The Mandelbrot set and pretty pictures The tutorials below assume that you have a basic knowledge of algebra. They are roughly in order of difficulty. Later tutorials may depend on earlier ones, but I've tried my best to ensure that the reverse is never true. The tutorials are in Adobe Acrobat format, so to view them you will need Acrobat Reader, which is available from here.
The most efficient way to get better at maths is to practise. The links below point to a series of Acrobat documents (reader here) which include both questions and answers, in some case with very detailed working. The questions are roughly in order of difficulty, with the later ones building on techniques tested in the earlier ones.
Being able to do maths under time pressure is a bonus. The following set of Acrobat documents (reader here) are sets of questions (no answers, I'm afraid) with some idea of how long they should be taking. These exams were set for the first year elementary maths course at the University of Cambridge.
Unfeasible as this may seem when you're trying to do a calculus problem, there really are some interesting bits of maths. The following items use more difficult maths than anything else on the page, which is a bit of a downer. On the other hand, they're probably about 50 times as interesting.
Finally, here are some more outlandish questions. The questions in this section are open-ended (and in some cases very difficult... if you take them too seriously).