May 2013 - mathfun@mailman.xmission.com

[math-fun] Fwd: [SIGMAA-HOM] Dover Republishes Moore on Zermelo
by Thane Plambeck 10 May '13

10 May '13

I'm forwarding this representative message from the SIGMAA History of Mathematics (HOM) email list in case people on math-fun haven't heard of it and are interested in joining it. I don't have anything to do with it beyond being a subscriber, but I enjoy its traffic. Thane ---------- Forwarded message ---------- From: Drucker, Thomas L. <druckert(a)uww.edu> Date: Fri, May 10, 2013 at 6:45 AM Subject: [SIGMAA-HOM] Dover Republishes Moore on Zermelo To: "sigmaa-hom(a)lists.maa.org" <sigmaa-hom(a)lists.maa.org> When I was a teenager, I bought all sorts of books on mathematics published by Dover, knowing that they weren’t hot off the press but appreciative of their making classics available. By now I’m seeing Dover publishing books that I did buy hot off the press, and I hope that a younger generation of teachers and students can take advantage of them. What brings this to mind is Dover’s having republished Gregory H. Moore’s ‘Zermelo’s Axiom of Choice’, originally published by Springer in 1982. It is one of the most impressive and important works in the history of logic with which I’m familiar, and it still sets a high standard for scholarship in the broader history of mathematics. Those historians who don’t have a copy of Moore’s book now have one fewer excuse. **** Thomas Drucker**** University of Wisconsin—Whitewater**** druckert(a)uww.edu**** ** ** You received this message as a subscriber to sigmaa-hom, the discussion list of the MAA Special Interest Group on the History of Mathematics. To unsubscribe, send an email consisting of the single line SIGNOFF sigmaa-hom to sympa(a)lists.maa.org. You can also choose to change your subscription mode to digest, among other options. To manage your subscription to the list, you can establish a login to the web interface at http://lists.maa.org/wws, or obtain a list of email commands available by sending an email consisting of the single line HELP to sympa(a)lists.maa.org. -- Thane Plambeck tplambeck(a)gmail.com http://counterwave.com/

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[math-fun] Extremal graph problem: avoid 5-cycles
by Allan Wechsler 10 May '13

10 May '13

While I wait for my approval from Seqfans (why did it take me so long to subscribe? I think it's because I was getting OEIS editor mail, and wrongly assumed it was the same thing) here's a sequence for which I would love to know the next couple of entries. What is the largest number of edges possessed by a graph that lacks 5-cycles? These graphs are, as usual, forbidden from having self-loops or multiple edges. A(1 .. 4) = 0, 1, 3, 6. I am pretty sure that A(5) = 7; in other words, you can't do better than K4 plus a whisker. If A(6) is anything bigger than 9 I will be extremely surprised. There are only seven sequences in OEIS matching 0, 1, 3, 6, 7, 9. I know that A(7) >= 12, and only three of the seven sequences satisfy that constraint. All the sequences except A047242 (0, 1, or 3 mod 6) are eliminated by the fact that A(1+3n) >= 6n; this number of vertices is achieved by n copies of K4 sharing one vertex. And finally, A(18) >= 36, which rules out A047242. My example here is a necklace of 6 copies of K4, arranged in a 6-cycle, each sharing one vertex with the next. So I am reasonably sure this sequence is missing from OEIS, but would like some confirmation from other funsters.

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Re: [math-fun] Hilbert(Hilbert)
by Henry Baker 09 May '13

09 May '13

Very cool! Do you have this plot in a vector graphics format -- e.g., ".svg" ? At 11:48 PM 5/8/2013, Bill Gosper wrote: >Tonight, after a couple of weeks of work, Neil produced >http://gosper.org/hilbert.png . >This is *way* harder that Peano(Peano) or Gosper(Gosper). >--rwg

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Re: [math-fun] z^n = 1 for Gaussian integer n
by Henry Baker 09 May '13

09 May '13

The map of Gaussian integers in the complex plane has symmetries around the x & y axes and the x=+-y lines. If you take the square root, you get 2 copies, but unrolled (about the origin). If you take the cube root, you get 3 copies, with hexagon & other symmetries. Yes, each point in the original map maps to n points in the root(n,x) map. Etc. At 11:25 PM 5/8/2013, Kerry Mitchell wrote: >Hi all, > >I am playing with a problem that has boiled down to this: for positive >integer n, there are n complex roots of 1 (or any complex number). What >happens when n is a Gaussian integer? How many roots are there and what >are they like? > >I've done some preliminary work on this; can someone point me to a >reference so I can see if I'm on the right track? > >Thanks, >Kerry

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[math-fun] quantum computers "1000s of times faster"?
by Warren D Smith 09 May '13

09 May '13

I wonder what this meant? It is very mysterious: https://www.amherst.edu/aboutamherst/news/faculty/node/466477 I failed to find any actual paper this was based on, but she gave a lecture, and here is the advert for the lecture: ========= I will describe experiments to evaluate the performance of a quantum computing system (hardware plus software) for solving NP-hard combinatorial optimization problems. This unusual computing platform is manufactured by D-Wave Systems of Burnaby, Canada. It comprises a Linux front end with an analog hardware chip that contains up to 512 quantum bits (qubits) capable of quantum superposition. The hardware chip solves optimization problems by a process known as quantum annealing (QA), based on the principles of adiabatic quantum computation (AQC). Performance comparisons included three conventional solvers-- IBM CPLEX, an open-source implementation of Tabu Search and a branch-and-bound solver that performed well in a recent satisfiability competition. The solvers were tested using instances from three NP-hard optimization problems: Quadratic Unconstrained Boolean Optimization (QUBO), Weighted Max 2-SAT (W2SAT) and the Quadratic Assignment Problem (QAP). On general problems, the hybrid software/quantum hardware solver was competitive with, and sometimes outperformed, the conventional solvers. On "native" instances that can be solved directly in hardware, the quantum system found optimal solutions 3,000 times faster than CPLEX. (Recent tests on a newer chip suggest that speedup factors of 10,000 or more are possible.) I will also describe some tests to learn how performance of the quantum hardware depends on input properties. This is joint work with Cong Wang of Simon Fraser University. --end. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] "Ponder This"
by Bill Gosper 09 May '13

09 May '13

Keith F. Lynch: "I've heard good things about Mathematica. Too bad it's so expensive. I've been doing everything in C. I'm curious whether Mathematica is reasonably fast." HansH>I think Mathematica is a wonderful toy for the recreationalist (especially, with ready-made "black box" procedures for all manner of mathematical situations. For example, if I wanted to duplicate Bill Gosper's "representions of 31415 as sums of four squares" I'd use something like PowersRepresentations[31415,4,2]] and it might even be somewhat faster than his from-scratch procedure but, in general, I'll guess (based on C programmers trouncing my Mathematica-produced output in the past) that you can do things faster in C. ------- Yow! In[36]:= tim[Length[PowersRepresentations[31415, 4, 2]]] During evaluation of In[36]:= 1.875057 Out[36]= 829 Anybody feel like speedbumming this in C? --rwg

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Re: [math-fun] "Ponder This"
by Bill Gosper 07 May '13

07 May '13

Fred lunnon: Magma running on iMac core-i7 is 10x faster.. q := 31415; time squsq := foursquares(q); Time: 0.170 #squsq; 829 HansH>Since Bill Gosper was using his own timing function (as opposed to one of Mathematica's built-in timing functions), I guess it needs to be asked: Is your time absolute or CPU-time only? ----------- My timer is absolute: SetAttributes[tim, HoldAll]; tim[xp_] := ReleaseHold[(Print[#1]; If[#1 > 69, Speak[#1]]; #2) & @@ AbsoluteTiming[xp]] Retrying, In[37]:= tim[Length[PowersRepresentations[31415, 4, 2]]] During evaluation of In[37]:= 0.000200 Out[37]= 829 Harrumph. In[38]:= ClearSystemCache[]; tim[Length[PowersRepresentations[31415, 4, 2]]] During evaluation of In[38]:= 0.000229 Out[38]= 829 Harrumph. Did someone say "memoizing"? Switching to system timing in 9.0.0 In[34]:= Timing[Length[PowersRepresentations[3, 4, 2]]] Out[34]= {0.019141, 1} In[35]:= Timing[Length[PowersRepresentations[31415, 4, 2]]] Out[35]= {1.698000, 829} --rwg

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Re: [math-fun] "Ponder This"
by Dave Dyer 07 May '13

07 May '13

> >Magma running on iMac core-i7 is 10x faster Magma running through an imac? Sounds dangerously hot.

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Re: [math-fun] "Ponder This"
by Dave Dyer 07 May '13

07 May '13

> >Magma running on iMac core-i7 is 10x faster Magma running through an imac? Sounds dangerously hot.

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[math-fun] More details about recreational math conference
by James Propp 07 May '13

07 May '13

MoMath, the National Museum of Mathematics, invites you to register for the first MOVES (Mathematics of Various Entertaining Subjects) Conference in New York City this August 4-6, immediately following MAA MathFest on July 31-Aug 3. There are trains from Hartford to New York City that can help move you from MathFest to MOVES! Registration and more information for MOVES is available online at http://moves.momath.org . The MOVES registration deadline is June 1 or until the conference reaches capacity. Registration for MathFest is at www.maa.org/mathfest/reginfo.html and is open through May 10. We have a very exciting list of speakers for MOVES this year, with over 40 research talks on recreational mathematics and the mathematics of games and puzzles and over 20 family activities, including: KEYNOTE ADDRESSES BY Erik Demaine, Massachusetts Institute of Technology: *Geometric puzzles: Algorithms and complexity* Noam Elkies, Harvard University: *The Numberplay arithmetic progression challenge* FEATURED TALKS BY Jennifer Beineke, Western New England University and Lowell Beineke, Indiana University, Purdue University Fort Wayne: *Some of the A-B-Cs (and Ds) of graphs and games* David Richeson, Dickinson College: *Making the impossible possible: how to trisect an angle* Jason Rosenhouse, James Madison University: *Non-classical knights and knaves* Henry Segerman, Oklahoma State University: *Puzzling the 120-cell* Bruce Torrence,Randolph-Macon College: *Lights Out for gamers and mathematicians* Jade Vinson, Renaissance Technologies: *Shapes of space: The challenge of negative curvature* FEATURED EVENING ENTERTAINMENT BY: Tim and Tanya Chartier: *Mime-matics* Colm Mulcahy: *Mathematics, magic, and mystery with a deck of cards* Greg Warrington: *Mathematical juggling* Also: the day after the conference ends, Terry Tao will be speaking at MoMath. MoMath expects his talk to fill quickly, and it will be open only to MOVES attendees at first. Jim Propp

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