Discrete Mathematics and its Applications
Teaching Mathematics and Its Applications
Volume 29 Issue 3
Abstract:
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be interested in a subject if they are able to appreciate its use. There is, therefore, a strong case for teaching Discrete Mathematics in context. Lecturers are faced with the task of conveying mathematical material, some of which is new to students and some of which they will have met before. Lecturers must attempt to foster mathematical dexterity. All of this takes time. Teaching the subject in context can be achieved using little, or no, additional time. Of the wide range of Computer Science subjects, Artificial Intelligence and Software Agents are particularly rich in problems that are easy to understand and for which mathematics is needed in order to formally describe the problem as well as to solve it.
I am teaching Discrete Mathematics right now, so I was intrigued by what they had to say. I found, however, that the course they describe and the course I am teaching are very, very different. I am not a computer scientist and I do not approach the course from the perspective of computer science. I instead treat the course as a first course in mathematical proofs. Where they emphasize computer architecture and and the applications of propositional logic in computer science, I take my students through logic, set theory, and ultimately into combinatorics and graph theory. The examples and applications I give are thus within mathematics, and not within the “real world”.
I do see the utility in their approach, however. If I were teaching this course for a computer science department I think I would definitely try to apply some of their thinking. If the purpose of the course is commonly accepted to be a foundation to the mathematical ideas necessary to study data structures and algorithms, then anchoring the course in concrete examples of computer science makes sense. On the other hand, if the course is offered through a mathematics department, even if it is being offered as a pre- or co-requisite for classes in another department, the motivation of the class should be, in my opinion, within mathematics.
An interesting article, and one I will consider making available to my students if they are interested.
Early in your post, before you alluded to it towards the end of your post, I had the same thought that this article was probably geared towards someone in the computer science field. My curiosity had me click on the link and saw that the author was indeed part of a computer science and information management department. I agree with your assessment, that if I were teaching in a math department, the approach would probably be different.