most recent 30 from http://mathoverflow.net 2013-05-25T21:21:15Z http://mathoverflow.net/feeds/user/1354 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/3819/why-do-functions-in-complex-analysis-behave-so-well-as-opposed-to-functions-in Yoo 2009-11-02T17:22:52Z 2012-04-14T16:02:59Z

<p>Complex analytic functions show rigid behavior while real-valued smooth functions are flexible. Why is this the case?</p>

http://mathoverflow.net/questions/6093/does-it-help-to-learn-statistical-mechanics-in-order-to-learn-thermodynamic-forma Yoo 2009-11-19T13:37:22Z 2010-02-16T14:54:10Z

<p>Does it help to learn statistical mechanics or thermodynamics (as in physics or mathematical physics) in order to learn thermodynamic formalism: the study of equilibrium states, Gibbs measure, maximal measures mostly on shift spaces or &#8484;ⁿ?</p> <p>I've not taken a course on thermodynamics, but so far my learning of the concept of Gibbs states, pressures, equilibrium states on shift spaces seems to be going fine. But then maybe I'm missing physical intuitions that may be necessary later.</p>

http://mathoverflow.net/questions/7998/most-general-way-to-generate-pairwise-independent-random-variables Yoo 2009-12-06T13:48:25Z 2010-01-13T07:02:55Z

<p>Is there a sort of structure theorem for pairwise independent random variables or a very general way to create them?</p> <p>I'm wondering because I find it difficult to come up with a lot of examples of nontrivial pairwise independent random variables. (by 'nontrivial', i mean not mutually independent)</p> <h1>one example (three r.v.):</h1> <p>X = face of dice 1</p> <p>Y = face of dice 2</p> <p>Z = X + Y mod 6</p> <h1>another example (three events) from some book:</h1> <p>Throw three coins. A = the number of heads is even, B = the first two flips are the same, C = the second two flips are heads.</p> <h1>another example:</h1> <p>$A_{ij}$ = dice i and dice j having the same face</p> <p>($A_{ij}$, $i\neq j$) form a set of pairwise independent events, but the triple ($A_{ij}$, $A_{jk}$, $A_{ki}$) is not mutually independent.</p>

http://mathoverflow.net/questions/9218/probabilistic-proofs-of-analytic-facts/9657#9657 Yoo 2009-12-24T05:35:22Z 2009-12-24T05:35:22Z

<p>Doeblin's proof of the fundamental limit theorem for regular Markov chains: (450 p. in <a href="http://www.dartmouth.edu/~chance/teaching%5Faids/books%5Farticles/probability%5Fbook/book.html" rel="nofollow">Introduction to probability</a>, available online.) The proof uses <a href="http://en.wikipedia.org/wiki/Coupling%5F%28probability)" rel="nofollow">coupling</a>.</p>

http://mathoverflow.net/questions/5386/typo-grammar-checker-for-latex/6989#6989 Yoo 2009-11-27T21:39:18Z 2009-11-27T21:39:18Z

<p>For checking grammar, try <a href="http://www.languagetool.org/" rel="nofollow">LanguageTool</a>. But it's not latex aware. I'd run some script to remove all latex commands and then check with LanguageTool.</p>

http://mathoverflow.net/questions/3250/multiplication-of-0-1-matrices/4236#4236 Yoo 2009-11-05T09:43:31Z 2009-11-05T09:43:31Z

<p>To add to other answers, you might want to play with a weighted path counting interpretation (rather than composition of linear maps interpretation) for multiplication of matrices with not necessarily integer entries. Strongly related is to view a n by m matrix as a bipartite graph (with weighted edges) with n vertices on one side and m vertices on the other side (instead of viewing a matrix as a linear map). This viewpoint is useful when you are learning Markov chains or shifts of finite types.</p>

http://mathoverflow.net/questions/2340/what-is-the-first-interesting-theorem-in-insert-subject-here/4109#4109 Yoo 2009-11-04T16:13:36Z 2009-11-04T16:13:36Z

<p>Euclidean geometry: a triangle on a semicircle has a right angle.</p>

http://mathoverflow.net/questions/1354/what-are-examples-of-good-toy-models-in-mathematics/3801#3801 Yoo 2009-11-02T15:03:42Z 2009-11-02T15:03:42Z

<p>Shift spaces are examples of topological dynamical systems, but they also serve as a toy model for topological dynamical systems.</p>

http://mathoverflow.net/questions/3079/most-helpful-heuristic/3794#3794 Yoo 2009-11-02T13:21:28Z 2009-11-02T13:21:28Z

<p>Every set or function you can build in a concrete fashion starting from (countablye many) other measurable sets or functions is measurable.</p> <p>There are some <a href="http://mathoverflow.net/questions/879/most-interesting-mathematics-mistake/898#898" rel="nofollow">counterexample</a> to this. But it gets you a feel for measurability like we have a feel for what is continuous and what is not.</p>

http://mathoverflow.net/questions/2340/what-is-the-first-interesting-theorem-in-insert-subject-here/3786#3786 Yoo 2009-11-02T12:12:51Z 2009-11-02T12:12:51Z

<p>Symbolic dynamics: There is a unique minimal right resolving presentation for an irreducible sofic shift.</p>

http://mathoverflow.net/questions/11044/what-is-the-probability-that-4-points-determine-a-hemisphere Yoo 2010-08-17T14:37:59Z 2010-08-17T14:37:59Z

An equivalent problem is a Putnam problem phrased as &quot;Four points are chosen at random on the surface of a sphere. What is the probability that the center of the sphere lies inside the tetrahedron whose vertices are at the four points&quot;. Solutions are written in detail here: <a href="http://books.google.com/books?id=QZ1QY4CWZv4C&amp;lpg=PA160&amp;ots=ojXfjy1x3A&amp;dq=putnam%20sphere%20hemisphere%20probability&amp;pg=PA159#v=onepage&amp;q&amp" rel="nofollow">books.google.com/&hellip;</a>;

http://mathoverflow.net/questions/1924/what-are-some-reasonable-sounding-statements-that-are-independent-of-zfc/30561#30561 Yoo 2010-07-05T09:35:08Z 2010-07-05T09:35:08Z

Speaking of stuff on the plane, a certain problem of coloring the plane with no corners is equivalent to CH too - <a href="http://www.artofproblemsolving.com/Forum/viewtopic.php?f=73&amp;t=137999" rel="nofollow">artofproblemsolving.com/Forum/&hellip;</a>

http://mathoverflow.net/questions/23478/examples-of-common-false-beliefs-in-mathematics/23495#23495 Yoo 2010-06-15T18:21:37Z 2010-06-15T18:21:37Z

A related thread: <a href="http://mathoverflow.net/questions/7998/most-general-way-to-generate-pairwise-independent-random-variables" rel="nofollow" title="most general way to generate pairwise independent random variables">mathoverflow.net/questions/7998/&hellip;</a>

http://mathoverflow.net/questions/23478/examples-of-common-false-beliefs-in-mathematics/23481#23481 Yoo 2010-06-15T16:59:13Z 2010-06-15T16:59:13Z

AB and BA share the same invertible part : <a href="http://www.artofproblemsolving.com/Forum/viewtopic.php?f=349&amp;t=112209" rel="nofollow">artofproblemsolving.com/Forum/&hellip;</a>

http://mathoverflow.net/questions/7155/famous-mathematical-quotes/7182#7182 Yoo 2010-01-07T18:56:09Z 2010-01-07T18:56:09Z

like blue collar versus cubicle

http://mathoverflow.net/questions/7155/famous-mathematical-quotes/7182#7182 Yoo 2010-01-07T18:55:25Z 2010-01-07T18:55:25Z

like physics versus mathematics

http://mathoverflow.net/questions/11044/what-is-the-probability-that-4-points-determine-a-hemisphere Yoo 2010-01-07T18:30:39Z 2010-01-07T18:30:39Z

Related thread: <a href="http://mathoverflow.net/questions/2014/if-you-break-a-stick-at-two-points-chosen-uniformly-the-probability-the-three-re" rel="nofollow" title="if you break a stick at two points chosen uniformly the probability the three re">mathoverflow.net/questions/2014/&hellip;</a>

http://mathoverflow.net/questions/9218/probabilistic-proofs-of-analytic-facts/9657#9657 Yoo 2009-12-24T05:37:26Z 2009-12-24T05:37:26Z

I realize this isn't an analytic fact

http://mathoverflow.net/questions/3038/errata-database Yoo 2009-11-27T21:11:09Z 2009-11-27T21:11:09Z

Similar thread in tricki: <a href="http://www.tricki.org/node/406" rel="nofollow">tricki.org/node/406</a>

http://mathoverflow.net/questions/4499/cures-for-mathematicians-block-as-in-writers-block/4557#4557 Yoo 2009-11-17T19:45:52Z 2009-11-17T19:45:52Z

One can also lose his desire when it seems that his hard work is not being rewarded: no promising stable job, no stable income, not much vacation.

http://mathoverflow.net/questions/3973/what-should-be-offered-in-undergraduate-mathematics-thats-currently-not-or-isn/4026#4026 Yoo 2009-11-05T10:16:05Z 2009-11-05T10:16:05Z

I hope more mathematics bloggers write on such subjects for us who haven't had such a class.

http://mathoverflow.net/questions/1363/regular-languages-and-the-pumping-lemma/1366#1366 Yoo 2009-11-05T08:53:14Z 2009-11-05T08:53:14Z

As to intuition for regular languages (and hence also for sofic shifts), suppose a very long word is displayed on a screen one letter at a time (let's say you can press a button to see the next letter, but no buttons for going back), if you can decide if the word is in L with a bounded amount of memory (either your memory or jotting things down and erasing on physical papers), then the language L is regular. And if you write your decision algorithm in an automata, you will only need a finite number of states because your algorithm requires a bounded amount of memory.

http://mathoverflow.net/questions/1048/why-is-it-so-cool-to-square-numbers-in-terms-of-finding-the-standard-deviation/1087#1087 Yoo 2009-11-05T07:57:26Z 2009-11-05T07:57:26Z

If we define the standard deviation with absolute value instead of squares, we would still have Chebyshev's theorem except with 1/k in place of 1/k^2

http://mathoverflow.net/questions/2144/a-single-paper-everyone-should-read/2478#2478 Yoo 2009-11-04T15:18:20Z 2009-11-04T15:18:20Z

I think I might need to explain my above comment. Music (and painting too) is taught just like that in those nightmares at least in South Korea where I live.

http://mathoverflow.net/questions/2144/a-single-paper-everyone-should-read/2478#2478 Yoo 2009-11-04T14:14:02Z 2009-11-04T14:14:02Z

I guess that how music teachers teach music to high school students is a parody of how math teachers teach math and vice versa.