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I haven't had many good math teachers, the one that I did was some poor frazzled adjunct who had to run over to CMU after he was done teaching my class at Pitt.

I haven't had many good math teachers, the one that I did was some poor frazzled adjunct who had to run over to CMU after he was done teaching my class at Pitt. (I'm an alumni.) The textbook isn't the barrier, it's the end of chapter activities. If I decided to learn, say, geometry, something that wasn't really taught much in my middle school, I'd probably do Khan academy or try to find a set of finished problem sets. (When you remove the academic dishonesty angle, the real issue with math courses is it's difficult to craft a math question, so then you need to keep the answer and steps leading to it secret lest folks memorize them for an A. That issue disappears completely if you adopt a more realistic model like "can you figure out which algorithm to use on Wikipedia, search out if it's already used in a common language like Python, then import your data in a simple format like a .csv and use the trustworthy code you found. - Greg.

shanusmagnus 4y ago
I think this is a huge part of it. Realistic hacky workaround is to get one of those "1000 calculus problems solved" books, and work through the examples -- there's a zillion books for math topic X online, you can read through the relevant parts of a few. But your progress / insight will be in proportion to the problems you actively engage with. I've often thought that a really pedestrian, but possibly world-shaking, application of AI would be generating math problems (and solutions) appropriate to someone's state of knowledge. Such a thing would make problem-solving practically as fun as a game, at least for many people. Imagine the consequences of a generation of kids obsessive solving of interesting multi-area math / engineering problems the way recent kids played Minecraft or whatever. (Q: Is there anything vaguely like this in the world now?)
- dontbenebby 4y ago
  If you know a good resource on learning calculus on your own, I'd add it to my todo list. Every algorithm I reverse engineer or develop has been very... I think linear is the phrasing? No curves? >I've often thought that a really pedestrian, but possibly world-shaking, application of AI would be generating math problems (and solutions) Maybe read up on plagarism detectors? I can't recall the title but there was one some people used in grad school to spot code re-use that was engineered much differently from Turnitin. (Play around with the latter, and notice how the "plagarism" score jumps when you tell it to ignore what you cited. I had way too many stories told to me of professors who'd start the academic misconduct proces because they forgot to do that, paired with witnessing some egregious academic misconduct that I'll simply never be able to get away with.) - Greg.

shanusmagnus 4y ago

I think this is a huge part of it. Realistic hacky workaround is to get one of those "1000 calculus problems solved" books, and work through the examples -- there's a zillion books for math topic X online, you can read through the relevant parts of a few. But your progress / insight will be in proportion to the problems you actively engage with. I've often thought that a really pedestrian, but possibly world-shaking, application of AI would be generating math problems (and solutions) appropriate to someone's state of knowledge. Such a thing would make problem-solving practically as fun as a game, at least for many people. Imagine the consequences of a generation of kids obsessive solving of interesting multi-area math / engineering problems the way recent kids played Minecraft or whatever. (Q: Is there anything vaguely like this in the world now?)

dontbenebby 4y ago
If you know a good resource on learning calculus on your own, I'd add it to my todo list. Every algorithm I reverse engineer or develop has been very... I think linear is the phrasing? No curves? >I've often thought that a really pedestrian, but possibly world-shaking, application of AI would be generating math problems (and solutions) Maybe read up on plagarism detectors? I can't recall the title but there was one some people used in grad school to spot code re-use that was engineered much differently from Turnitin. (Play around with the latter, and notice how the "plagarism" score jumps when you tell it to ignore what you cited. I had way too many stories told to me of professors who'd start the academic misconduct proces because they forgot to do that, paired with witnessing some egregious academic misconduct that I'll simply never be able to get away with.) - Greg.