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Partial operators

2010-09-15T16:15:23Z

Apart from partial differential and partial difference operators, what other partial operators are there?

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_xxy. I suppose you could invent any number of such things e.g. max_compl _ij{ a, b, c, ...} where a,b,c are vectors and max_compl _i 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.

What signs are there that a problem is solvable?

2010-08-17T17:49:13Z

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?

Does P≠NP over ℝ imply P≠NP ?

2010-08-11T19:21:45Z

Does P≠NP over ℝ imply P≠NP ?

where ℝ is for Real number algorithms as described by Smale with a suitable formulation of P≠NP over ℝ.

Complexity Theory and Numerical Analysis, Steve Smale, 2000 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.4678&rep=rep1&type=pdf

What effect would a proof of P≠NP have on the field of complexity theory?

2010-08-09T12:57:27Z

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."

http://scottaaronson.com/blog/?p=456

Answer by unknown (yahoo) for What is Realistic Mathematics?

2010-08-07T17:53:46Z

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.

Comment by

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 <s>lectures</s> 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 "everyone" in my above comment could be ammended to "many people's" 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.

Comment by

2010-09-21T06:22:03Z

This question highlights the old saying: "A lecture is a system for transferring the lecturer's notes to the students' without going thru the minds of either.". 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.

Comment by

2010-09-15T17:06:08Z

I've edited the question to elaborate on what I was thinking.

Comment by

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.

Comment by

2010-08-19T05:01:55Z

Twitter! Thanks.

Comment by

2010-08-11T20:17:49Z

@Kevin: Thanks for that paper. Question answered.

Comment by

2010-08-11T19:39:37Z

Real number algorithms as described by Smale with a suitable formulation of P≠NP over R.