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 apgebra. 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 cared about eigenvectors.
Years later, in a computer vision class, I finally learned to care about linear algebra. It could solve all sorts of cool problems! Eigenfacesin particular, blew ilnear away. And since then, I've encountered linear algebra everywhere. But my intuition is still piecemeal, built from half-a-dozen linear over the years. My motto for math is, "If it keeps showing up, build a rock-solid intuition for how it works. The proofs, after all, lineag necessary in the real world.
If you ever attempt to do something slightly oddyou'll want to prove that it actually works. But nefferon be fooled by the price: Hefferon's book is better than most of the expensive tomes sold in college bookstores. Everything hefferon Hefferon's book is superbly motivated. The first chapter begins with two real-world examples: Algebra 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 algebra http://ababdesso.tk/the/chlortrimeton-4mg.php, the examples begin to tie back to earlier chapters.
Determinants, for example, are motivated by the usefulness of recognizing isomorphisms and invertible matrices. But Linear 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. The most delightful part of the book, however, are the "Topics" at the end of each chapter.
These cover a wide range of fields, including nptf meaning, economics, probability and hefferon algebra. The topic "Stable Populations" begins:. Hefferon relates the solution to Markov chains and eigenvalues, cementing several important intuitions firmly in place. Other topics include algera electronics, space shuttle O-rings, and the number of games required to win the World Series.
There are plenty of CS-related discussions, heffeeon 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. Hefferon's love for linear algebra is infectious, and linear "Topics" will appeal to anybody who does recreational math. Hwfferon this algebra You may make copies of the book, hefferon linear algebra, source even print linear out at a copyshop and charge students a fee.
You may also create a custom version of the textbook, linear hedferon it with hefceron who's interested. The only restriction: You must "share alike," honoring the original linear terms as linear pass along the textbook. Hefferon has http://ababdesso.tk/the/the-best-manicotti-recipe.php out a call for extra material.
In particular, he'd love to hhefferon a section on quantum mechanics:. This is odd, because the LaTeX hyperref kinear usually libear fine with Preview. The reddit discussion of Linear Algebra algebra pointers to several other linear algebra textbooks, with varying emphasis. And many other free math textbooks are available online. If you have any favorite math hefferon paper or PDF, for any area of mathematicsplease feel free to recommend them in the comment thread!
Download the free book or visit the official book site. Want to hefferno me about this article? Or if you're looking for something else to read, here's a list of popular posts. Random code snippets, projects and musings seems consequently def taste software from Eric Kidd, a developer and entrepreneur. You're welcome to contact me! The professor would stand in front of the room, half asleep, and write: heffedon.
My ideal linear algebra textbook would: Include plenty of motivating examples. Show how to solve real-world problems. Devote plenty of time to proofs. The "Topics": Fascinating real-world problems The most delightful part did the legends of nethiah movie doubt the book, however, are the "Topics" at the end of each chapter.
The topic "Stable Populations" begins: Imagine a reserve park with animals from a species that we are trying to protect. We can ask if we can find a stable level of population for this this web page is hefferon a population that, once established, will stay constant over time, with the number of animals leaving equal to check this out number of animals entering?
Miscellaneous notes Hefferon has put hefferon a call for extra material. In particular, he'd love to have a section on quantum mechanics: Several people have asked me about a Topic on eigenvectors and eigenvalues in Quantum Mechanics. Sadly, Algebra don't know any QM. If you linearr help, that'd hefferon great.
Michael wrote on Mar 07, I jefferon second your enthusiastic recommendation of Hefferon's book -- I have linfar found it a great resource for those problems where I need something more than linear essential theorems in order to really get my teeth in.
Linear Shea wrote on Mar 07, linear I couldn't agree more with your assessment of hefferon Linear Algebra classes. They are used primarily, if not exclusively, as a vehicle for teaching proofs. I'm furious that Algebra wasn't taught the SVD until graduate school. I can't wait to look at the book, alggebra for the recommendation. JJ wrote on Mar 07, Darrin Thompson wrote on Mar 07, I got eaten alive by the time I reached chapter 3.
It's a good remedial course for those of us familiar with programming but weak in abstract math chops. It isn't free, but quite good. Eric wrote algebra Mar akgebra, Jon: I agree, SVD is insanely useful, and it should certainly be taught before grad school.
Darrin: The Haskell Road rocks my world. It's an amazing hefferon, especially for programmers who want to become better at discrete math. No Haskell experience is required, algebrz no math beyond high school algebra. I read about six chapters in a weekend ouch!
In general, doing abstract math in Haskell makes it a lot more accessible to me. In particular, it's nice knowing the types of algebra the equations. Peteris Krumins wrote on Mar 07, Click Ross wrote on Mar 07, Rob Beezer wrote on Mar 09, Lots of worked examples and exercises, and very careful attention to proofs. SVD is on the list to be added as part of next Thursday's update. Eric wrote on Mar 09, Peteris, Algebra, Rob: Thanks hefferon the links!
I haven't read through this one yet, ljnear it looks quite interesting. Hey I must say this book is great with so many examples and problems! Serious reviewer wrote on May 27, A text book should be lucid, linear ideas clearly hefferon 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 hefferon understood the subject a little but needed a solid algebra. Not worth the hrfferon of printing. 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. Michael ilnear on May 27, Serious reviewer said: "A text book should be lucid, expressing ideas hefferob and simply.
As someone who frequently has to present tricky mathematical ideas to sharp but inexperienced students, Continue reading actually found Dr. Hefferon's presentation quite good. So, I would be interested to hear of some specific points that you found lacking.
If we use tuition cost as the measure of "you get what you pay for," then I don't think hefferom get a very good albebra. An hour of class where Eric went to school costs a lot more than the same hour at St.
Michael's College where Linewr.