In this presentation we would like to share our experience with teaching an analysis course using Mathematica at the University of Warsaw. This presentation is done jointly with Dr. Andrzej Kozłowski. We have been teaching the course of analysis for computer science students for several years and augmented the standard course with computations in Mathematica. The problems that we choose for our classes are the ones in which Mathematica could be genuinely useful in a way that did not involve simply applying some standard algorithm or plotting a graph, but which required the students to think and come up with some mathematical idea. Sometimes this idea is a guess inspired by a Mathematica calculation or a visual representation of the problem. Sometimes Mathematica can only verify this guess in special cases, and sometimes it can prove its correctness in full generality. In all such cases, we normally still want to obtain a rigorous mathematical proof. When using a computer program as an aid in mathematics, it is important to understand what such programs are well suited to and what they are not, and also what kind of problems (including incorrect answers) one can run into. In this presentation, we give examples of problems where Mathematica can be used effectively as an aid in solving mathematical problems, or at least to inspire the idea of a solution.