User doug chatham - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T08:14:41Z http://mathoverflow.net/feeds/user/5883 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/71990/zermelos-stone-game-in-3-dimensional-space/71992#71992 Answer by Doug Chatham for Zermelo's stone game in 3 dimensional space Doug Chatham 2011-08-03T12:53:33Z 2011-08-03T12:53:33Z <p>By a strategy-stealing argument, the three-dimensional game is a win for the first player. (If the most northeast-rearward cell isn't a winning first move, the second player must have a winning response A(i,j,k). But then A(i,j,k) would be a winning move for the first player also.) See <a href="http://www.win.tue.nl/~aeb/games/chomp.html" rel="nofollow">http://www.win.tue.nl/~aeb/games/chomp.html</a> for more information.</p> http://mathoverflow.net/questions/33510/christening-fermats-little-theorem/33518#33518 Answer by Doug Chatham for Christening Fermat's Little Theorem Doug Chatham 2010-07-27T14:26:32Z 2010-07-27T14:26:32Z <p>The MathWorld entry for <a href="http://mathworld.wolfram.com/FermatsLittleTheorem.html" rel="nofollow">Fermat's Little Theorem</a> claims "Fermat's simple theorem" has been used as an alternate name. Also the entry for <a href="http://mathworld.wolfram.com/FermatsCongruence.html" rel="nofollow">Fermat's Congruence</a> consists of a link to the Fermat's Little Theorem page.</p> http://mathoverflow.net/questions/31476/the-worst-possible-winner/31489#31489 Answer by Doug Chatham for The Worst Possible Winner Doug Chatham 2010-07-12T01:12:20Z 2010-07-12T09:39:36Z <p>With the "right" scoring function, it is possible that $best(\alpha_{i}) = p-1$: Suppose our winner is next-to-last in every race, that each of the other racers is last in at least one race, and the scoring function awards $100^{p}-k+1$ (or some other large enough number) points for position $k=1,\ldots, p-1$ and $0$ points for position $p$. (EDIT: Also suppose $n \geq p-1$.) The scoring function gives roughly equal awards to the racers who don't come in last and severely penalizes a racer who comes in last. Our consistently next-to-last racer is the overall winner since he or she is the only one who never comes in last. </p> http://mathoverflow.net/questions/1270/alternatives-to-pi-day/31322#31322 Answer by Doug Chatham for Alternatives to pi day Doug Chatham 2010-07-10T19:08:46Z 2010-07-10T19:08:46Z <p>How about <a href="http://mathaware.org/about.mam.html" rel="nofollow">Mathematics Awareness Month</a>?</p> http://mathoverflow.net/questions/31153/problem-suggestions-for-polymath-for-undergraduates-research/31169#31169 Answer by Doug Chatham for Problem suggestions for polymath for undergraduates research Doug Chatham 2010-07-09T10:05:28Z 2010-07-09T10:05:28Z <p>Consider this generalization of the $N$-queens problem:</p> <blockquote> <p><strong>The $N + k$ Queens Problem</strong>: Let $N > 0$ and $k \geq 0$ be integers. On an $N \times N$ chessboard, can you place $N + k$ queens and $k$ pawns so that any two queens on the same row, column, or diagonal have at least one pawn between them?</p> </blockquote> <p>We've had many math and computer science undergraduates working on projects related to this problem. For more information, please see the $N + k$ Queens Problem Page at <a href="http://npluskqueens.info" rel="nofollow">http://npluskqueens.info</a> .</p> http://mathoverflow.net/questions/31072/colourings-of-graphs-with-extra-conditions/31139#31139 Answer by Doug Chatham for Colourings of Graphs with extra conditions Doug Chatham 2010-07-09T01:43:24Z 2010-07-09T01:43:24Z <p>Qiaochu Yuan commented that your problem is equivalent to coloring what is known as the <strong>square</strong> $G^{2}$ of the graph $G$. For more details on coloring the square of a graph, see "The chromatic number of graph powers", N. Alon and B. Mohar, Combinatorics, Probability and Computing (1993) 11, 1-10. On-line at <a href="http://www.math.tau.ac.il/~nogaa/PDFS/am8.pdf" rel="nofollow">http://www.math.tau.ac.il/~nogaa/PDFS/am8.pdf</a> </p> http://mathoverflow.net/questions/30330/is-there-a-good-argument-for-why-you-cant-place-4-queens-which-cover-a-chessboar/30354#30354 Answer by Doug Chatham for Is there a good argument for why you can't place 4 queens which cover a chessboard? Doug Chatham 2010-07-02T21:30:08Z 2010-07-02T21:30:08Z <p>The problem of finding the minimum number of queens needed to cover an n-by-n board is the queens domination problem. According to <a href="http://ajc.maths.uq.edu.au/pdf/15/ocr-ajc-v15-p145.pdf" rel="nofollow">http://ajc.maths.uq.edu.au/pdf/15/ocr-ajc-v15-p145.pdf</a> , "Although there is currently no mathematical proof that these values [the known minimum numbers of queens] are correct, they have been verified by computer."</p> <p>According to <a href="http://www.combinatorics.org/Volume_8/PDF/v8i1r29.pdf" rel="nofollow">http://www.combinatorics.org/Volume_8/PDF/v8i1r29.pdf</a> , "...current knowledge that [among other things, the queens domination number for an 8-by-8 board is greater than 4], comes from exhaustive search." </p> http://mathoverflow.net/questions/29602/a-game-on-a-finite-projective-plane/29610#29610 Answer by Doug Chatham for A Game on a Finite Projective Plane Doug Chatham 2010-06-26T13:28:24Z 2010-06-26T13:28:24Z <p>See "Tic-Tac-Toe on a Finite Plane", Maureen T. Carroll and Steven T. Dougherty, Mathematics Magazine, Vol. 77, No. 4 (Oct., 2004), pp. 260-274. (Preprint here: <a href="http://academic.scranton.edu/faculty/carrollm1/tictac.pdf" rel="nofollow">http://academic.scranton.edu/faculty/carrollm1/tictac.pdf</a>) The second player can force a draw on the 3-by-3 and 4-by-4 projective planes.</p> http://mathoverflow.net/questions/28423/ways-to-regularize-a-graph/28461#28461 Answer by Doug Chatham for Ways to "regularize" a graph Doug Chatham 2010-06-17T04:39:21Z 2010-06-17T10:00:42Z <p>You may find the following article useful: The Minimal Regular Graph Containing a Given Graph, by ErdÅ‘s and Kelly, available at <a href="http://www.math-inst.hu/~p_erdos/1967-26.pdf" rel="nofollow">http://www.math-inst.hu/~p_erdos/1967-26.pdf</a></p> http://mathoverflow.net/questions/28010/boxplot-iqr-and-confidence-interval/28046#28046 Answer by Doug Chatham for Boxplot IQR and confidence interval Doug Chatham 2010-06-13T17:20:54Z 2010-06-13T17:20:54Z <p>First, the interquartile range (IQR) is the difference between the third and first quartiles, which is a single number, not an interval.</p> <p>The interval $(Q_{1},Q_{3})$ might be considered <em>a</em> 50% confidence interval, but it's not a 50% confidence interval for the mean that you'd get from any of the usual formulas. </p> http://mathoverflow.net/questions/94742/examples-of-interesting-false-proofs/94744#94744 Comment by Doug Chatham Doug Chatham 2012-04-22T21:24:15Z 2012-04-22T21:24:15Z For more examples and analysis of these &quot;weird fractions&quot;, see A Pumping Lemma for Invalid Reductions of Fractions, Michael N. Fried and Mayer Goldberg, The College Mathematics Journal, Vol. 41, No. 5 (November 2010), pp. 357-364. http://mathoverflow.net/questions/90246/theorems-equivalent-to-the-parallel-postulate Comment by Doug Chatham Doug Chatham 2012-03-09T11:33:13Z 2012-03-09T11:33:13Z Here's a list of 26 with a reference to the source of the list: <a href="http://www.ics.uci.edu/~eppstein/junkyard/parallel-postulate.html" rel="nofollow">ics.uci.edu/~eppstein/junkyard/&hellip;</a> http://mathoverflow.net/questions/78149/what-is-this-subclass-of-k-colorable-graphs-called Comment by Doug Chatham Doug Chatham 2011-10-16T12:30:16Z 2011-10-16T12:30:16Z This reminds me of the m-pire (or empire) problem (see <a href="http://mathworld.wolfram.com/EmpireProblem.html" rel="nofollow">mathworld.wolfram.com/EmpireProblem.html</a> or Coloring Ordinary Maps, Maps of Empires, and Maps of the Moon, Joan P. Hutchinson, <i>Mathematics Magazine</i>, Vol. 66, No. 4 (Oct., 1993), pp. 211-226): you want to color a map where some of the countries consist of disjoint regions, but each country must be assigned a single color. An &quot;m-pire&quot; is a country consisting of m disjoint regions. So we could call the $P_{k}$ property &quot;k-colorable with one 2-pire&quot;. http://mathoverflow.net/questions/72691/can-we-axiomatize-omnific-integers-without-the-surreal-number-system Comment by Doug Chatham Doug Chatham 2011-08-14T19:36:24Z 2011-08-14T19:36:24Z Yes, $t \omega$ is an omnific integer for all real $t$. http://mathoverflow.net/questions/72691/can-we-axiomatize-omnific-integers-without-the-surreal-number-system Comment by Doug Chatham Doug Chatham 2011-08-12T16:22:08Z 2011-08-12T16:22:08Z @Qiaochu: According to p. 45 of Conway's On Numbers and Games (2nd edition, ISBN 1-56881-127-6), a surreal number x is an omnific integer if x = {x-1|x+1}. http://mathoverflow.net/questions/47738/what-is-the-name-fora2-b2-c2-a-b-c Comment by Doug Chatham Doug Chatham 2010-11-30T00:33:32Z 2010-11-30T00:33:32Z Do you like &quot;contraharmonic mean&quot; better? See <a href="http://en.wikipedia.org/wiki/Contraharmonic_mean" rel="nofollow">en.wikipedia.org/wiki/Contraharmonic_mean</a> for details and references. http://mathoverflow.net/questions/36272/when-is-arctan-a-rational-multiple-of-pi Comment by Doug Chatham Doug Chatham 2010-08-22T20:18:48Z 2010-08-22T20:18:48Z A reference of possible interest, even though it only deals with the case where $x$ is rational: <a href="http://www.ma.utexas.edu/users/jack/gausspi.pdf" rel="nofollow">ma.utexas.edu/users/jack/gausspi.pdf</a> http://mathoverflow.net/questions/35949/how-can-i-prove-this-general-equations Comment by Doug Chatham Doug Chatham 2010-08-18T11:21:00Z 2010-08-18T11:21:00Z This is not a research-level math question and is therefore inappropriate for this site. Read the faq at <a href="http://mathoverflow.net/faq" rel="nofollow">mathoverflow.net/faq</a> . http://mathoverflow.net/questions/35947/is-there-any-solution-to-the-diophantine-equation-l-xmu-ynv-zt Comment by Doug Chatham Doug Chatham 2010-08-18T11:15:36Z 2010-08-18T11:15:36Z Each of your equations is missing an =. http://mathoverflow.net/questions/35600/what-are-your-favorite-puzzles-toys-for-introducing-new-mathematical-concepts-to/35609#35609 Comment by Doug Chatham Doug Chatham 2010-08-15T00:57:49Z 2010-08-15T00:57:49Z It seems to have been used to teach set theory: <a href="http://www.setgame.com/set/set_theory.htm" rel="nofollow">setgame.com/set/set_theory.htm</a> . Also see <a href="http://www.setgame.com/set/mathtricks.htm" rel="nofollow">setgame.com/set/mathtricks.htm</a> for other discussion of SET-related mathematics. http://mathoverflow.net/questions/34325/how-do-i-create-a-new-field Comment by Doug Chatham Doug Chatham 2010-08-08T23:33:43Z 2010-08-08T23:33:43Z Of possible interest to those wanting to &quot;combine&quot; mathematics and language study: <a href="http://www.metacarta.com/Collateral/Documents/English-US/Mathematical-linguistics-Kornai.pdf" rel="nofollow">metacarta.com/Collateral/Documents/English-US/&hellip;</a> http://mathoverflow.net/questions/30759/in-a-graph-is-it-always-possible-to-construct-a-set-of-cycle-bases-with-each-an Comment by Doug Chatham Doug Chatham 2010-08-03T11:48:48Z 2010-08-03T11:48:48Z Mac Lane's paper is also available online: <a href="http://matwbn.icm.edu.pl/ksiazki/fm/fm28/fm2814.pdf" rel="nofollow">matwbn.icm.edu.pl/ksiazki/fm/fm28/fm2814.pdf</a> http://mathoverflow.net/questions/30759/in-a-graph-is-it-always-possible-to-construct-a-set-of-cycle-bases-with-each-an Comment by Doug Chatham Doug Chatham 2010-08-02T15:07:30Z 2010-08-02T15:07:30Z Additional reference. Available online and shorter than the Mac Lane paper: <a href="http://www.ams.org/journals/proc/1973-037-02/S0002-9939-1973-0313098-X/S0002-9939-1973-0313098-X.pdf" rel="nofollow">ams.org/journals/proc/1973-037-02/&hellip;</a> http://mathoverflow.net/questions/34126/good-name-for-a-future-of-math-blog Comment by Doug Chatham Doug Chatham 2010-08-01T17:33:20Z 2010-08-01T17:33:20Z Try <a href="http://www.reddit.com/r/math" rel="nofollow">reddit.com/r/math</a> as an alternate forum to pose this type of question. http://mathoverflow.net/questions/33898/help-with-a-monte-carlo-question/33902#33902 Comment by Doug Chatham Doug Chatham 2010-07-30T16:18:09Z 2010-07-30T16:18:09Z @Eric Tressler, the problem could be a probabilistic primality test like <a href="http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test" rel="nofollow">en.wikipedia.org/wiki/&hellip;</a>