Abstract. Since 1998, we have designed a course called Mathematical Experiment at the University of Science and Technology of China. The purpose of the course is to provide opportunities for students to explore mathematics using software such as Mathematica, and to activate their interests in studying mathematics. In each experiment, we give a brief introduction of some topic and then pose a series of problems for the students to answer. The students are required to explore these problems with their own thoughts. The course is something like "guided research". In this talk, I will illustrate it with some examples in exploring mathematical problems with Mathematica.