Teeth and Talks
Jul. 22nd, 2004 06:45 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowBen got his teeth cleaned today; I dropped him off at about 7:30 and then picked him up around 5:00. He was so anxious to get out of that place! (They tried to give me more antibiotics for him, until I pointed out that I still had 24 pills.) He seems chipper, and he didn't have any trouble eating a Milkbone, so his teeth can't be hurting him too much. I will be giving him painkillers for a few days, along with the antibiotics. Murphy's turn will be next Tuesday.
J, the poetry-loving student I mentioned a while back, gave his Masters presentation today. It was quite an interesting talk; he's been studying the mathematics of leukemia chemotherapy, aiming at determining which treatment methods - specifically, the timing and dosage of the drugs - is most effective. Of course, he had to work with some simplifying assumptions, so his work isn't immediately applicable. But what he showed was that (given those assumptions) the best treatments are what are called "bang-bang" methods, in which one alternates high dosages of the cytotoxin with periods of no drug at all. There are theoretical and practical reasons for hoping for that to be true. On the theoretical side, if it turned out that other methods were preferable, it would be much harder to determine exactly which methods were best (given the current state of mathematical technique); pragmatically, other methods would simply be harder to implement (given the current state of medical technology), since they would require more-or-less constant monitoring of the state of the patient's bloodstream. The next step is to reintroduce some of the complicating factors that he sloughed over, but that's doctoral or professorial work.
Last night, I discussed the sea-change that mathematics underwent in the 19th century, with the increased stress on rigor and the great expansion of abstraction. I traced through how these forces acted in geometry (the emergence of non-Euclidean geometry, the proliferation of exotic geometries after the time of Riemann, and the reformulation of Euclidean geometry by David Hilbert) and in analysis (the clarification of the limit concept by Cauchy and Weierstrass and the reinterpretation of the real numbers in terms of Cauchy sequences and Dedekind cuts); I began doing the same with algebra, but only got as far as the discovery of the quaternions by Hamilton before we ran out of time. Next week, I'll finish off algebra and start in on the beginnings of mathematical logic. I love talking about this particular period - being able to show students the broad sweep of things, rather than focusing on the achievements of this mathematician or that one (fascinating though they may be). But I'm running out of time - only one more week, and I haven't even made it to the 20th century. It would be dismal to let students out of a class on the history of mathematics without letting them hear the name of Goedel.
J, the poetry-loving student I mentioned a while back, gave his Masters presentation today. It was quite an interesting talk; he's been studying the mathematics of leukemia chemotherapy, aiming at determining which treatment methods - specifically, the timing and dosage of the drugs - is most effective. Of course, he had to work with some simplifying assumptions, so his work isn't immediately applicable. But what he showed was that (given those assumptions) the best treatments are what are called "bang-bang" methods, in which one alternates high dosages of the cytotoxin with periods of no drug at all. There are theoretical and practical reasons for hoping for that to be true. On the theoretical side, if it turned out that other methods were preferable, it would be much harder to determine exactly which methods were best (given the current state of mathematical technique); pragmatically, other methods would simply be harder to implement (given the current state of medical technology), since they would require more-or-less constant monitoring of the state of the patient's bloodstream. The next step is to reintroduce some of the complicating factors that he sloughed over, but that's doctoral or professorial work.
Last night, I discussed the sea-change that mathematics underwent in the 19th century, with the increased stress on rigor and the great expansion of abstraction. I traced through how these forces acted in geometry (the emergence of non-Euclidean geometry, the proliferation of exotic geometries after the time of Riemann, and the reformulation of Euclidean geometry by David Hilbert) and in analysis (the clarification of the limit concept by Cauchy and Weierstrass and the reinterpretation of the real numbers in terms of Cauchy sequences and Dedekind cuts); I began doing the same with algebra, but only got as far as the discovery of the quaternions by Hamilton before we ran out of time. Next week, I'll finish off algebra and start in on the beginnings of mathematical logic. I love talking about this particular period - being able to show students the broad sweep of things, rather than focusing on the achievements of this mathematician or that one (fascinating though they may be). But I'm running out of time - only one more week, and I haven't even made it to the 20th century. It would be dismal to let students out of a class on the history of mathematics without letting them hear the name of Goedel.
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no subject
Date: 2004-07-22 05:51 pm (UTC)Alec says that you should pass on his full support to your student, J., regarding his research into the efficacy of leukemia treatment regimens (OWTTE). And a BIG "me, too" to that! WJW (Work, J, Work!)
Interesting. Hearing his Master's presentation now, you probably have a different perspective on his topic choice now, than you would have 9 months ago, what?