There was a discontinuity in my math studies during year 2007, for various reasons, but in 2008 I have been once again working on math though not as much as before. I did a review of basic trigonometry, which I needed, and having found that I could manage at least the simpler trigonometric identity problems, I could return to calculus.

One of the most useful books for me is "Calculus for Dummies" by Mark Ryan. I also have the companion "Calculus Workbook for Dummies." I am not a dummy and in fact these books are not at all made for "dummies." What they do is explain in more detail, and with more worked out problems, what the teacher doesn't have the time to do. Or if you are not in a class at all, as with me, the book is the only teacher I have (unless I try to reach one of my Friendly Mathematicians, all of whom live in different cities from me).

Much of first year calculus is, as other students have told me, lots of heavy-duty algebra. I was fascinated and relieved to learn some basic algebra processes from the book, that I never learned in my own studies, such as how to remove fractions from the numerator of an expression. There are some basic calculus "identities" that the book presents which were not all discussed in my previous textbook, which also weighed about twice as much as "Calculus for Dummies." This does not mean that the "Dummies" book is lightweight.

I am back in the land of limits, those calculus essentials which occur everywhere, even in real life. In mathematics, they are safely graphed on paper rather than expanding into the three-dimensional world of traffic. Are calculus limits also aesthetic limits? It is possible for a person in the arts to have such demanding, high, and elite standards for a work of art, that nothing can ever be done nowadays that would be worthy of the name of "art." This equation of perfection can never be satisfied, and a working artist must then toil under a sense of perpetual inadequacy when faced with the unyielding graphed standard. But adopting this mathematical attitude to aesthetic work is like finding that place in some functions where the output hits a discontinuity. The graphed line loses itself in "positive" or "negative" infinity, an abyss which defeats any purpose, any understanding, and any possibility of progress.

Posted at 2:56 am | link