Mr. Hermann’s Update
Greetings! We’re still doing math, and still mostly (see below about alligators) happy, especially now that the weather is turning.
Calculus II just emerged victorious from a unit on differential equations, which is no mean feat. Differential equations is the math they use to weed out shaky engineers in college.
Calculus I has recently discovered the product rule, quotient rule and, as of yesterday, the chain rule. We did proofs for all of these in class. The proofs are optional, but are great fun for some students. Other students find the proofs somewhat less enjoyable; when I was proving the quotient rule, for example, and I writing the long result of particularly tricky step on the board, I heard a dismayed voice from behind me say, “Oh my God.” I was said in the same tone of voice as a person who has just stepped into his backyard for a quick dip in the pool only to discover that the pool was filled to the brim with alligators.
Precalculus is in the middle of a big review of graphing. It’s a tricky subject that, unfortunately, a lot of students reach precalculus not understanding. So we went back to the basics, and I’m seeing a lot of students with vastly improved graphing confidence.
Math for Mathematicians is all over the place, as usual. I’ve got one student who just derived the formula for the area of a torus (a hard calculus problem!), another who discovered a new solution to a tricky area fraction problem, several students who are new in second quarter but humming along at a good pace already, and some who are exploring Geogebra as a tool for creating technical drawings. And a dozen other things; everybody’s working at their own pace in their own style.
Have a good one!