Tripping up on vector spaces

So it's been a month and this is only my second post. I had originally intended to give a brief description of the field of linear algebra, but I got horribly tripped up in two places. This last month I've been either struggling with these two things or else sticking my head into the sand and ignoring them.

1) Linear algebra is described everywhere as the study of "vector spaces." Well vector spaces strike fear into my heart the way "mathematics" seems to strike fear into the heart of half the country. When I went to college the first math course I took was multivariable calculus, which is filled with vectors, and, presumably, vector spaces. Princeton had three levels of multivariable: regular, advanced, and some kind of theoretical honors thing. I started out in the mid level course, and I had one of the few female professors in the department and one of the few who was a native speaker of English, which should have given me a big advantage.

Well I didn't do very well. I just couldn't process the images of planes and arrows and axes. I got panicked. The professor was so kind and spent a lot of time trying to help and encourage me, but in the end I dropped down a level into the regular course, which was still strenuous but was more routine. (This, for any of my old college friends, is where I had the professor who seemed to own a single pair of pants.)

Anyway, I think this story illustrates two things: that math panic happens to everyone, even people who were raised around math, and that different mathematical fields attract different people. I felt far more comfortable in other courses.

You may wonder here, though, why vector spaces show up in the definition of linear algebra, when I am talking about them in multivariable calculus. Well, this is where my jig is up. Heck if I understand it all yet. I'll get back to you on that.

2. The best way to explain anything is through an example, but to discuss a matrix-related example, I have to draw some matrices. I couldn't for the life of me figure out how to do it in Word. I might just scan some hand drawn ones and upload them.

So now you might never want to read any more posts here. You have seen how unqualified I am to lead you along the linear algebra path. Or, you may say, Hey! She doesn't know anything about this stuff either! And she, like me, is baffled by Word 2007! So maybe we are kindred spirits and I'll be able to understand what she is talking about!

Let's hope for option number two.