I was going through mathematics tonight, and I realized that multiplying matrices tends to be similar to multiplying in numerical algebra, the famous FOIL. Using vectors, the multiplication of (x+y)(x+y) becomes x^2+2xy+y^2 in two dimensions. It’s as much a discovery as vectors themselves. Nowhere in the book of linear algebra does it show geometrically.

Meanwhile, I’ve been going through the advanced placement of calculus, and I’ve been finding nothing of what I had at Penn State. It only proves what I wrote about teaching mathematics – missing pieces of mathematics becomes critical in higher courses.

My overall view of mathematics reflects the struggles I’ve had with both subjects and the rules of life. Mainly it’s not spending the time and reviewing the subject.

I went on Zach Star on what linear algebra and its matrices mean. He used a circuit to illustrate the nullspace, which caused a flashback to the incident I had in eighth grade. It was a simpler circuit, but it appeared broken. I figured it could still work, which seems to match a nullspace.