The most useful mathematical areas for a programmer are
- trigonometry and linear algebra, especially to draw and recognise shapes, ray tracing, animations and so on,
- combinatorics, particularly to cleverly enumerate sets, estimate running times of simple loops and recursions etc.,
- some elementary group theory and particularly permutation groups, for algorithms that involve tracing out graphs (particularly trees) and also for clever enumeration, as above.
There are lots of introductory books on each of the above subjects, although maybe other people can comment on which ones are best suited for non-mathematicians. Note that the three areas are fairly independent, at least at the beginning, and you can learn them in any order or in parallel.
Edit: I forgot the possibly best way to get started: once you know the definition and some basic facts about groups, you should read the book Indra's Pearls. It is a very beautiful book that explains how to draw certain types of fractals with the computer. It introduces all the relevant mathematics pretty much from zero and it provides the actual programs in pseudo-code, ready for you to implement in your favourite language. The mathematics and the algorithms it introduces are very relevant to other situations, but since you are particularly interested in graphics, you will hardly find a better way to get started! There is even a computer graphics artist who bases some of his work on that book.