Mathematics and Technology (eBook)

Christiane Rousseau, Yvan Saint-Aubin (Autoren)

eBook Download: PDF

2008 | 1. Auflage
XVI, 598 Seiten
Springer New York (Verlag)
978-0-387-69216-6 (ISBN)

Infos

The authors present useful, elegant mathematical concepts such as Markov chains, function iteration and simple groups, and develop these concepts in the context of applications to important, practical problems such as web-navigation, data compression and error correcting codes. The authors highlight how mathematical modeling, together with the power of mathematical tools and abstraction, have been crucial for innovation in technology. The topics are presented with clarity, and the mathematics is expressed in a straightforward manner. Numerous exercises at the end of every section provide practice and reinforce the material in the chapter. An engaging quality of this book is that the authors also put the mathematical material in a historical context and not just a practical one. Mathematics and Technology is intended for undergraduate students, instructors and high school teachers. Prerequisites are essentially linear algebra and Euclidean geometry. Additionally, its lack of calculus centricity as well as a clear indication of the more difficult topics and relatively advanced references make it suitable for any curious individual with a decent command of high school math.

---

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 "e;Mathematics and Technology"e; 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.

Inhalt

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 Page Rank Algorithm.- Why 44100 Samples per Second.- Image Compression Iterated Function Systems.- Image Compression The JPEG Standard.- The DNA Computer.- Calculus of Variations.- Science Flashes.

Produkt-Details

• Erscheint lt. Verlag: 29.10.2008
• Co-Autor: Helene Antaya, Isabelle Ascah-Coallier
• Übersetzer: Chris Hamilton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: algorithm • algorithms • Calculus • Geometry • Innovation • linear algebra • Markov • Mathematical Modeling • Modeling • Navigation • robot • Text
• ISBN-10: 0-387-69216-9 / 0387692169
• ISBN-13: 978-0-387-69216-6 / 9780387692166