Mathematics and Technology (Springer Undergraduate Texts in Mathematics and Technology)

Of what use is mathematics? Hasn’t everything in mathematics already been disc- ered? Thesearenaturalquestionsoftenaskedbyundergraduates. Theanswersprovided by their professors are often quite brief. Most university courses, pressed for time and rigidly structured, o?er little opportunity to present and study actual applications and real-world examples. Evenmorehigh-schoolstudentsaskthesamequestionswithmoreinsistence. Tea- ers in these schools generally work under even tighter constraints than university prof- sors. 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 ?rst 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 ?rst time in the winter semester of 2001. It was created after observing that most courses in the department neglect to present real applications. Sinceitscreationthecoursehasbeenopentobothundergraduatemathematicsstudents 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.

Mathematics and Technology presents technological applications of mathematics making use of elegant mathematical concepts. The selected subjects consist of: public key cryptography, error correcting codes, the global positioning system (GPS) and cartography, image compression using fractals and the JPEG format, digital recording, robot movement, DNA computing, Google's PageRank algorithm, savings and loans, gamma ray surgery and random number generators. The authors highlight how mathematical modeling, together with the power of mathematical tools, have been crucial for innovation in technology. The exposition is clear, straightforward, motivated by excellent examples, and user-friendly. Numerous exercises at the end of every chapter reinforce the material. An engaging quality is the various historical notes accompanying the mathematical development.

This book is intended mainly for undergraduate students in pure and applied mathematics, physics and computer science, instructors, and high school teachers. The main prerequisites are linear algebra and Euclidean geometry. A few chapters require multivariable calculus and elementary probability theory. A clear indication of the more difficult topics and relatively advanced references make it also suitable for an independent reader mastering the prerequisites.