MATH 218

Linear Algebra

As for all our math courses, we have a couple of different options here: the Khan Academy and MIT OpenCourseWare. In MIT's case, we have a set of assignments and exams (all with solutions) to check our knowledge. The Khan Academy doesn't seem to have gotten that far yet, but it may just be a matter of time. You probably don't need me to tell you that you're far more likely to understand a concept if you actually take the time to do the math . . . over and over. Links are provided below.

Don't let the 200-level course number make you nervous. This course is really just an extension of algebra, and it's extremely cool (see "Why Linear Algebra?", below). It will challenge you and make you think in new ways, just like calculus. A typical linear algebra course will present you with a large number of related but somewhat independent concepts to learn. If you find that the going gets tough, take some time to figure out how much the particular concept you're struggling with is going to be needed in your future efforts. You may want to save it for later. Better to do that than to get discouraged.

If you don't absolutely love linear algebra but just want to gather all the tools you'll need later to tackle, say, the mathematics of general relativity, here's my advice: Study all the Khan Academy material ("Vectors and spaces","Matrix transformations", and "Alternate coordinate systems (bases)"). They seem to have really hit the bullseye on identifiying what you'll need for "later." Then pick through the corresponding MIT material, maybe the videos for a second perspective or teaching style, but especially the problems and solutions for the concepts you studied with KA.

We're starting to put ourselves pretty far ahead of the common student now, so the odds of finding a good study guide or textbook at the public library or thrift store are starting to decline. But by all means, go and look. If you're here on line because you aren't able to attend a university, you might consider a community college. This course may be offered there.

Content provider Where to Start
Khan Academy https://www.khanacademy.org/math/linear-algebra
MIT OpenCourseWare MIT 18.06 Linear Algebra, Spring 2005 (34 lectures on YouTube)
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ (full course materials)

Why Linear Algebra?

It's a crying shame that all the Wikipedia pages for math seem to have been written by mathematicians: technically accurate, but incomprehensible to outsiders. Here's an explanation of what it is for someone who doesn't already know: Linear algebra shows you how to analyze a group of linear equations and determine their common solution(s), if any. It also teaches you about something called a "matrix," which is a grid of numbers that can take a vector as input and give another (possibly, but not necessarily the same) vector as output. The result may be a rotation, re-scaling, and/or re-location of the original vector. What it can do with one vector, it can do to all, which is why (for instance) video game programmers rely on linear algebra to perform rotations of images and put them in perspective. This same concept is absolutely key to being able to translate measurements from one coordinate system to another, as we will do with relativity.

Other Resources

Paul Falstad has a couple of nifty Linear Algebra apps at http://www.falstad.com/mathphysics.html (requires Java).