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.

I was trying to think of what a more rational response to this, since I agreed with your points and also used a very similar trick. I then came up with 'The rational thing to do is to say you agree, upvote, and then get back to the other tasks you have, rather than spending an hour worrying about a perfect response, which sounds a lot like the very social anxiety she was trying to avoid.'

I agree with your post. Upvoted.

Wasting time fixing a problem rather then starting a fresh i.e. biology/genetics - rather then just ordering in new primers(oligos), reagents(Taq, nucleotides etc) wasted a few weeks trying to find out which specific component was faulty. All the components are not very expensive while time tends to be - especially for scholarships.

I'm not as interested as others in effective altruism, although that's certainly a secondary goal of mine. My primary goal in a career was to optimize happiness by focusing on what I enjoy and am good at, namely research and deep thinking. I didn't want to go for academia for many of the reasons you mention. Instead I'm currently shooting for data science. My reasoning is as follows:

• I enjoy programming, although not as much as theoretical research.
• There are plenty of data science or related jobs available from the looks of it. And the pay is very good, so although that's not a primary goal of mine it's certainly a good bonus.
• I'm making a somewhat educated guess that there are research-related jobs available for people with a data science background. A lot of research these days seems to use data analysis / big data as an input (especially in the social sciences, which is one of my favorite areas of study), so I'm hoping to use these skills to get my foot in the research door.
• There are enough large data sets publicly available, and there seems to be enough meaningful research problems out there that use that data, that if all else fails I could probably use data science to do meaningful research as a hobby.
• My secondary idea was to go for a career as a statistician. Good statistics are crucial for well-designed studies, and many scientists hire statisticians to help with their research. So again I could maybe hope to use statistics to get my foot in the research door, or at least to do research on the side. I'm still keeping statistics open as a possibility, but in any case data science and statistics have a very large amount of overlap, so a lot of the areas of study are the same.
• If I change my mind and decide to go into academia after all, I can always do so in the areas of data science or statistics or some area related to those, and my previous learning will help me a great deal.

This is all pretty theoretical - I'm still in the very early stages of studying for any career. Also, I could probably have researched my options a bit better. I did talk to some people who do data analysis at least.

What do others think of my analysis?

Ask me almost anything. I'm very boring, but I have recovered from depression with the help of CBT + pills, am a lurker since back from the OB days and know the orthodoxy here quite well, started to enjoy running (real barefoot if >7 degrees Celsius) after 29 years of no physical activity, am chairman of the local hackerspace (software dev myself, soon looking for a job again), and somehow established the acceptance of a vegan lifestyle in my conservative familiy (farmers).

I am under the impression that a lot of those Brain Training games you may find won't work as claimed i.e. those (Luminosity etc) that claim working memory improvement --> intelligence improvement/cognitive improvement.

Here is a relevant meta-analysis of such (haven't been able to get an original copy have just read through this article

Tis a shame cause I watched the same program and got excited but decided to investigate before I paid up for it.

I implemented the Secret Weapon--a productivity system that combines Evernote and GTD--and have been making use of it quite effectively. I also have kept up on my recently started gratitude journal.

In other news, Evernote is simply awesome.

Use the amount of unobvious subtleties involved in a subject you know very well to remind you of the unobvious subtleties that are probably present in the subject you don't know very well.

Re exercise: Good point, but I'd emphasize making a strong habit over doing it a lot. Spending a lot of time is easier during summer, but harder to carry over. Sure, do that, but also make sure you have a 15 minute routine, say, that you do every morning. Even a five minute routine isn't to be sneezed at, if you're doing bodyweight exercises like pushups.

Doing a stretch and 5 minutes of exercise during study breaks is worth a try. Could help avoid some of the physical problems with long hours of computer use. (Press down with your whole hand during pushups - strong fingers, hands and arms will help avoid RSI.)