An experiment concerning mathematical proofs on computers with French undergraduate students

The undergraduate students in mathematics of the University of Chambéry ha opportunity of an optional course in logic during their third year. Some years ago course was a classical introduction to logic as, for example, in [3]. Due to the difficultie of the students, it became, step by step, a trai ning course in mathematical reasoning. T use of PhoX, the proof assistant developed by C. Raffalli (see [14]), allowed to carr in detail, “real” proofs during lab sessions on computers. We started to use PhoX with students in 1999. At the beginning, the examples w sidered were very simple but, step by ste p, they became more and more intricate a in 2001, the students spent about 10 hour s with PhoX. During the 2002–2003 academ year, this course (i.e., 50 hours) has totally been devoted to work on computers. T dents had to do, first with the computer and then on paper, the proof of three cla mathematical theorems (see Section 3 .3). During the 2003–2004 academic year, onl short course (10 hours) of training to mathematical reasoning was maintained: ou leagues (mathematicians but not logicians as we are) did not consider that this cou important and they decided to suppress it. During the 2001–2003 academic years, so first year students also did some (more elementary) proofs with PhoX. It is, as far as we know, the first time in France that math students, at this level done proofs of that difficulty with a computer. The goal of this paper is to describe various experiments. We will mainly con centrate on the 2002–2003 acad emic year since i is, in some sense, its apogee. We also give the main important points concerning th years and the experiment for the first year students. This paper is not, strictly speaking, a research paper. Even though it gives some on the way PhoX works and thus can be considered as a short introduction to this so we are here more concerned with pedagogical matters. However, the problems we m