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Linear Algebra

AuthorJim Hefferon Entered2000-12-23 00:44:45 by bcrowell
Editedit data record FreedomCopylefted: anyone can read, modify, and sell (disclaimer)
SubjectQ.A - Mathematics. Computer science (linear algebra)
This link was reported to be OK by user Ben Crowell on 2005-10-26 14:43:26
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Excellent applications, modern approach
by Ben Crowell (crowell09 at (change 09 to current year)) on 2000-12-23 00:44:46, review #37
better than 90%
I may not be the optimal person to review this book. I have an undergraduate degree in math and physics, but my PhD is in physics, and I teach physics, not math. Furthermore, I have to admit that I haven't read this 446-page text from cover to cover.

Anyhow, throwing caution to the winds, I'll risk giving my opinion that this is an excellent book. The fact that it's free is just an added bonus.

One thing that makes this book very different from the undergraduate math texts I used is the many interesting applications. Some of these are in separate sections, and some are interspersed throughout the text. The physics applications -- such as crystals, electrical networks, and dimensional analysis -- are excellent. Some seem like they might be a little on the difficult side for students with weaker preparation, but it is of course up to the instructor which ones to cover. It's a measure of the quality of the book that I was intrigued by the applications that were outside my specialty, such as voting paradoxes. When's the last time you found yourself getting interested in a textbook?

Many of the homework problems relate directly to these real-life applications. This is in welcome contrast to the usual, dreary set of "drill and kill" problems without any real context. The drudgery is also reduced by the explicit introduction of computer algebra systems in the first chapter. Many of the problems explicitly state that they are to be solved on a computer, and the assumption that the students will use computers has also allowed Hefferon to include many realistic problems that result in larger matrices than could be handled by hand.

In some ways, this book strikes me as more advanced than the ones used in my lower-division course. Says Hefferon,

I was especially interested in the treatment of determinants, since I clearly recalled how the text used in my own undergraduate linear algebra course had introduced them abruptly and without motivation. I only really felt that I understood what a determinant was once I learned that it could be interpreted as the product of the eigenvalues. Hefferon takes an interesting in-between approach. He doesn't do eigenvalues until after determinants, but he doesn't just introduce determinants through a deus ex machina either. Instead, he discusses the invertibility of 1x1, 2x2, and then 3x3 matrices, and develops the concept naturally and straightforwardly. Three cheers!

All in all, it's hard for me to imagine why anyone would go on using linear algebra texts that are not free information when there's a free book as good as this one.

Information wants to be free, so make some free information.

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