Exploring Topics in Higher Mathematics

with MAPLE V

- Spring 2000. Writing Enriched Math Elective.

The availability of increasingly sophistocated symbolic/numeric/graphics math computing packages like MAPLE V enables individuals to more easily explore more advanced topics in mathematics using these packages as a tool to extend their learning power, as well as to tackle questions that could not even be considered by hand without them. Linear algebra, differential equations, complex analysis, numerical analysis, discrete mathematics, geometry, statistical analysis, and programming are just a few topics where one can use the power of a computer algebra system to study interesting problems that would not be so accessible if approached without them.

The course will start as a computer laboratory, familiarizing the students with MAPLE and its worksheet interface (and mathematical typesetting capabilities) with the help of a suitable introductory text, and exploring common mathematical topics to build up some experience in using MAPLE as a tool in studying various kinds of mathematical questions. Ideally students will work in teams of two to help each other both in interfacing with MAPLE and in thinking about the mathematics. Students will learn to organize their work in mathematical reports using the worksheet interface in order to develop their ability to communicate about technical material in an effective way. This includes the blending of the mathematics with written discussion in clear English.

As the course progresses, students will pick individual team topics of interest either of their own choice from topics they may have touched upon in other courses but would like to explore more deeply or from topics chosen in consultation with the instructor based on their mathematical interests, provided that the topics are suitable for using MAPLE as a tool in their study. Toward the end of the course students will work on a longer project of their choice for their final team report. Topics will be informally discussed among the different teams as the work progresses by projecting worksheets with some discussion, combined with some board work explanation if appropriate. MAPLE consulting with the instructor will help overcome any hurdles that it may present in accomplishing the goals of an individual team project. Worksheets for the individual team projects will first be submitted as drafts for feedback about the presentation and content from the instructor and then resubmitted as final documents.

The required text *Discovering Mathematics with Maple* by R.J. Stroeker and J.F.
Kaashoek (1999) will help us get acquainted with Maple and show us how it can be used to
do more interesting mathematics than just calculus-like calculations. [The **optional**
text *MAPLE V Learning Guide* is only available if you would like to have a book to
read about using MAPLE and to understand how it works more methodically. ]