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. We give the titles and quick descriptions of the articles. (To see the latter, click on the words "Quick description".)

How to use the Cauchy-Schwarz inequality

How to use cohomology

How to use fixed point theorems

How to use the Fourier transform

How to use generating functions

How to use the Hahn-Banach theorem

How to use the mean value theorem

How to use Zorn's lemma. If you are building a mathematical object in stages and find that (i) you have not finished even after infinitely many stages, and (ii) there seems to be nothing to stop you continuing to build, then Zorn's lemma may well be able to help you.