http://yomcat.geek.nz/lifetype/index.php?blogId=1 Michael Welsh, the runner of Michael's Blog. Michael Welsh is also known as yomcat, and has a beautiful wifey called Melissa. Michael Welsh will talk about random stuff in Michael's blog. Stuff like advanced mathematics and pretty beads. If it doesn't offend people, it's not worth saying. yomcat 2010-09-06T21:29:41Z http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1302&blogId=1 So, tonight at CU (which was much better than last week, by the way) we were discussing the fact that every subject is really just applied maths.<br/>Sure, there are the obvious ones, like Physics, but what about History? This is where we bring in the magic of <a href="http://xkcd.com/435/">xkcd</a>. So, anything that can be reduced to Sociology (that's Social Studies in school terms) is basically applied maths.<br /> I might make a pretty poset, but I can't be bothered. A big list of subjects would be a good start.<br /><br /> What I need are subjects that can't be reduced to maths via a partial order of "applied". For example, pedophilia is just applied Biology, which is applied Chemistry, which is applied Physics, which is applied Maths.<br /> Other things that go straight to Maths are Music, Computer Science, Linguistics and Statistics. Maths 2010-03-25T20:55:44Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1300&blogId=1 On Wednesday, I am giving a talk, nominally about what I got up to all summer. This talk is currently unnamed, but it could do with a name. Vote.<br/><ul> <li>Quantum Gravity</li> <li>Parastrophic Quasigroups: A Kindergarten View</li> <li>Matroids Hate Me</li> <li>Computer Science In Disguise</li> <li>Partitions: A Czech View</li> </ul> <p>Alternatively, you could suggest other possible titles. And you can't come, and no notes will be posted on the <a href="http://yomcat.geek.nz/maths/">Internet</a>.</p> Maths 2010-03-13T18:01:34Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1296&blogId=1 As part of my research, I have needed to understand the quadrangle criterion, in relation to quasigroup multiplication tables and latin squares. I have <a href="http://yomcat.geek.nz/maths/quadrangle.pdf">a proof</a> of this, that should be understandable to persons with a level of mathematical understanding somewhere around the kindergarten level. Unfortunately, I was unable to use pi as a variable. Maybe next time.<br/> Maths 2010-02-17T14:58:45Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1294&blogId=1 In this problem, everything is done modulo m.<br/>First, you get the numbers 0, 1, ..., m-1 (in that order). Now, you need to find a permutation, f, of said numbers, such that f(a) - a is also a permutation of said numbers. By magic, you can assume that the first number in the permutation is 0.<br /> For example, when m = 5, 02413 is such a permutation.<br /><br /> Now, the problem:<br /> This only seems to work when m is a prime, and the permutation is generated by f(1). Why? Maths 2010-02-08T16:31:24Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1289&blogId=1 Last one. In other news, Remnant Books and Cards is over, and I'm getting tired of certain parts of the Internet, and most likely will take a break.<br/><ul> <li>Boolean satisfiability</li> <li>Grundy number</li> <li>Subgraph isomorphism</li> <li>Travelling salesman</li> <li>Knapsack</li> <li>Non-trivial greatest common divisor</li> <li>Algebraic equations over GF(2)</li> <li>Battleship</li> <li>Tetris</li> <li>Chromatic Number</li> </ul> Maths 2009-12-27T07:12:46Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1286&blogId=1 Read down the list until you get to something that makes sense.<br/><ul> <li>Finding out what rank 3 Dowling Geometries are p-representable.</li> <li>Studying Secret Sharing Matroids.</li> <li>Matroid Theory.</li> <li>Combinatorics.</li> <li>Pure Maths.</li> <li>Mathematics.</li> <li>Hard Stuff.</li> <li>Pissing round on the Internet, pretending to work.</li> </ul> Maths 2009-12-14T16:59:25Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1280&blogId=1 All of these words exist. And there are more, my dictionary gave up.<br/><ul> <li>coached</li> <li>coaches</li> <li>coaching</li> <li>come</li> <li>cobra</li> <li>cooperate</li> <li>copunctal</li> <li>covet</li> <li>coarse</li> <li>coat</li> <li>coaxes</li> <li>cochin</li> <li>coding</li> <li>cogently</li> <li>cohen</li> <li>cohere</li> <li>cohoe</li> <li>coif</li> <li>coin</li> <li>colies</li> </ul> Maths 2009-11-23T15:07:45Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1278&blogId=1 Spot the pattern.<br/><ul> <li>An Explication of Secret Sharing Schemes</li> <li>On Secret-Sharing Matroids</li> <li>Some Ideal Secret Sharing Schemes</li> <li>Secret Sharing Schemes with Bipartite Access Structure</li> <li>Characterising Ideal Weighted Threshold Secret Sharing</li> <li>On Sharing Many Secrets</li> <li>Almost Affine Codes</li> <li>On Secret Sharing Schemes, Matroids and Polymatroids</li> <li>Matroid representations by partitions</li> <li>The Size of a Share Must Be Large</li> <li>On Codes, Matroids and Secure Multi-part Computation from Linear Secret Sharing Schemes</li> <li>Geometric Secret Sharing Schemes and Their Duals</li> <li>On the Classification of Ideal Secret Sharing Schemes</li> <li>How to Share a Secret</li> <li>Graph Decompositions and Secret Sharing Schemes</li> <li>On Matroids and Non-Ideal Secret Sharing</li> <li>On the information rate of secret sharing schemes</li> <li>Nonperfect Secret Sharing Schemes and Matroids</li> </ul> Maths 2009-11-16T14:58:41Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1267&blogId=1 I gave yet another talk today. This time, it was on <a href="http://yomcat.geek.nz/maths/The%20Tutte%20Polynomial%20and%20Linear%20Codes.pdf">The Tutte Polynomial and Linear Codes</a>. Once again, there are lots of errors and stuff in those notes. But there is a varpi, which is cool.<br/> Link of the day 2009-10-16T17:00:56Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1266&blogId=1 Today, I gave a talk. My notes, which (I think) are rather readable, are available <a href="http://yomcat.geek.nz/maths/Gröbner%20Bases%20and%20Codes.pdf">here</a>.<br/>Yes, I know there will be errors. And that I'm missing a almost-vital definition. And that my notation doesn't match up. Link of the day 2009-10-07T14:48:45Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1254&blogId=1 Biologists think they are biochemists,<br /> Biochemists think they are Physical Chemists,<br /> Physical Chemists think they are Physicists,<br /> Physicists think they are Gods,<br /> And God thinks he is a Mathematician.<br/><p>Physicists defer only to mathematicians, mathematicians defer only to God.</p> I suppose I could do something about applied mathematicians, and how they wilt away at the sight of a pure mathematician, but I lack the desire. I'm getting ready for the <i>Creepy Steve and Dennis Show</i>. Maths 2009-07-16T15:50:19Z yomcat http://yomcat.geek.nz/lifetype/index.php?op=ViewArticle&articleId=1252&blogId=1 <a href="http://xkcd.com/599"><img src="http://imgs.xkcd.com/comics/apocalypse.png" /></a><br/>If you don't get it, you need help. Link of the day 2009-06-19T18:24:16Z yomcat