any products implementing these methods also welcomed. Guy

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Re: [math-fun] non-square products of squares?
by asimovd＠aol.com 18 Sep '03

18 Sep '03

Marc asks: << Let some set be closed under an associative multiplication operator. If it commutes then the product of distinct squares is also square: aabb = abab. Contrarily, can you construct a non-commuting system where this is usually false? >> The simplest example I can imagine is the set of all finite strings of a's and b's with the operation of concatenation, aka the free semigroup on 2 generators. --Dan.

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[math-fun] TUP's and TOP's
by Jon Perry 18 Sep '03

18 Sep '03

New paper @; http://www.users.globalnet.co.uk/~perry/maths/threadedpartitions/threadedpar titions.htm Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] Total Harmony?
by Guy Haworth 15 Sep '03

15 Sep '03

Does the hairy-ball theorem prove that total harmony in the world is impossible - or is it rendered possible by the existence of areas of sea? Guy Haworth

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[math-fun] stalking the wild quaternary game, or misere .3102 with a bounty
by Thane Plambeck 15 Sep '03

15 Sep '03

I'll pay US $200 for a complete analysis of the following impartial game, which (for lack of a better term), I'll call the WILD QUATERNARY GAME. The game is played with a number of heaps of beans of various sizes. There are two players. They take turns making legal moves. The person who makes the last legal move *loses* the game. There are three types of legal moves. Each type of move involves selecting one particular heap, and then removing 1, 2 or 4 beans from that heap, subject to the following additional conditions: 1) A single bean can be removed from any heap, no matter how many beans are in it. 2) Two beans can be removed only if the heap contains exactly two beans. 3) Four beans can be removed from a heap, but only if the heap contains more than 4 beans. In the Winning Ways "octal code" notation, this is the misere game .3102. By a "complete analysis", I mean an explicit mathematical description of the first- or second-player winning positions of the game for arbitrarily-many arbitrarily-sized heaps (ie, 'algorithmic'' solutions that boil down to a recursive search of a game tree don't cut it). For example, if I had changed the problem statement so that the last player to make a legal move *wins* the game, a complete description of the second-player winning positions is All positions with a) An even number of heaps of size (5k+1 or 5k+4) AND b) An even number of heaps of size (5k+2). Thane Plambeck thane(a)best.com 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/ehome.htm

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[math-fun] BSD
by Jon Perry 12 Sep '03

12 Sep '03

With the Birch-Swinnerton-Dyer conjecture, has anyone ever taken the logarithmic derivative of the Euler product in question wrt to the Euler product, and followed this line of argument through into the Taylor series? Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] n is prime iff
by Jon Perry 11 Sep '03

11 Sep '03

[1+sum(i=1,n-1,sigma(i)*part(n-i)}]/part(n-1) = n where part(k) is the k-th partition number. (see http://www.users.globalnet.co.uk/~perry/maths/morepartitionfunction/morepart itionfunction.htm for derivation; { parts=makePartitions(40); partSigma=vector(40); partSigma[1]=1; for (i=2,40,partSigma[i]=i*parts[i]-sum(j=1,i-1,parts[j]*partSigma[i-j])); partSigma } towards the end. Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] New books on experimental math
by David H Bailey 11 Sep '03

11 Sep '03

As some of you are aware, Jon Borwein of Canada, myself and Roland Girgensohn of Germany(for vol 2) are co-authoring a two-volume work on experimental math. This is now complete, and should be out on the street in two or three months. In the meantime, we are pleased to announce that a "Reader's Digest" version is freely available on the Web, at the URL: http://www.expmath.info/expbook-C.pdf This is about 70 pages long, and includes excerpts from three chapters of the first volume, and three from the second. It gives a good taste of what the two books are about. In general, you may also be interested in the website http://www.expmath.info, where the condensed book is located, which was set up specifically to support our book. It includes numerous links to interesting and useful math websites. Cheers, David H Bailey david(a)dhbailey.com or dhbailey(a)lbl.gov

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[math-fun] more 51 star designs
by Richard Schroeppel 11 Sep '03

11 Sep '03

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Rich rcs(a)cs.arizona.edu

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Antwort: [math-fun] World Flag
by dirk.lattermann＠bgs-ag.de 11 Sep '03

11 Sep '03

The premise of this question is void: If there were total harmony in the world, no flag would be needed, or at least, its appearance would not matter. Greetings, Dirk Lattermann "Jon Perry" <perry(a)globalnet.co.uk>@mailman.xmission.com am 11.09.2003 14:17:48 Bitte antworten an math-fun <math-fun(a)mailman.xmission.com> Gesendet von: math-fun-bounces(a)mailman.xmission.com An: "Maths is Fun" <math-fun(a)mailman.xmission.com> Kopie: Thema: [math-fun] World Flag With all this flag talk, let's imagine total harmony in the world, and a world flag is needed. What would it look like? Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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