Tricki - Article requests

Constructive mathematics

AndrejBauer — Fri, 08 May 2009 11:35:11 +0000

Do you think there would be sufficient interest for articles "how to tell if my proof is constructive" and "how to make constructive proofs". Most proofs are mostly constructive and there is a limited set of "gotchas" that one has to be aware of. Also, proofs which are not constructive can often be made constructive by a simple change. I could write such articles or aticle. Probably it's better to start with a single article and split it up if and when it gets too big.

A general idea in "for all" statements

luke — Tue, 05 May 2009 14:20:55 +0000

I have a proposition for the page Proving "for all" statements.

There is a more general approach/view, which generalize induction and the articles in the subsection Prove the result for some cases and deduce it for the rest.

It is the following: If you have to show a statement it is useful to exploit the structure of the set .

If there are for example some operations acting on such that you can write every as with a special point and you can show:

When constructing sequences, keep track of the size of the terms (elementary real analysis)

Brendan Murphy — Sun, 03 May 2009 15:10:49 +0000

The example that sticks in my mind is proving that k-cells are compact. The proof is by contradiction: suppose that an open over has no finite subcover, and find a sequence of nested k-cells with no finite subcover. Eventually, one must be small enough to be covered with one neighborhood. When I first attempted the proof, I figured this much out for myself, but I didn't think to put a bound on the size of the terms and couldn't finish the proof. Now it seems like an obvious trick.

computing integrals by differentiating under the integral sign

Mon, 27 Apr 2009 06:22:39 +0000

Seems like this basic technique should have a tricki page.

Erlangen program

JoseBrox — Sat, 25 Apr 2009 10:24:40 +0000

What about an article explaining the ideas behind the Erlangen program? It could link to the symmetries article discused at the forum.

A definitions tricki article

ioannis.parissis — Thu, 23 Apr 2009 17:02:01 +0000

Those who have started writing or editing tricki articles probably have come across the same problem. Suppose you need to define a mathematical notion (an operator, a function space, a property and so on). Then there is the obvious question if whether need to define the space from scratch, and If I do so, will this be compatible with other definitions other people have given in different articles? Also, it seems totally redundant to define the same notions over and over again. What I suggest is a tricki article containing definitions of basic notions, operators, function spaces and so on.

Universal properties

JoseBrox — Wed, 22 Apr 2009 23:44:00 +0000

In Universal Algebra, Category Theory, Abstract Algebra and Homological Algebra, "universal properties" and "commutative diagrams" are common place. Maybe an article about them (what are, how to use them, a bit of history, good examples) could be ok.

Proof of correctness of algorithms

brownh — Wed, 22 Apr 2009 21:40:18 +0000

I propose that there should be a page (probably several pages) on how to prove correctness for a (deterministic or randomized) algorithm.

Differential equations front page

emerton — Wed, 22 Apr 2009 15:20:03 +0000

I noticed that there is a link for this page, even with a brief summary, on the Equation-solving front page, but the link is dead. There are a couple of pages related to solving DEs already on the uncategorized list, and I would guess that this number will likely grow, since this is a big topic!

I could make the DE front page and start to collect these, but it might be better if someone who knows more about the subject does this.

Change of variables/ symmetries

devin — Tue, 21 Apr 2009 15:17:26 +0000

Using the correct variables or using a symmetry of the structure underlying the problem to convert a problem to another: this is a principle that I try to use when I think about a question. What is the right representation for a given problem? What are the correct variables? I am curious if others think that this idea deserves a page of its own.

I tried to write an initial article on what I think to be a special case of this, namely use of bijections in counting. If a general article is written, a link to this special case could make both articles more useful.