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Feb. 16th, 2005 04:49 amI don't know what I think of Algebra II anymore.
On the one hand, Galois theory, with its interplay between groups and fields, is elegant. To think, for instance, that there's a deep connection between the polynomial x^4 - 2 over the rationals and folkdancing... (the Galois group G(K/Q), where K is the splitting field over C of x^4 - 2, is isomorphic to D4, the group of symmetries of the square, whose relations to folkdance the Movement and Cognition people can tell you about).
On the other hand, I feel like I don't understand the stuff anymore. Compared to last semester, I don't think I have anywhere close to the level of gut comprehension of what's going on... the abstraction is way up and the structures we're studying are a lot more complicated. I don't know how this is going to work out; there'll be a midterm on ring/field theory in two weeks, about which I'm beginning to worry seriously. I don't think I've ever felt this lost in a class before -- except perhaps in second grade when I failed a written gym test on the rules and principles of baseball, because it was something I never really watched or played.
I suppose, if Algebra II is a complete disaster, I could still graduate in the Honors program if I switched my minor to chemistry. I should probably check with the chem department, but this presumably could be done by taking 2 semesters of Pchem and the spectroscopy seminar next year. I'll have studied quantum, stat mech, and thermo pretty thoroughly in physics by then, so I don't expect the academic portion of Pchem to be so bad, but the labs are the notoriously tough part of the course. Although after Orgo I, I swore I would never take a chem class again...
I really ought to try to get a couple of hours of sleep before I spend tomorrow morning
a) discussing quantum presentation with Catherine
b) getting last minute algebra help from Cheryl Grood
On the one hand, Galois theory, with its interplay between groups and fields, is elegant. To think, for instance, that there's a deep connection between the polynomial x^4 - 2 over the rationals and folkdancing... (the Galois group G(K/Q), where K is the splitting field over C of x^4 - 2, is isomorphic to D4, the group of symmetries of the square, whose relations to folkdance the Movement and Cognition people can tell you about).
On the other hand, I feel like I don't understand the stuff anymore. Compared to last semester, I don't think I have anywhere close to the level of gut comprehension of what's going on... the abstraction is way up and the structures we're studying are a lot more complicated. I don't know how this is going to work out; there'll be a midterm on ring/field theory in two weeks, about which I'm beginning to worry seriously. I don't think I've ever felt this lost in a class before -- except perhaps in second grade when I failed a written gym test on the rules and principles of baseball, because it was something I never really watched or played.
I suppose, if Algebra II is a complete disaster, I could still graduate in the Honors program if I switched my minor to chemistry. I should probably check with the chem department, but this presumably could be done by taking 2 semesters of Pchem and the spectroscopy seminar next year. I'll have studied quantum, stat mech, and thermo pretty thoroughly in physics by then, so I don't expect the academic portion of Pchem to be so bad, but the labs are the notoriously tough part of the course. Although after Orgo I, I swore I would never take a chem class again...
I really ought to try to get a couple of hours of sleep before I spend tomorrow morning
a) discussing quantum presentation with Catherine
b) getting last minute algebra help from Cheryl Grood
