Only tangentially related, sorry.
I am incredibly slow at computation (such that on every math test I have ever taken, it took me at least 3 times as long as the second slowest person in the class to finish).
I have tutored a fair amount, and my experience is that when someone says "I am incredibly slow at computation", the real issue is their lack of fluency. After you simplified your first thousand of trig expressions, when you look at the expression 1001, you already see most of the answer, all you have to do is write out the steps.
My model of a learner is that a person is a sort of Markov chain, where you try to go from the NO-SKILL state through the LEARNING state into the HAVE-SKILL state, also known as fluency or mastery.
Learning goes like this:
NO SKILL ----- learning rate ----> LEARNING- ---- internalization rate ----> HAVE SKILL
Forgetting goes like this:
HAVE SKILL ---- slow forgetting rate ---> NO SKILL <---- fast forgetting rate ---- LEARNING
People are extremely different in their learning and forgetting rates, which are also individually subject-dependent. Some learn a new skill quickly, others take awhile. Some retain 90% of the skill from one session to the next, others barely 1%. The internalization rate is less variable. As long as you manage to mostly keep in the LEARNING state for some period of time, you eventually get to the HAVE SKILL state.
The slow forgetting rate is well,,, slow for almost everyone, so it takes a long time to forget a well-mastered activity. You can probably do long division still (maybe after 5-10 min ramp-up), even if you haven't done any in a decade and it was a real pain to learn the first time.
The apparent learning and forgetting rates also depend on already having the skills similar to the one you are learning, like when building the jig-saw puzzle.
Anyway, my point is that you have likely misdiagnosed yourself. The symptom "incredibly slow at computation" could be a manifestation of one or more of the following:
If you figure out which of these apply to you, odds are you will no longer consider yourself "slow at computation", but, say, "requiring more frequent repetitions than average to master a new computational skill".
This model is, of course, rather simplified, as everyone appears to have their limits which they hit eventually for an advanced enough skill, but hopefully helpful enough for the initial diagnosis.
I think it's also useful to clarify the relevant meaning of "fluency" in a technical topic, so that we can talk about fluency in smaller topics and work the ratchet of getting more and more stuff towards "have skill", without juggling too much at once in the "learning" state and forgetting things before they are fixed.
The relevant sense of fluency is not about speed or quality of results or diffculty of the problems that can be solved, even though these things come with fluency, but about skill at answering most simple questio...
Not too long ago, I asked LessWrong which math topics to learn. Eventually, I want to ask for what the prerequisites for each of those topics are and how I should go about learning them. This is a special case of that.
I'm rereading the sequences and Eliezer seems to love E.T. Jaynes. As part of my rationality self-study, I want to work my way through his Probability Theory: the Logic of Science. What math topics do I already need to understand to prepare myself for this? I learned calculus once upon a time, but not fantastically well, and I plan to start by reviewing that.
Also,
Despite Eliezer's praise of the "thousand-year-old vampire", it there a better book to learn probability theory?
Does anyone want to learn this (or the other math from my post above) with me? I'd love to have a partner or maybe even a work group. Location is no obstacle. [Two caveats: 1. I'm busy with stuff and may not be able to get into this for a few months 2. I hard, but I am incredibly slow at computation (such that on every math test I have ever taken, it took me at least 3 times as long as the second slowest person in the class to finish). You might find that I go to slow for you.]