Christiane Rousseau and Yvan Saint-Aubin here present a valuable collection of diverse and detailed applied mathematics examples. The collection explores a gamut of modern technological applications. It is presented to work as a standalone guide to mathematics at work today, usable for self-study and enlightenment or as a text for coursework.
The varied topics presented in each chapter are made accessible by an initial conceptual overview. After this high-level introduction, supporting theorems are exemplified with specific, applicable techniques. Chapters conclude with a rich collection of exercises followed by references for further study. This structure allows the chapters to stand alone for reference on the topic covered.
Among the real-world examples illuminated with mathematics is the Global Positioning System (GPS), basic group theory through friezes and mosaics, matrix theory as applied to robotic motion, and more, including finance, DNA computing, error-correcting codes, and public key cryptography. Google’s PageRank algorithm gets a chapter along with random-number generators and examination of the reason why digital audio commonly comes in 44,100 samples per second. Image compression, including the JPEG standard, is covered in two chapters.
Intended for undergraduate students, the pre-requisites for getting the most out of this book are basically only linear algebra and Euclidean geometry. The authors clearly decided to avoid calculus. That choice, together with the clear signposts to help students get around and through the more difficult topics, make Mathematics and Technology suitable for any diligent reader with a grasp of high school math.
Using the text for supporting a course is explicitly aided by lead-ins to each chapter. These chapter lead-ins suggest the time that should be taken to cover each chapter. Further, specific pre-requisites are suggested and individual sections and exercises are indicated for special attention based on the students’ level.
Preface.- Positioning on Earth and in Space.- Friezes and Mosaics.- Robotic Motion.- Skeletons and Gamma-Ray Radiosurgery.- Savings and Loans.- Error-Correcting Codes.- Public Key Cryptography.- Random-Number Generators.- Google and the PageRank Algorithm.- Why 44,100 Samples per Second?.- Image Compression: Iterated Function Systems.- Image Compression: The JPEG Standard.- The DNA Computer.- Calculus of Variations.- Science Flashes.- Index.