Advice/help needed: how do I study math by doing lots of exercises when there's nobody there to clue me in when I get stuck?
It's a stupid problem, but because of it I've been stuck on embarrassingly simple math since forever, when (considering all the textbooks and resources I have and the length of time I've had it as a goal) I should have been years ahead of my peers. Instead, I'm many years behind. (Truth be told, when performance is tested I'm about the same as my peers. But that's because my peers and I have only struggled for a passing grade. That's not what my standard of knowledge is. I want to learn everything as thoroughly as possible, to exhaust the textbook as a source of info; I usually do this by writing down the entire textbook, or at least every non-filler info.)
There is a great disparity between the level of math I've been acquainted with during my education, and the level of math at which I can actually do all the exercises effortlessly. In theory by now I'm well into undergraduate calculus and linear algebra. In practice I need to finish a precalculus exercise book (tried and couldn't). While I'm learning math, I constantly oscillate between boredom ("I'm too old for this shit" ; "I've seen this proof tens of times before") and the feeling of getting stuck on a simple matter because of a momentary lack of algebraic insight ("I could solve this in an instant if only I could get rid of that radical"). I've searched for places online where I could get my "homework" questions answered, but they all have rather stringent rules that I must follow to get help, and they'd probably ban me if I abused the forums in question.
This problem has snowballed too much by now. I kept postponing learning calculus (for which I've had the intuitions since before 11th grade when they began teaching it to us) and therefore all of physics (which I'd terribly love to learn in-depth), as well as other fields of math or other disciplines entirely (because my priority list was already topped by something else).
I've considered tutoring, but it's fairly expensive, and my (or my tutor's) schedule wouldn't allow me to get as much tutoring as I would need to - given that I sometimes only have time to study during the night.
Do any LessWrongers have resources for me to get my questions answered? Especially considering that, at least at the beginning until I get the hang of it, I will be posting loads of these. Tens to hundreds in my estimation.
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Is this a case of multiple discovery?[1] And might something similar happen with AGI? Here are 4 projects who have concurrently developed very similar looking models:
(1) University of Toronto: Unifying Visual-Semantic Embeddings with Multimodal Neural Language Models
(2) Baidu/UCLA: Explain Images with Multimodal Recurrent Neural Networks
(3) Google: A Neural Image Caption Generator
(4) Stanford: Deep Visual-Semantic Alignments for Generating Image Descriptions
[1] The concept of multiple discovery is the hypothesis that most scientific discoveries and inventions are made independently and more or less simultaneously by multiple scientists and inventors.
How meaningful is the "independent" criterion given the heavy overlaps in works cited and what I imagine must be a fairly recent academic MRCA among all the researchers involved?