There's a lot of familiar mathematics at the beginning of my calculus book, including the aforementioned set theory. It is as I remembered it from my "new math" childhood, where for some incomprehensible reason, someone decided that seventh-graders should learn set theory. What I remember most are the Venn diagrams, named after the nineteenth century British mathematician John Venn who worked them out as diagrams illustrating sets and outcomes of logic problems. For an arty kid like me, anything that made a picture was more interesting than words or numbers, so that's what stayed in my mind. I've always thought that this was a failing of mine, because words and numbers are what really count in this world. Yet I am constantly told by both scientists and mathematicians that pictures and diagrams are immensely important in thinking about science. I still have the nagging feeling that they are somehow less macho and heroic than rigorous, abstract numbers and letters.

To get back to the Venn diagrams: They existed in many cultures long before John Venn's name got put on them. The intersecting circles are known in Hellenistic and Christian lore as the vesica piscis, the fish-shaped form created by the intersecting arcs of the circles. As the learned articles in Wikipedia convey, there is a wealth of non-Christian symbolism to it as well as the more familiar Christian "fish" symbol. The intersection, for Christians, symbolizes the character of Jesus Christ, who has both a divine and human nature, rather than just one or the other. Thus set theory supports theology.

Set theory leads in to inequalities, which I did a fairly long section on back in 2002 when I was re-learning algebra. These are all tricky, with their solutions switching negative and positive in many complex ways, as well as being either closed (including their terminal number) or open (up to but not including the cited number). I remember coloring in a lot of graphs back then, and I was pleased that I still remember how to solve algebraic equations, whether for equality or inequality.

I don't pretend to remember everything, or be able to solve everything as if I had just finished studying it. Back when I was re-learning algebra, I had a strict "no-mistake" rule. I also forced myself to solve every problem in the sets at the end of the chapter. If I couldn't solve it, I kept it until I could ask for help. I should be able to correctly solve anything the book figuratively threw at me. In fact, if I were really a "math whiz," I should be able to solve anything any problem set contained, right away without review, as long as it was something I had already learned. After all, if I were an aspiring high school student, any one of these could be on the upcoming test. And my marks on the upcoming tests, one after another, would help to determine whether I had any future as a scientist. Get too many wrong, and no high-powered, prestigious college or graduate school for me, and no career in science no matter how much I loved it.

But I'm not an aspiring high school student or potential graduate student, far from it. So does it matter whether I get the problems right the first time? For calculus, I've adopted a more lenient, and probably lazier, approach. It's also more pragmatic. I am not in formal school, and face-to-face contact with teachers is difficult and rare. Since I have the teacher's manual for this book, I have the resource to go back to in the absence of a live professor, even at 3 AM. My policy for calculus is to do as many problems as I can, and try to get them right. Then I will refer to the manual and figure out why I got them wrong. After I do a respectable number of them right, then I can move on. There will not be a test.

Posted at 8:38 pm | link