Random Hacks: Jim Hefferon's Linear Algebra: A free textbook with fascinating applications
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review
en-us40Technology and Other Fun Stuff"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Regnessem<p>“SVD is insanely useful” is true but in very limited sense. There’s plenty of richfull life out of the realm of ortonormal basis. Jim Hefferon really paves the road to move on beyond <span class="caps">SVD</span>!</p>Mon, 01 Jun 2009 17:00:40 +0000urn:uuid:850c900f-8913-43fc-838c-91396529b06c
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-635
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Roger<p>Jim Hefferon’s Linear Algebra is a very balanced, substantial yet concise, with fascinating exercises. Thank you so much Mr. Hefferon for making such a book free. More power to you!!!</p>Mon, 04 May 2009 09:26:48 +0000urn:uuid:bf4ea060-ae49-49ad-b0b9-47f196bf57b3
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-616
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Anand<p>Sorry forgot to leave the web link to the book. It can be downloaded from:</p>
<p>http://www.maths.abdn.ac.uk/~bensondj/html/music.pdf</p>Thu, 22 Jan 2009 09:50:46 +0000urn:uuid:2e4bb59b-7a81-4aad-b726-3d3e27888898
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-600
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Anand<p>The book “Music: A Mathematical Offering” is another book that I find fascinating. It explains the mathematics behind signal processing in a very interesting manner. I love the way the book is titled and it does not disappoint you as you read through it.</p>
<p>Enjoy!</p>Thu, 22 Jan 2009 09:50:16 +0000urn:uuid:225843e3-baa8-47a3-a2f5-814456d23dc6
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-599
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Anon<p>You should also take a look at Gilbert Strang’s Linear Algebra video lectures on <span class="caps">MIT</span>’s open courseware site. They’re pure gold.</p>
<p>http://web.mit.edu/18.06/www/Video/video-fall-99-new.html</p>Mon, 03 Nov 2008 07:38:50 +0000urn:uuid:84ff28ea-5098-4549-8c11-48b5a66d6887
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-587
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Arun J. C.<p>I just searched linear agebra and this came up wonderful , really benifical better than any other book.
thanks ….</p>Wed, 05 Mar 2008 08:47:23 +0000urn:uuid:03f1ebba-1a33-4202-a78a-cfed2889baf8
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-555
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Bjorn<p>Funny, I was googling linear algebra Mac os x and I found this page because of the comment on the broken links in Preview. Well, they work well in Preview in Leopard so maybe you could put a footnote pointing that. And now I have this book to refresh my linear algebra.</p>Wed, 27 Feb 2008 13:56:53 +0000urn:uuid:3c463f53-90f8-4792-9e2b-d3434d0bb3e9
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-554
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Michael<p><b>Serious reviewer</b> said: “A text book should be lucid, expressing ideas clearly and simply. Every time its revisited it should leave one with a newer better insight. Hefferonâ€™s book is too simplistic.”</p>
<p>I’m surprised to hear you say this—can you give us an example of some section of the text you found to be particularly lacking clarity or lucidity? As someone who frequently has to present tricky mathematical ideas to sharp but inexperienced students, I actually found Dr. Hefferon’s presentation quite good. So, I would be interested to hear of some specific points that you found lacking.</p>
<p>If we use tuition cost as the measure of “you get what you pay for,” then I don’t think we get a very good correlation. An hour of class where Eric went to school costs a lot more than the same hour at St. Michael’s College where Dr. Hefferon teaches. And yet, if the textbook is any proxy for the quality of his lectures, then it seems like the cost doesn’t track the quality at all.</p>Sun, 27 May 2007 13:44:01 +0000urn:uuid:89a8d4c4-8b6d-4a4f-8cee-f7783e9ab689
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-463
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Serious reviewer<p>A text book should be lucid, expressing ideas clearly and simply. Every time its revisited it should leave one with a newer better insight.
Hefferon’s book is too simplistic. Not the book i would want to go to once i understood the subject a little but needed a solid reference.
Not worth the trouble of printing.</p>
<p>All professors who teach LA dont look asleep. That you get what you pay for is pretty true as far books (and linear algebra courses) go.</p>Sun, 27 May 2007 08:47:13 +0000urn:uuid:cb59d5a1-f88c-42e0-8591-0d90f3591efa
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-462
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Sanchit!<p>Hey I must say this book is great with so many examples and problems!</p>
<p>Thankxxxxxxx</p>Mon, 19 Mar 2007 02:00:37 +0000urn:uuid:6a124206-56b0-4fa5-b5bd-8126537f8704
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-376
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Eric<p>Peteris, Fred, Rob: Thanks for the links!</p>
<p>There’s also an <a href="http://www.uwlax.edu/faculty/will/svd/"><span class="caps">SVD</span> overview</a> at <span class="caps">UW </span>La Crosse. I haven’t read through this one yet, but it looks quite interesting.</p>Fri, 09 Mar 2007 11:08:33 +0000urn:uuid:d507d316-305a-4683-82f1-ed4874ba82da
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-345
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Rob Beezer<p>Another <span class="caps">GFDL</span>’ed linear algebra text is <a href="http://linear.ups.edu/">A First Course in Linear Algebra</a>. Lots of worked examples and exercises, and very careful attention to proofs. Links in <span class="caps">PDF</span> or MathML versions reference previous theorems or definitions. <span class="caps">SVD</span> is on the list to be added as part of next Thursday’s update.</p>Fri, 09 Mar 2007 10:45:48 +0000urn:uuid:fd8dca18-17fa-4f5c-9288-79a94da482e6
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-344
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Fred Ross<p>Funnily enough, I wrote something apropos yesterday: <a href="http://madhadron.auditblogs.com/2007/03/06/a-mathematics-curriculum/">A Mathematics Curriculum</a> <i>[Ed: Converted <span class="caps">URL</span> to link.]</i></p>
<p>Mind you, it’s aimed at an engineer I know, and I know his background (including quantum mechanics) in detail.</p>Wed, 07 Mar 2007 16:07:03 +0000urn:uuid:16ea6e36-759b-4913-a1f8-6702ad9a0ec8
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-341
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Peteris Krumins<p>Check out this blog post about free mathematics video lectures:
<a href="http://freescienceonline.blogspot.com/2006/06/free-mathematics-video-courses.html">Mathematics Video Lectures @ Free Science Online</a></p>
<p>There is a free Linear Algebra video course available from <span class="caps">MIT</span>!
<a href="http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/VideoLectures/index.htm"><span class="caps">MIT</span>’s <span class="caps">OCW </span>Linear Algebra Video Lectures</a></p>Wed, 07 Mar 2007 16:02:09 +0000urn:uuid:6fc53b0e-7b12-4db6-afc7-e1c1db29cdc1
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-340
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Eric<p>Jon: I agree, <a href="http://en.wikipedia.org/wiki/Singular_value_decomposition"><span class="caps">SVD</span></a> is insanely useful, and it should certainly be taught before grad school.</p>
<p>Darrin: <a href="http://www.amazon.com/Haskell-Road-Logic-Maths-Programming/dp/0954300696">The Haskell Road</a> rocks my world. It’s an amazing book, especially for programmers who want to become better at discrete math. (No Haskell experience is required, and no math beyond high school algebra.) I read about six chapters in a weekend (ouch!), and my understanding of logic, relations and functions improved dramatically.</p>
<p>In general, doing abstract math in Haskell makes it a lot more accessible to me. In particular, it’s nice knowing the types of all the equations.</p>Wed, 07 Mar 2007 15:14:34 +0000urn:uuid:4cbba497-5ca7-4fa4-9aa0-e0cfe72a0b6e
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-339
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Darrin Thompson<p>I got eaten alive by the time I reached chapter 3. But I’m getting better with producing proofs because I found the Haskell Road to Logic Maths and Programming. It’s a good remedial course for those of us familiar with programming but weak in abstract math chops.</p>
<p>It isn’t free, but quite good.</p>Wed, 07 Mar 2007 14:25:27 +0000urn:uuid:7d10865c-8935-47b5-bd6a-a1cd69e4921a
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-338
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by JJ<p>I fully agree when you said Hefferon’s text was superior to a lot of college Linear Algebra books selling for over $ 100.</p>Wed, 07 Mar 2007 11:58:04 +0000urn:uuid:ac26df01-a82c-4f00-b2ef-faac93ffb43f
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-337
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Jon Shea<p>I couldn’t agree more with your assessment of undergraduate Linear Algebra classes. They are used primarily, if not exclusively, as a vehicle for teaching proofs. I’m furious that I wasn’t taught the <span class="caps">SVD</span> until graduate school.</p>
<p>I can’t wait to look at the book, thanks for the recommendation.</p>Wed, 07 Mar 2007 11:24:31 +0000urn:uuid:555bcbe5-accc-4c2f-bc0f-fc078f795e0e
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-335
"Jim Hefferon's Linear Algebra: A free textbook with fascinating applications" by Michael<p>I definitely second your enthusiastic recommendation of Hefferon’s book—I have also found it a great resource for those problems where I need something more than the essential theorems in order to really get my teeth in.</p>Wed, 07 Mar 2007 11:04:16 +0000urn:uuid:d71b5b84-68e4-4278-903d-71b38e5f5b4c
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review#comment-334
Jim Hefferon's Linear Algebra: A free textbook with fascinating applications<p style="text-align: center"><big><a href="http://joshua.smcvt.edu/linearalgebra/book.pdf">Download the free book</a></big> or <a href="http://joshua.smcvt.edu/linearalgebra/book.pdf">visit the official site</a></p>
<p>My college linear algebra course was held early in the morning, and
it was devoted almost entirely to blackboard proofs. The professor would
stand in front of the room, half asleep, and write:</p>
<p>“Theorem. Lemma. Lemma. Proof. Theorem…”</p>
<p>Despite this experience, I somehow managed to learn about eigenvectors
and kernels. Or at least, I learned how to write proofs about them. But I
had no intuition for linear algebra: I couldn’t visualize it, and I couldn’t
explain why anybody, anywhere, ever <i>cared</i> about eigenvectors.</p>
<p>Years later, in a computer vision class, I finally learned to care about
linear algebra. It could solve all sorts of cool problems!
(<a href="http://en.wikipedia.org/wiki/Eigenface">Eigenfaces</a>, in particular, blew me away.) And since then, I’ve
encountered linear algebra everywhere. But my intuition is still
piecemeal, built from half-a-dozen applications over the years.</p>
<p>My motto for math is, “If it keeps showing up, build a rock-solid intuition
for how it works.” And towards that end, I’ve been looking for a good
linear algebra textbook.</p>
<p>My ideal linear algebra textbook would:</p>
<ol>
<li>Include plenty of motivating examples.</li>
<li>Show how to solve real-world problems.</li>
<li>Devote plenty of time to proofs.</li>
</ol>
<p>The proofs, after all, are necessary in the real world. If you ever
attempt to do something <a href="http://www.randomhacks.net/articles/2007/03/03/smart-classification-with-haskell">slightly odd</a>, you’ll want to
prove that it actually works.</p>
<h3>Jim Hefferon’s <i>Linear Algebra</i></h3>
<p>Professor Jim Hefferon’s <i>Linear Algebra</i> is available as a <a href="http://joshua.smcvt.edu/linearalgebra/">free PDF
download</a>. But don’t be fooled by the price: Hefferon’s book is
better than most of the expensive tomes sold in college bookstores.</p>
<p>Everything in Hefferon’s book is superbly motivated. The first chapter
begins with two real-world examples: Unknown weights placed on balances,
and the ratios of complex molecules in chemical reactions. These examples
are used to introduce Gauss’s method for solving systems of linear
equations. Further into the book, the examples begin to tie back to
earlier chapters. Determinants, for example, are motivated by the
usefulness of recognizing isomorphisms and invertible matrices.</p>
<p>But Hefferon’s emphasis on real-world examples is admirably balanced by an
abundance of proofs. The first proof appears on page 4, and nearly
everything is proven either in the main text or in the exercises. This
will be helpful for readers who (like me) are trying to bring more rigor to
their mathematical thinking.</p>
<h3>The “Topics”: Fascinating real-world problems</h3>
<p>The most delightful part of the book, however, are the “Topics” at the end
of each chapter. These cover a <a href="http://joshua.smcvt.edu/linearalgebra/toc.html">wide range</a> of fields, including biology,
economics, probability and abstract algebra. The topic “Stable
Populations” begins:</p>
<blockquote>Imagine a reserve park with animals from a species that we are
trying to protect. The park doesnâ€™t have a fence and so animals cross the
boundary, both from the inside out and in the other direction. Every year,
10% of the animals from inside of the park leave, and 1% of the animals
from the outside find their way in. We can ask if we can find a stable
level of population for this park: is there a population that, once
established, will stay constant over time, with the number of animals
leaving equal to the number of animals entering?</blockquote>
<p>Hefferon relates the solution to Markov chains and eigenvalues, cementing
several important intuitions firmly in place.</p>
<p>Other topics include basic electronics, space shuttle O-rings, and the
number of games required to win the World Series. There are plenty of
CS-related discussions, too: a survey of things that can go wrong in naive
numeric code, the time required to calculate determinants, and
how the memory hierarchy affects array layout.</p>
<p>Hefferon’s love for linear algebra is infectious, and his “Topics” will
appeal to anybody who does recreational math.</p>
<h3>“Free” as in “freedom”</h3>
<p><i>Linear Algebra</i> is published under the <a href="http://www.gnu.org/copyleft/fdl.html">GNU Free Documentation
License</a> and the <a href="http://creativecommons.org/licenses/by-sa/2.5/">Creative Commons Share Alike</a> license.</p>
<p>What
this means: You may make copies of the book, or even print them out at a
copyshop and charge students a fee. You may also create a custom version of
the textbook, and share it with anybody who’s interested. The only
restriction: You must “share alike,” honoring the original author’s terms
as you pass along the textbook.</p>
<h3>Miscellaneous notes</h3>
<p>Hefferon has put out a call for extra material. In particular, he’d love
to have a section on quantum mechanics:</p>
<blockquote>Several people have asked me about a Topic on eigenvectors and
eigenvalues in Quantum Mechanics. Sadly, I don’t know any QM. If you can
help, that’d be great.</blockquote>
<p>On the downside, the internal PDF links in <i>Linear Algebra</i> are broken
in MacOS X Preview. This is odd, because the LaTeX <code>hyperref</code>
package usually works fine with Preview.</p>
<p>The <a href="http://programming.reddit.com/info/1129o/comments">reddit</a> discussion of
<i>Linear Algebra</i> has pointers to several other linear algebra textbooks, with varying emphasis. And many other <a href="http://www.math.gatech.edu/~cain/textbooks/onlinebooks.html">free math
textbooks</a> are available online. </p>
<p>If you have any favorite math books (paper or PDF, for any area of
mathematics), please feel free to recommend them in the comment thread!</p>
<p style="text-align: center"><big><a href="http://joshua.smcvt.edu/linearalgebra/book.pdf">Download the free book</a></big> or <a href="http://joshua.smcvt.edu/linearalgebra/book.pdf">visit the official site</a></p>Wed, 07 Mar 2007 08:01:00 +0000urn:uuid:413e2cc5-fe86-4c3d-a313-1d96098b939dEric Kidd
http://www.randomhacks.net/articles/2007/03/07/hefferon-linear-algebra-review
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