Case Studies in the Shortcomings of Maple in Teaching Undergraduate Mathematics

In this paper, we will investigate some of the algorithmic inadequacies and limitations of Maple as well as the common misuses of the software when used as a tool in teaching undergraduate mathematics. We will present examples for which Maple produces misleading or inaccurate results. We will also refer to situations where Maple gives accurate, but incomplete, results which are misused or misinterpreted by novice users of the software, specifically the undergraduate students. The authors have over ten years of experience in using Maple as a teaching tool and some examples presented here are based on those classroom experiences. Other cases have been reported by our students, by our colleagues and in various newsgroups devoted to discussions on Computer Algebra Systems (CASs). Many of the previously reported software bugs, observed in the earlier versions of Maple, are now corrected in the most recent release of the software. So, although we have occasionally referred to the older versions, we have presented the actual output only from the latest version of Maple, namely Maple7, in this paper. For the sake of brevity, we have limited our discussions to the topics which are ordinarily covered in the first two years of a typical undergraduate mathematics curriculum such as limits, single and multivariable integration, series, and floating point arithmetic. We have also tried to limit our case studies to the most common features of Maple, specifically those features that are widely used by the undergraduate students who are new to Maple.