I have sometimes liked to learn math from textbooks by doing all, or most, of the exercises. This can be really engaging when it is going well. A problem I have often run into is that I will get stuck. Sometimes talking about the problem unsticks it. Maybe writing about
An interesting thing about approximation is that it goes both ways. That is: If \(f(x)\) approximates \(g(x)\) under conditions \(Z\), then it's also true that \(g(x)\) approximates \(f(x)\) under conditions \(Z\). The most interesting example to me is approximating a discrete thing with a
I had a professor once who used little-o notation to describe error terms in matrix calculations. I had no context for this notation so had close to zero understanding of what he meant by any of these cryptic equations. I still wonder about this sometimes. These would look something like