This paper is based on an experience in teaching functional programming to mathematics students. This experience had two objectives. The first one was to help the student assimilate some mathematical concepts by putting them to practical use in programs. The second one was to give them a good start in programming by emphasizing the fact that abstraction, which is so useful in mathematics, is equally useful in programming and allows for more powerful and more easily extensible programs. The mathematical domain used here is geometry and more precisely geometrical transformations, and their group structure. The programming projects are oriented towards 2D tilings, both Euclidean and hyperbolic.