User - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T02:48:18Z http://mathoverflow.net/feeds/user/8232 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/38839/partial-operators Partial operators unknown (yahoo) 2010-09-15T16:15:23Z 2010-09-15T17:15:05Z <p>Apart from partial differential and partial difference operators, what other partial operators are there?</p> <p>I was thinking about multivariable situations in which you can focus on single variables and combine several single variables at a time e.g. f<sub>xxy</sub>. I suppose you could invent any number of such things e.g. max_compl <sub>ij</sub>{ a, b, c, ...} where a,b,c are vectors and max_compl <sub>i</sub> produces a new set without the vector(s) whose ith component is larger than that of the other vectors in the set, and here max_compl is the partial version of the ordinary version that would work on a set of scalars. I was just wondering after partial differential operators what would be the most common such operators.</p> http://mathoverflow.net/questions/35893/what-signs-are-there-that-a-problem-is-solvable What signs are there that a problem is solvable? unknown (yahoo) 2010-08-17T17:49:13Z 2010-08-17T17:49:13Z <p>What signs are there that a problem is solvable, but not so easy that it isn't worthwhile doing, and not so hard like P=NP? </p> http://mathoverflow.net/questions/35268/does-pnp-over-imply-pnp Does P≠NP over ℝ imply P≠NP ? unknown (yahoo) 2010-08-11T19:21:45Z 2010-08-13T08:39:04Z <p>Does P≠NP over ℝ imply P≠NP ?</p> <p>where ℝ is for Real number algorithms as described by Smale with a suitable formulation of P≠NP over ℝ. </p> <p>Complexity Theory and Numerical Analysis, Steve Smale, 2000 <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.4678&amp;rep=rep1&amp;type=pdf" rel="nofollow">http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.4678&amp;rep=rep1&amp;type=pdf</a> </p> http://mathoverflow.net/questions/34995/what-effect-would-a-proof-of-pnp-have-on-the-field-of-complexity-theory What effect would a proof of P≠NP have on the field of complexity theory? unknown (yahoo) 2010-08-09T12:57:27Z 2010-08-09T12:57:27Z <p>This question is motivated by Scott Aaronson's comment about his bet: "If P≠NP has indeed been proved, my life will change so dramatically that having to pay \$200,000 will be the least of it."</p> <p><a href="http://scottaaronson.com/blog/?p=456" rel="nofollow">http://scottaaronson.com/blog/?p=456</a></p> http://mathoverflow.net/questions/34843/what-is-realistic-mathematics/34851#34851 Answer by unknown (yahoo) for What is Realistic Mathematics? unknown (yahoo) 2010-08-07T17:53:46Z 2010-08-07T17:53:46Z <p>I may be wrong, missing the point and in way over my head, but given that category theory is useful in physics (is it?) and that category theory deals with classes, then I don't think that set theories can say everything that we can say about physical reality. </p> http://mathoverflow.net/questions/39424/teach-a-course-in-1-month Comment by 2010-09-21T11:26:07Z 2010-09-21T11:26:07Z I'd prefer sets of notes and then tutorial sessions for asking questions, rather than many hours a week of &lt;s&gt;lectures&lt;/s&gt; copying sessions. Lectures really get my goat. If the fact that they get my goat, gets your goat, then your goat is easily got. The word &quot;everyone&quot; in my above comment could be ammended to &quot;many people's&quot; to take into account those who find lectures useful. Uni is for getting a degree/understanding/other stuff, not for spending time as a human photocopier. http://mathoverflow.net/questions/39424/teach-a-course-in-1-month Comment by 2010-09-21T06:22:03Z 2010-09-21T06:22:03Z This question highlights the old saying: &quot;A lecture is a system for transferring the lecturer's notes to the students' without going thru the minds of either.&quot;. Why not just give the students a set of photocopied notes and be done with it. The way most lectures are conducted is absurd and utterly wasteful of everyone's time. http://mathoverflow.net/questions/38839/partial-operators Comment by 2010-09-15T17:06:08Z 2010-09-15T17:06:08Z I've edited the question to elaborate on what I was thinking. http://mathoverflow.net/questions/36824/applications-of-measure-integration-and-banach-spaces-to-combinatorics Comment by 2010-08-27T17:06:24Z 2010-08-27T17:06:24Z The existence of the internet means that the days of - Me Teacher. Me Teach. You Pupil. You Learn. - are over. Instead tell the students how interconnected mathematics is, and ask each of them to search the internet to find papers that link functional analysis to their own favourite topics and perhaps ask the students to present their findings to the class. Make it a competition to see who can find the most interesting links. http://mathoverflow.net/questions/36058/this-years-medals Comment by 2010-08-19T05:01:55Z 2010-08-19T05:01:55Z Twitter! Thanks. http://mathoverflow.net/questions/35268/does-pnp-over-imply-pnp Comment by 2010-08-11T20:17:49Z 2010-08-11T20:17:49Z @Kevin: Thanks for that paper. Question answered. http://mathoverflow.net/questions/35268/does-pnp-over-imply-pnp Comment by 2010-08-11T19:39:37Z 2010-08-11T19:39:37Z Real number algorithms as described by Smale with a suitable formulation of P≠NP over R.