most recent 30 from http://mathoverflow.net 2013-05-23T21:39:26Z http://mathoverflow.net/feeds/user/2266 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/19930/writing-papers-in-pre-latex-era psihodelia 2010-03-31T10:39:29Z 2012-12-14T10:56:16Z

<p>I wonder how people wrote papers in the pre-LaTeX era? I mean, when typewriters and simple computers were (60th-70th?). Did they indeed put formulas by hand in the already printed articles?</p>

http://mathoverflow.net/questions/7794/feasibility-of-a-list-of-prescribed-distances-in-r3 psihodelia 2009-12-04T18:20:43Z 2011-09-27T12:21:25Z

<p>I am puzzled with the following problem:</p> <p>Given $n$ real numbers it is to obtain a Yes/No answer to: "whether it is possible to arrange different points in the Euclidean $\mathbb{R}^3$ so that every of the given numbers represents a shortest distance which belongs to a distinct pair of points?"</p> <p>What is an efficient algorithm to solve such problem? If I understand properly, first I have to find $m$ from $n=\frac{m(m+1)}{2}$ which is the number of such points. But what is the next step? Should I deal with checking the triangle inequality (which seems to be very inefficient) or what?</p> <p>Thank you in advance!</p>

http://mathoverflow.net/questions/7772/applied-mathematics-books-graduate-level psihodelia 2009-12-04T12:42:51Z 2011-04-23T02:50:57Z

<p>What are some good graduate level books on applied mathematics which explain in-depth the general modern problem-solving methods of the real-world typical hard problems? </p> <p>There is a lot of books on numerical methods, engineering math, but I do not know any good modern book, which emphasizes algorithmic complexity of the discussed problems.</p>

http://mathoverflow.net/questions/7627/set-theory-and-alternative-foundations psihodelia 2009-12-03T00:49:34Z 2011-03-22T21:06:14Z

<p>Every foundational system for mathematics I have ever read about has been a set theory, from ETCS to ZFC to NF. Are there any proposals for a foundational system which is not, in any sense, a set theory? Is there any alternative foundation which is not a set-theory? </p>

http://mathoverflow.net/questions/19824/the-limits-of-parallelism psihodelia 2010-03-30T12:50:45Z 2010-03-30T20:17:10Z

<p>Is it possible to solve a problem of O(n!) complexity within a reasonable time given unlimited number of processing units and infinite space? </p> <p>The typical example of O(n!) problem is brute-force search: trying all permutations.</p> <p>I have asked this question on Stackoverflow, but it seems to be more appropriate to ask it here.</p>

http://mathoverflow.net/questions/9968/how-to-transform-a-plane-into-a-sphere-solved psihodelia 2009-12-28T17:16:04Z 2009-12-28T18:10:39Z

<p>Given a 2-dimensional array of MxN heights, how to transform it to a sphere? Every element of this array is just a 3D point (x,y,z) where z represents some height. One has to transform this array into a sphere, twisting it around the origin so, that only minimal distortions will happen.</p> <p>Representing it by spherical coordinates is not very good, because of the severe distortions. It's probably better if there is no direct one-to-one mapping from 2D plane to a surface of 3D sphere - many plane's points will not be involved. But what is the best possible mapping and how to transform involved points (elements of array)? </p> <p>This is for a 3D-planet terrain simulation. First, fractal landscape is produced, then, it is to be transformed to 3D sphere.</p> <p>Thanks in advance!</p> <p><strong>SOLUTION</strong>: <a href="http://en.wikipedia.org/wiki/Map%5Fprojection" rel="nofollow">Map projection</a></p>

http://mathoverflow.net/questions/9293/what-is-the-max-number-of-points-in-r3-interconnected-by-generic-curves psihodelia 2009-12-18T17:41:35Z 2009-12-18T19:25:23Z

<p>The largest complete graph that embeds in 2 dimensions is $K_4$, while the largest complete graph that embeds in 3 dimensions is $K_{\infty}$, right? However, I don't know any constructive proof of it.</p> <p><strong>Informal Explanation</strong>: What is the max number of points in $\mathbb{R}^3$, interconnected by lines of any curvature, such that no line intersects any other line? Each point is connected with all other points. For $\mathbb{R}^2$ it is only 4 points (smth. like Mercedes symbol) - why 4 and not 3 or 5? How many points are possible to connect in such way in $\mathbb{R}^3$? (I suggest, infinite number, but it is interesting to look at a proof). What are some special properties of the Euclidean $\mathbb{R}^3$ such that the number of interconnected points jumps from 4 in $\mathbb{R}^2$ to infinity in $\mathbb{R}^3$?</p> <p><strong>PS</strong>: I don't understand why my question has got already 4 downvotes? No comments, no critics, why? English is not my native language, that's why?</p>

http://mathoverflow.net/questions/9279/what-are-some-special-properties-of-the-euclidean-r3 psihodelia 2009-12-18T15:46:38Z 2009-12-18T17:10:27Z

<p><strong>Premise</strong>: Any physically possible process of computations requires an underlying physical process. Such physical process can exist only in the available physical space, which can be modeled by the Euclidean $\mathbb{R}^3$ (most simplest model).</p> <p><strong>Question</strong>: What are some special properties of the Euclidean $\mathbb{R}^3$, which are very different from $\mathbb{R}^2$ and from $\mathbb{R}^4$ and from more dimensional metric spaces? </p> <p><strong>Example 1</strong>: I know that in the $\mathbb{R}^2$, an Euclidean minimum spanning tree (EMST) for a given set of points may be found in asymptotically optimal O(n log n) time using O(n) space. For more dimensions, finding optimal EMST algorithm remains an open problem. It is interesting to know, how $\mathbb{R}^2$ is different from $\mathbb{R}^3$.</p> <p><strong>Example 2</strong>: Another example is the max number of points interconnected (every-to-every) by lines of any curvature, such that no line intersect any other line. For $\mathbb{R}^2$ it is only 4 points (smth. like Mercedes symbol) - why 4 and not 3 or 5? How many points are possible to connect in such way in $\mathbb{R}^3$? (I suggest, infinite number, but it is interesting to look at a proof). What are some special properties of the Euclidean $\mathbb{R}^3$ such that the number of interconnected points jumps from 4 in $\mathbb{R}^2$ to infinity in $\mathbb{R}^3$?</p> <p>Please excuse my non-professional questions, I am not mathematician.</p> <p>Thank you in advance!</p>

http://mathoverflow.net/questions/5372/dimension-leaps/9288#9288 psihodelia 2009-12-18T16:57:33Z 2009-12-18T16:57:33Z

<p>The max number of points interconnected (every-to-every) by lines of any curvature, such that no line crosses any other line. For $\mathbb{R}^2$ it is only 4 points (smth. like Mercedes symbol) - why 4 and not 3 or 5? How many points are possible to connect in such way in $\mathbb{R}^3$? (I suggest, infinite number, but it is interesting to look at a proof). What are some special properties of the Euclidean $\mathbb{R}^3$ such that the number of interconnected points <strong>jumps from 4</strong> in $\mathbb{R}^2$ to <strong>infinity</strong> in $\mathbb{R}^3$?</p>

http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8356#8356 psihodelia 2009-12-09T15:11:47Z 2009-12-09T15:11:47Z

<p>$\mathbb{N}$ comes from the German "Natürliche Zahlen"=natural number<br> $\mathbb{Z}$ comes from the German "ganZe Zahl"=integer numbers<br> $\mathbb{Q}$ comes from the Latin "Quotient"= result of a division<br> $\mathbb{R}$ comes from the German "Reelle Zahl"=real numbers<br> $\mathbb{C}$ comes from the French "nombre Complexe"=complex numbers<br></p>

http://mathoverflow.net/questions/7624/the-discrete-logarithm-problem psihodelia 2009-12-03T00:25:18Z 2009-12-03T01:04:28Z

<p>I am puzzled with the following discrete logarithm problem:</p> <p>Given positive integers <code>b, c, m</code> where <code>(b &lt; m) is True</code> it is to find a positive integer <code>e</code> such that</p> <pre><code>(b**e % m == c) is True </code></pre> <p>where two stars is exponentiation (e.g. in Ruby, Python or ^ in some other languages) and % is modulo operation. Using general math symbols it looks like:($b^e \equiv c (\mod m)$). </p> <p>What is the most effective algorithm (with the lowest big-O complexity) to solve it ?</p> <p>Example: Given b=5; c=8; m=13 this algorithm must find e=7 because 5**7%13 = 8</p> <p>Thank you in advance!</p>

http://mathoverflow.net/questions/7794/feasibility-of-a-list-of-prescribed-distances-in-r3/76487#76487 psihodelia 2011-11-27T17:54:29Z 2011-11-27T17:54:29Z

Thank you! Your info is very helpful!

http://mathoverflow.net/questions/395/reading-list-for-basic-differential-geometry psihodelia 2010-04-27T13:51:46Z 2010-04-27T13:51:46Z

Asking these homework questions just encourages more people to ask them! Gr&#233;tar Amazeen (tm)

http://mathoverflow.net/questions/22714/how-to-describe-a-solution-which-involves-a-representation-of-the-numbers psihodelia 2010-04-27T12:38:09Z 2010-04-27T12:38:09Z

@Keenan Kidwell: My question is about how to describe concatenation of any representation of the numbers in a strict proper math way. Shown solution involves representation of the numbers (str() function returns it) as a string.

http://mathoverflow.net/questions/22714/how-to-describe-a-solution-which-involves-a-representation-of-the-numbers psihodelia 2010-04-27T12:20:20Z 2010-04-27T12:20:20Z

Yes of course! It is a mathematical question.

http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8356#8356 psihodelia 2010-04-27T10:41:48Z 2010-04-27T10:41:48Z

The word Quotient is actually a Latin word, inherited by many modern languages.

http://mathoverflow.net/questions/19824/the-limits-of-parallelism psihodelia 2010-03-30T13:07:47Z 2010-03-30T13:07:47Z

@rgrig: thanks, I know already well enough about NP theory :)

http://mathoverflow.net/questions/3044/tools-for-collaborative-paper-writing psihodelia 2010-03-30T12:45:45Z 2010-03-30T12:45:45Z

Stay with git, it is most advanced revision control system.

http://mathoverflow.net/questions/7772/applied-mathematics-books-graduate-level/9314#9314 psihodelia 2010-02-08T22:26:10Z 2010-02-08T22:26:10Z

Thanks a lot! This book is very useful!

http://mathoverflow.net/questions/9293/what-is-the-max-number-of-points-in-r3-interconnected-by-generic-curves/9299#9299 psihodelia 2009-12-19T22:57:52Z 2009-12-19T22:57:52Z

Thank you very much! I understand and appreciate your answer. However, I give you my vote, but Yuan's proof is explained clearer and simpler for a layman like me - his answer I mark as accepted.

http://mathoverflow.net/questions/9293/what-is-the-max-number-of-points-in-r3-interconnected-by-generic-curves/9295#9295 psihodelia 2009-12-19T22:54:07Z 2009-12-19T22:54:07Z

Thanks, I've got it now ! :)

http://mathoverflow.net/questions/9293/what-is-the-max-number-of-points-in-r3-interconnected-by-generic-curves psihodelia 2009-12-19T22:49:27Z 2009-12-19T22:49:27Z

@Greg: I've spent long time thinking on every of the given answers. Yuan's answer was most helpful. I've thanked him and accepted his answer. I just do not understand why so many downvotes for my answer? My claims in commentaries about non-constructive proofs were done before the answers was corrected and extended by their respectful authors.

http://mathoverflow.net/questions/9293/what-is-the-max-number-of-points-in-r3-interconnected-by-generic-curves/9305#9305 psihodelia 2009-12-19T09:39:57Z 2009-12-19T09:39:57Z

Thanks, I've spent whole evening thinking about your solution and I am starting to understand it now :)

http://mathoverflow.net/questions/9293/what-is-the-max-number-of-points-in-r3-interconnected-by-generic-curves psihodelia 2009-12-18T19:09:11Z 2009-12-18T19:09:11Z

@Reid: if it's so trivial, then why there is no any constructive proof being given?

http://mathoverflow.net/questions/9293/what-is-the-max-number-of-points-in-r3-interconnected-by-generic-curves/9295#9295 psihodelia 2009-12-18T18:58:44Z 2009-12-18T18:58:44Z

@Matt: What if I try to connect all real numbers? Will it still work?

http://mathoverflow.net/questions/9293/what-is-the-max-number-of-points-in-r3-interconnected-by-generic-curves/9298#9298 psihodelia 2009-12-18T18:45:28Z 2009-12-18T18:45:28Z

This is not a proof at all. How to prove that the number of such points is infinite in R^3?