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Recently I've been trying to catch up in math, with a goal of trying to get to calculus as soon as possible. (I want to study Data Science, and calculus / linear algebra seems to be necessary for that kind of study.) I found someone on LW who agreed to provide me with some deadlines, minor incentives, and help if I need it (similar to this proposal), although I'm not sure how well such a setup will end up working.
Originally the plan was that I'd study the Art of Problem Solving Intermediate Algebra book, but I found that many of the concepts were a little advanced for me, so I switched to the middle of the Introduction to Algebra book instead.
The Art of Problem Solving books deliberately make you think a lot, and a lot of the problems are quite difficult. That's great, but I've found that after 2-3 hours of heavy thinking my brain often feels completely shot and that ruins my studying for the rest of the day. It also doesn't help that my available study time usually runs from about 10am-2pm, but I often only start to really wake up around noon. (Yes, I get enough sleep usually. I also use a light box. But I still often only wake up around noon.)
One solution I've been thinking of would be to take the studying slower: I'd study math only from 12-2, and before that I'd study something else, like programming. The only problem with that is that cutting my study time in half means it'll take twice as long to get through the material. At that rate I estimate it'll take approximately a year, perhaps a bit more, before I can even start Calculus. Maybe that's what's needed, but I was hoping to get on with studying data science sooner than that.
Another possible solution would be to try an easier course of study than the AoPS books. I've had some good experiences with MOOCs, so perhaps that might be a good route to take. To that end I've tentatively signed up to this math refresher course, although I don't really know anything about it. Or perhaps I could just CliffNotes my way through Algebra II and Precalculus, and then take a Calculus MOOC. I wouldn't get the material nearly as well, of course, but at least I'd be able to get to Calculus and move on with my data science studies from there. I could even do one of these alternatives while also doing the AoPS books at a slower pace. That way I could get to data science studying as soon as possible, and I'd also eventually get a more thorough familiarity with the material through the AoPS books.
What would you suggest?
One of my professors once mentioned that there's an upper limit to how much learning you can do in a sleep cycle [citation needed]. This is congruent with my experience, both before and after he mentioned that, so I tend to believe it. Personally, I tend to max out around 3-4 hours, so the times you're talking about seem reasonable. If you can restructure your work times, napping is a good strategy; I've talked to a few people who report getting through grad school by napping once they'd saturated their brain's capacity to learn new stuff.
Interleaved practice is good. This study had subjects practice finding the volume of unconventional geometric solids. One group clustered their practice; they found the volumes of a bunch of wedges, then a bunch of spheroids, etc. The other group had their practice problems mixed. On a final test, the former group got 20% right, and the latter group got 63% right. citation.
What this suggests is you should perhaps study programming and algebra at the same time, switching between the two fairly frequently. It feels like you're going slower, but, as the authors of the book emphasize, you're trading the illusion of learning for more durable learning.
The AoPS textbooks are really, really good. In fact, I'm pretty sure they're the only good algebra textbooks you're going to find, unless you count abstract or linear algebra; most textbooks at that level are mediocre. As luke_prog has mentioned, good textbooks are the usually the quickest and best way to learn new material. Quality learning takes time, and you're doing yourself no favors by spending that time looking for faster alternatives.