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Jan. 23rd, 2009
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Two Weeks In
Jan. 23rd, 2009 09:43 amThe semester is two weeks old, and so far I'm pretty pleased with my classes.
The university has a number of "smart classrooms", equipped with networked computers and projectors. Given my deplorable artistic talents, I've found them useful, especially in my geometry classes. This semester, for the first time, my differential geometry class is in a smart room, and it's making quite a difference. Most of the calculations I need to do I can do by hand, but Mathematica does them faster and with less likelihood of error; also, the students (if they're paying attention) are getting some ideas as to how to use Mathematica effectively themselves. Being able to see the curves and (later on) surfaces we're studying should also be a big help. The students seem engaged; they're asking good questions and hanging around after class for more.
In the history of math class, also, I'm getting good questions from the students. I always set up group assignments, in which they spend one class period working together and then have a week to write up the results. This year I plan to do a bit more of that than previously, so I'm having to revamp the problem sets. There are twenty students, enough for five groups; the first sets of problems (one set per group), which I'll be handing out Monday, look like this:
It's tricky to put together different problem sets which are of comparable difficulty, but I think these are fairly close. I'm looking forward to seeing what they can do with them.
The university has a number of "smart classrooms", equipped with networked computers and projectors. Given my deplorable artistic talents, I've found them useful, especially in my geometry classes. This semester, for the first time, my differential geometry class is in a smart room, and it's making quite a difference. Most of the calculations I need to do I can do by hand, but Mathematica does them faster and with less likelihood of error; also, the students (if they're paying attention) are getting some ideas as to how to use Mathematica effectively themselves. Being able to see the curves and (later on) surfaces we're studying should also be a big help. The students seem engaged; they're asking good questions and hanging around after class for more.
In the history of math class, also, I'm getting good questions from the students. I always set up group assignments, in which they spend one class period working together and then have a week to write up the results. This year I plan to do a bit more of that than previously, so I'm having to revamp the problem sets. There are twenty students, enough for five groups; the first sets of problems (one set per group), which I'll be handing out Monday, look like this:
- Computation and Approximation: comparing the number of operations involved in multiplying two four-digit numbers a) by the traditional algorithm; b) by prosthaphaeresis; and c) by logarithms, and also trying out Viète's method of successive approximation.
- Astronomy: computations involving, among other things, the phases of Venus. (I haven't gotten to Galileo yet, but this will set up that incident nicely.)
- Calendars: examining the mathematics of the Gregorian reform, and comparing the Gregorian, Hebrew, and Islamic calendars.
- Cubic Equations: the techniques of Cardano et al.
- Commerce: computations involving currency exchange, interest, and the like.
It's tricky to put together different problem sets which are of comparable difficulty, but I think these are fairly close. I'm looking forward to seeing what they can do with them.
