Preserved Topic: The Use of Linear Algebra

Ok, today I started the the second half of my summer schooling.

One of the classes I am taking is Linear Algebra, my teacher seems to be good, but she is only a mathematician. She is able to tell me that this knowledge will benifit me in the computer industry, but I was wondering if anyone knew how.

I am at a lose with it. I can see how it would work for circutry, but I am not attempting to be a hardware god, leave that to the engineers.

So any ideas anyone? is it all just a waste of time (wouldn't surprise me)?


www.warmage.org

I've taken algebra, but not "linear" algebra, what's that about?

Your teacher's most likely right... I've found many things that I learned in the past couple of years (algebra & pre-calculus) very helpful, even on web pages: trig functions, rotation, graphs of functions, etc. If it's not directly helpful, it will probably be necessary to know to learn what *is* helpful.

From what I know so far, it is all about finding intersection points between lines. I think that is a bit simplistic, but I only know the basics, but in the class we work in up to 5 dimensions.

I can't even think in 4 dimensions, but I am told that it has real value in different perspectives. As in current running through different circuts, resistance, and the like.

It is really basic math, compunded to make it a little tricky. In linerar algebra for instance, there are no trig functions with a variable, no variables raised to exponents, no varibles under a radical, no variables multiplied or divided by another variable; hence linear, because anything else would create a fuction that is not linear. So that basically leaves us with multiplication and addition of real numbers.

But I have noidea how I would use it for computers... =[


www.warmage.org

Oooh, sounds like geomitry in multiple dimensions. Yeah, that's really important. When you learn enough about things like intersections, that will help... darn, i can't put my finger on how, but it does. Trust me on this! =)

If you plan on ever working with 3D graphics, this knowledge is essential. My skills in this area are limited only by my mathematical knowledge.

I have yet to take linear algebra, so I don't know exactly what it's about, but I took multi-variable calculus first, and they are supposedly the same level class. Although I heard linear algebra is more hard-core. (Multivar calc was easier than Calc 2 also, imho).

So I would be inclined to assume that the word linear does not mean working with strictly straight lines. I could be wrong on this, but I really don't see how they could make a whole semester class out of straight lines and not extrapolate to simple curves and such.

Regardless, high level math can help you in almost anything you do if you internalize the knowledge. Don't just learn how to do the problems, but strive to learn the proofs and what they mean, because it affects your thought patterns. You suddenly gain a deeper understanding of the way many things which you never thought had anything to do with math work. Solving the problems on paper will probably not do much for you in the graphics industry unless you plan on designing your own tools, but the thought processes you develop will.

BTW - I also recommend taking drawing and painting classes, as learning how to represent 3d things two-dimensionally has infinite application to computer graphics.

Orthogonal projections, inner product spaces and Fourier Series have a lot of applications in engineering and scientific fields. Some of these are more advanced linear algebra concepts that have to do with approximation problems. Hope that helps <img border=0 align=absmiddle src="http://www.ozones.com/forum/smile.gif">

CP

My best friend is a teacher and we've had a similar discussion several times about when he tries to convince kids why they should learn certain subjects. It's not just about the facts or the formulas--it's about learning problem-solving skills. It's about traning your mind to think in different directions, to take paths other than the obvious one to accomplish your goals. I'm no programmer, but I would imagine that although a particular type of math would not be used directly in technical computer work, the thinking skills developed in studying any kind of math would help in thinking through computer-related situations.

Of course, when my friend tries to to convince the kids that they should learn algebra or chemistry even though they all plan to be basketball players, they usually don't listen, anyway.

The book says that it has direct corrolation to web graphics imagine that...

I didn't really look to much into it, but it has a lot to do with 3d works, and perspective.


www.warmage.org

Can't really help you, I've only gotten to Calc 2, I'm going to be a junior in high school, just don't ask why I'm like 5 years ahead in math, ok? Seems like calc bc should be sufficient for web applications, although I haven't worked extensively with the higher-end 3d programs. Linear algebra sounds interesting, I might have to buy a book on that!