A few months ago, I rediscovered the Khan Academy after stumbling across a presentation by Salman Khan. If you aren't familiar with this, I recommend making it an absolute priority take a quick scan of some of the videos. Here's a summary video from the website:
Sal has an astonishingly approachable and understandable method of explaining topics in his videos, and also has an incredibly deep understanding of the material he talks about hinting at lower levels of complexity that he might be skimming over, but sometimes revisits in future videos. The Khan Academy videos are, in my opinion, perhaps one of the most interesting things to happen to education in a very very long time. If I may, "disruptive". Anyone with an Internet connection can go from basic fundamentals all the way up to a college level education in many topics in a clear, organized, understandable manner... all for free. His teaching style is more effective along many dimensions than any I have personally experienced in any classroom.
Recently, I've realized that I need to learn more linear algebra. Over the years, I have picked up little bits here and there doing computer graphics, basic data analysis, but I never had a proper understanding of it enough to understand why it really works or more importantly... apply it to solve completely new problems that might be somewhat non-standard. I managed to never take a proper linear algebra course in college or grad school.
So, why do I suddenly care about learning linear algebra now? and consequently should you care? Well if you want to understand how the Wiimote Whiteboard program works, you need a little bit of linear algebra. If you want to understand how video games are rendered on the screen you need linear algebra. If want to understand how Google works, how parts of Kinect work, or how the $1 million dollar Netflix Prize was won, financial modeling, or in general analyze the relationship between two large data sets in the world... you need linear algebra. I'm discovering more and more that any modern sophisticated engineering, modeling, prediction, analysis, fitting, optimization problem now usually involves computers crunching on linear algebra equations. Unfortunately, this fact was never properly explained to me in college so I never prioritized taking a class.
I understood the basics enough to do computer graphics, rendering stuff of the screen (3D to 2D). But much of modern computer vision, is about reversing those equations, going from 2D back to 3D, which involves solving a lot of linear algebra equations to recover unknown data. And I've found that computer vision papers seem to be the worst places to look for a clear explanation of the math being performed. The almost appears to be a desire to see how obtusely one can describe their work.
Fortunately, Khan Academy has over 130 videos on Linear Algebra. Since I knew I would be traveling this holiday, I decided to load up all of the videos on my phone to watch during down time. Watching videos here and there while sitting on the plane, trains, buses, or waiting in lines, I was able to watch all 130+ videos, which cover a 1st year college Linear Algebra course, in about 3 weeks. Pure awesome.
However, the Linear Algebra lectures stopped just as I though it was getting to the interesting part. I was hoping it would get to covering topics such as Singular Value Decomposition, numerical analysis, perspective projections...reversing them, sparse matrices, bundle adjustment, and then real-world application examples. I'm going to order some books on these topics, but I really really love the video lecture format Sal uses in the Khan Academy and wish they continued.
The $5000 challenge:
As an attempt to continue expanding this lecture series in the Khan Academy I want to encourage people who feel like they can give clearly understandable lectures on these topics to pick up where Sal left off. Apparently, there is an informal method of adding your own videos to the academy. I've already donated some money to the Khan Academy (a not-for-profit 501(c)(3)). But, as a call the community, to incentivize people who are able to produce good video lectures on advanced Linear Algebra - for each video posted (and passes the "clearly understandable", Khan academy style, 10 minute video lecture) that continues the Linear Algebra series I will donate $100 to Khan Academy up to $5000. So, not only would you be educating thousands (possibly millions of people), you will be ensuring that your material stays free.
If you do take me up on this offer and do post a video, let me know at firstname.lastname@example.org, and I will review the video. If it passes the bar, I will donate the money and then send you the receipt.
Sunday, January 2, 2011
Posted by Johnny Chung Lee at 1:37 AM