Mathematics and Technology - Faculty of Mathematics & Computer
Of what use is mathematics? Hasn’t everything in mathematics already been discovered? These are natural questions often asked by undergraduates. The answers provided by their professors are often quite brief. Most university courses, pressed for time and rigidly structured, offer little opportunity to present and study actual applications and real-world examples. Even more high-school students ask the same questions with more insistence. Teachers in these schools generally work under even tighter constraints than university professors. If they are able to competently respond to these questions it is probably because they received good answers from their teachers and professors. And if they do not have the answers, then whose fault is it? The genesis of this text It is impossible to introduce this text without first discussing the course in which it originated. The course “Mathematics and Technology” was created at the Universit´e de Montr´eal and taught for the first time in the winter semester of 2001. It was created after observing that most courses in the department neglect to present real applications. Since its creation the course has been open to both undergraduate mathematics students and future high-school teachers. Since no appropriate text or manual for the course we envisioned existed, we were led to write our own course notes, from which we taught. We got so caught up in writing these notes that they quickly grew to the size of a textbook, containing much more material than could possibly be taught in one semester. Despite the two of us being career mathematicians, we must admit that we both knew little or nothing about most of the applications presented in the following chapters. The goal of the “Mathematics and Technology” course The primary goals of the course are to demonstrate the active and evolving character of mathematics, its omnipresence in the development of technologies, and to initiate students into the process of modeling as a path to the development of various mathematical applications.