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Noodling on Mathematics while I take a break from reading about the annihilator method of undetermined coefficients (there's a mouthful - don't click the link if you're scared ;-)), I have come up with two most likely unoriginal theories:
Sliding Window Memory
As one learns more advanced information regarding a particular topic, earlier, fundamental information on that topic is forgotten. Not completely, but recall is less likely or at least more error-prone. Knowing that, especially as I progress through mathematics education, I have a higher tendency to make sign and/or arithmetic errors, I think I have this to some degree. Watching the professor I have for this summer class, he has it as well. He's much more educated in mathematics, and makes more algebra mistakes than I do, providing evidence for my theory that some subject memory acts as a sliding window - the farther along one progresses, the more earlier stuff drops off the tail end. :-)
F*cking Magic
I've always jokingly referred to mathematics techniques I don't understand as being FM. As I learn more advanced techniques (and, from what I've seen, even what I'm learning now is hardly advanced by comparison to what's out there), I have enough evidence in my opinion not to stop regarding such things as FM but rather to confirm them as such. For example, not to bore or cause headaches with details, but the topic I'm currently reading for class seems to me to be just a way some folks in the 1800s or since developed to play with the numbers to get a solution to some ugly calculus equations they couldn't work out otherwise. Yes, they follow mathematical rules, but I think a lot of these techniques come from a lot of playing around, seeing what works, and developing tricks (only be sure always to call it, please, "research"[1]). Sure, it works. And I get it. But it's still FM.
Anyway, back to it...
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[1] - From the song Lobachevsky by Tom Lehrer.
Sliding Window Memory
As one learns more advanced information regarding a particular topic, earlier, fundamental information on that topic is forgotten. Not completely, but recall is less likely or at least more error-prone. Knowing that, especially as I progress through mathematics education, I have a higher tendency to make sign and/or arithmetic errors, I think I have this to some degree. Watching the professor I have for this summer class, he has it as well. He's much more educated in mathematics, and makes more algebra mistakes than I do, providing evidence for my theory that some subject memory acts as a sliding window - the farther along one progresses, the more earlier stuff drops off the tail end. :-)
F*cking Magic
I've always jokingly referred to mathematics techniques I don't understand as being FM. As I learn more advanced techniques (and, from what I've seen, even what I'm learning now is hardly advanced by comparison to what's out there), I have enough evidence in my opinion not to stop regarding such things as FM but rather to confirm them as such. For example, not to bore or cause headaches with details, but the topic I'm currently reading for class seems to me to be just a way some folks in the 1800s or since developed to play with the numbers to get a solution to some ugly calculus equations they couldn't work out otherwise. Yes, they follow mathematical rules, but I think a lot of these techniques come from a lot of playing around, seeing what works, and developing tricks (only be sure always to call it, please, "research"[1]). Sure, it works. And I get it. But it's still FM.
Anyway, back to it...
----
[1] - From the song Lobachevsky by Tom Lehrer.
