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When Life is Linear: From Computer Graphics to Bracketology

When Life is Linear

by Tim Chartier

Catalog Code: NML-45
Print ISBN: 978-0-88385-649-9
Electronic ISBN: 978-0-88385-988-9
140 pp., Paperbound, 2015
List Price: $52.00
Member Price: $39.00
Series: Anneli Lax New Mathematical Library

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Tim Chartier has written the perfect supplement to a linear algebra course. Every major topic is driven by applications, such as computer graphics, cryptography, webpage ranking, sports ranking and data mining. Anyone reading this book will have a clear understanding of the power and scope of linear algebra. — Arthur Benjamin, Harvey Mudd College

I’m often asked which areas of mathematics should students study. I always say linear algebra. However, typical linear algebra texts I've seen either have very few applications, or the applications are contrived and not very relevant to students. Chartier's text is a refreshing change as it is driven by real-world applications that are inspiring and familiar to his audience. From Google searches and image processing, to sports rankings and (my favorite) computer graphics. — Tony DeRose, Pixar Animation Studios

From simulating complex phenomenon on supercomputers to storing the coordinates needed in modern 3D printing, data is a huge and growing part of our world. A major tool to manipulate and study this data is linear algebra. This book introduces concepts of matrix algebra with an emphasis on application, particularly in the fields of computer graphics and data mining. Readers will learn to make an image transparent, compress an image and rotate a 3D wireframe model. In data mining, readers will use linear algebra to read zip codes on envelopes and encrypt sensitive information. The books details methods behind web search, utilized by such companies as Google, and algorithms for sports ranking which have been applied to creating brackets for March Madness and predict outcomes in FIFA World Cup soccer. The book can serve as its own resource or to supplement a course on linear algebra.

Table of Contents

About the Author

Tim Chartier is an Associate Professor in the Departments of Mathematics and Computer Science at Davidson College. In 2014, he was named the inaugural Mathematical Association of America’s Math Ambassador. He is a recipient of the Henry Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member from the MAA. Published by Princeton University Press, Tim authored Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing and coauthored Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms with Anne Greenbaum. As a researcher, Tim has worked with both Lawrence Livermore and Los Alamos National Laboratories on the development and analysis of computational methods targeted to increase efficiency and robustness of numerical simulation on the lab’s supercomputers, which are among the fastest in the world. Tim’s research with and beyond the labs was recognized with an Alfred P. Sloan Research Fellowship. He serves on the Editorial Board for Math Horizons. He was the first of the Advisory Council for the Museum of Mathematics, which opened in 2012 and is the first museum of mathematics in the United States. Tim fields mathematical questions for the Sports Science program on ESPN, and has also been a resource for a variety of media inquiries, which include appearances with NPR, the CBS Evening News, USA Today, and The New York Times. He also writes for the Science blog of the Huffington Post.

MAA Review

One of the nice things about linear algebra, I’ve always thought, is that there is something in the subject for just about everybody. There’s a lot of beautiful theory, but at the same time those people who like to roll up their sleeves and get their hands dirty with computations, particularly in aid of interesting applications, will find much here to interest them as well.

At Iowa State University, we offer two different introductory undergraduate courses in linear algebra — one is a proof-based course intended for mathematics majors, the other is a more computational course with applications for non-majors. (There is also a more sophisticated joint undergraduate/graduate course in applied linear algebra.) I’ve taught the non-major course a couple of times, and enjoyed it, but have noted that most introductory texts are usually so busy developing the ideas behind linear algebra that they don’t really have time or space in which to really discuss the applications in any depth. Typically an application will just be developed rather briefly, which may result in it appearing somewhat contrived and artificial. The book under review does an excellent job of addressing these concerns, and would make a very useful supplement to a first course in linear algebra. Continued...

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