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Mathematics and Technology

  • Textbook
  • © 2008

Overview

Authors:
  1. Christiane Rousseau

    1. Dépt. Mathématiques et de Statistique, Université de Montréal, Montréal, Canada

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    You can also search for this author in PubMed   Google Scholar

  2. Yvan Saint-Aubin

    1. Centre de Recherches Mathématiques, Université de Montréal, Montréal, Canada

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Explains elegant mathematical concepts and develops them towards applications in technology
  • Clear and straightforward presentation
  • Numerous exercises at the end of every section provide practice and reinforce the material in the chapter
  • Presents historical context for material along with the practical one
  • Accessible to any individual with a decent command of high school mathematics
  • Includes supplementary material: sn.pub/extras

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Table of contents (15 chapters)

  1. Front Matter

    Pages 1-15
    Download chapter PDF

  2. Positioning on Earth and in Space

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-43

  3. Friezes and Mosaics

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-39

  4. Robotic Motion

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-33

  5. Skeletons and Gamma Ray Radiosurgery

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-34

  6. Savings and Loans

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-16

  7. Error Correcting Codes

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-35

  8. Public Key Cryptography

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-31

  9. Random Number Generators

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-23

  10. Google and the Page Rank Algorithm

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-24

  11. Why 44100 Samples per Second

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-33

  12. Image Compression Iterated Function Systems

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-42

  13. Image Compression The JPEG Standard

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-33

  14. The DNA Computer

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-43

  15. Calculus of Variations

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-52

  16. Science Flashes

    • Christiane Rousseau, Yvan Saint-Aubin
    Pages 1-67

  17. Back Matter

    Pages 1-12
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Keywords

About this book

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.

Reviews

From the reviews:

"Christiane Rousseau and Yvan Saint-Aubin here present a valuable collection of diverse and detailed applied mathematics examples. … presented to work as a standalone guide to mathematics at work today, usable for self-study and enlightenment or as a text for coursework. … Chapters conclude with a rich collection of exercises followed by references for further study. … 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 … ." (Tom Schulte, MAA Online, February, 2009)

"This book takes a more detailed view of mathematics in action, in several areas of technology … . This is an excellent book for a varied audience. … This book will also be attractive to college students … and to researchers in mathematics, computer science (CS), and technology, who want to acquire a more thorough understanding of the applications covered in the book. … the authors give several pointers and suggestions to instructors. … I like this book and I recommend it." (Edgar R. Chavez, ACM Computing Reviews, June, 2009)

“The authors highlight how mathematical modeling, together with the power of mathematical tools, has been crucial for innovation in technology. … The text is written for students who have a familiarity with Euclidean geometry and have mastered multivariable calculus, linear algebra, and elementary probability theory. … undergraduates in their junior or senior years are the ideal audience for the course.” (Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1211, 2011)

Authors and Affiliations

  • Dépt. Mathématiques et de Statistique, Université de Montréal, Montréal, Canada

    Christiane Rousseau

  • Centre de Recherches Mathématiques, Université de Montréal, Montréal, Canada

    Yvan Saint-Aubin

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