Tricki
a repository of mathematical know-how

Revision of Different kinds of Tricki article from Mon, 06/04/2009 - 10:40

Quick description

This page is a very general navigation page with links to other pages that list Tricki articles of similar types and give further links. For a different route into the Tricki, there is also a navigation page that is more concerned with the kinds of problems that the articles are helping to solve than with the nature of the articles themselves.

Categories of article

Expositions of mathematical techniques

The heart of the Tricki is a large collection of articles about specific mathematical techniques that are useful for various classes of problems. To find these articles, use the various search tools, or try following links from navigation pages.

Many Tricki articles are about methods for solving particular classes of problems. But when one is doing mathematical research, many of the most useful tips are not methods of this kind but are more like general research strategies that can in principle be applied to virtually any mathematical problem. This page contains links to many articles about such strategies.

While the Tricki is mainly about methods rather than subject matter, it may nevertheless be helpful to narrow down a search by concentrating on the area to which your problem belongs (though you then risk missing a method that applies to your problem but also applies more generally). This page contains links to general navigation pages for different areas of mathematics.

Some major classes of problems, such as solving equations, cut across subject areas. It is an important part of the Tricki philosophy that traditional subject classifications should be used only when they are useful in narrowing down a problem type, so there are also navigation pages for general classes of problem.

Anybody who has taken an undergraduate mathematics course, and certainly anybody who has taught undergraduate mathematics, will know that there is a huge difference between being familiar with a theorem and knowing how to use it. However, it is a widely adopted convention in textbooks and lectures to give a theorem and its proof and then to hope that the audience will somehow work out how it is applied. One way this is done is through the setting of exercises, and often the main difficulty in solving an exercise is spotting the appropriate theorem to use. Something similar can be true at the research level too: a problem that seems hard to one mathematician may well be easy to another who recognises that it is a consequence of a theorem that is designed to deal with exactly that difficulty. This is a navigation page with a list of Tricki articles, each of which is entitled "How to use X" for some X.

If you read an average mathematical paper, it will present you with some results, but it is most unlikely that it will tell you how those results were discovered. Part of the reason for this is that journals would tend to regard a detailed account of that kind as a bit self-indulgent and not what its pages are for. And yet such accounts can be hugely informative for other people, so it seemed a good idea to have a space for them on the Tricki. If you wish to write such an article, then it will be even better if you can write accompanying articles explaining the techniques you used (or else include links to existing Tricki articles that explain them).

Comments

Inline comments

The following comments were made inline in the article. You can click on 'view commented text' to see precisely where they were made.

Links in headings

The first time I read this article, I didn't notice that this was a link: It looks exactly like the other headings, and most other headings in the tricky are not links. The above "Expositions of mathematical techniques" is not a link, so I didn't expect this to be. Perhaps links in headings should be underlined, or have a different color? Or we should try to avoid link in headings (like wikipeda)?

I agree, and this dates from

I agree, and this dates from when I used to write articles differently. I'll try to do something about it soon.

Not too much is lost,

Not too much is lost, hopefully, since the link to each page also occurs in the paragraph immediately following the heading.

I've now turned the headings

I've now turned the headings into ordinary text-style links and removed the artificial links in the succeeding paragraphs, for stylistic consistency. And I think it's clearer too, though the headings do look a little small.