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I second the grind. There's not really a shortcut... like lifting weights or practicing scales/rudiments. I returned to grad school at 27 for math and had trou

by dls2016 5y ago

I second the grind. There's not really a shortcut... like lifting weights or practicing scales/rudiments. I returned to grad school at 27 for math and had trouble passing qualifying exams. I ended up using spaced-repetition to memorize large sections of books and old questions. I had previously shunned memorization... but coupled with focused practice it is a powerful tool. Memorizing forces you to distill the material and patterns to their essence and allows you to recognize the patterns in new situations.

300bps 5y ago
There's not really a shortcut... like lifting weights And just like lifting weights, you will lose it when you stop doing it. I remember doing the CFA program which is math and formula heavy. I had hundreds of formulas memorized. I couldn’t tell you the formula to calculate the standard deviation of a portfolio of three assets now if my life depended on it.
- solaxun 5y ago
  This is my main qualm with testing as a means of validating understanding. If you truly understand a topic, you will probably pass a test on it. However passing a test most definitely does not guarantee understanding. I remember very, very little from the CFA exams (passed L3 about 10 yrs ago), because it tested surface level knowledge of an incredibly broad array of subjects. Far too broad to allow a deep-dive in any one thing. At the time, I could fit a bunch of formulas in my head and regurgitate them on command, but it was like filling up a leaky bucket. I had to load that sucker up and run into the exam center before it poured out. IMO testing well is it's own skill, and has little to do with understanding a topic. Understanding is when you've forgotten all the stuff you've memorized, but you can work your way back to a solution from first principles. I think the only way to get to that point is genuine interest and sustained study.
- wyclif 5y ago
  And just like lifting weights, you will lose it when you stop doing it While this is 100% true, I hate putting it that way because it makes weight training (and mathematics) sound like drudgery. The way I like to think about it is that if you want to stay strong, you have to push against resistance on a constant basis. It's the same thing with math. You have to exercise that part of your brain with algebraic resistance.
HumanReadable 5y ago
I agree there are no shortcuts, but just like the scales will come much more easily to someone naturally gifted at music, so will algebraic operations to someone gifted at math. We can all improve our abilities, but those not gifted has a much steeper hill to climb.
Py-o7 5y ago
I am a big fan of the working out analogy. In all cases you need to have a decent plan then execute-- basically this means showing up and putting in the work. If you do it right it should be a bit painful at times. And just like working out some people will progress more rapidly than you and have an easier time at it. So what? As long as your goal isn't to 'place' at the elite level, this is irrelevant. You really just need to show up and embrace the struggle. (For elite level tasks including grad school, its a bit more involved.)

300bps 5y ago

There's not really a shortcut... like lifting weights And just like lifting weights, you will lose it when you stop doing it. I remember doing the CFA program which is math and formula heavy. I had hundreds of formulas memorized. I couldn’t tell you the formula to calculate the standard deviation of a portfolio of three assets now if my life depended on it.

solaxun 5y ago
This is my main qualm with testing as a means of validating understanding. If you truly understand a topic, you will probably pass a test on it. However passing a test most definitely does not guarantee understanding. I remember very, very little from the CFA exams (passed L3 about 10 yrs ago), because it tested surface level knowledge of an incredibly broad array of subjects. Far too broad to allow a deep-dive in any one thing. At the time, I could fit a bunch of formulas in my head and regurgitate them on command, but it was like filling up a leaky bucket. I had to load that sucker up and run into the exam center before it poured out. IMO testing well is it's own skill, and has little to do with understanding a topic. Understanding is when you've forgotten all the stuff you've memorized, but you can work your way back to a solution from first principles. I think the only way to get to that point is genuine interest and sustained study.
wyclif 5y ago
And just like lifting weights, you will lose it when you stop doing it While this is 100% true, I hate putting it that way because it makes weight training (and mathematics) sound like drudgery. The way I like to think about it is that if you want to stay strong, you have to push against resistance on a constant basis. It's the same thing with math. You have to exercise that part of your brain with algebraic resistance.

HumanReadable 5y ago

I agree there are no shortcuts, but just like the scales will come much more easily to someone naturally gifted at music, so will algebraic operations to someone gifted at math. We can all improve our abilities, but those not gifted has a much steeper hill to climb.

Py-o7 5y ago

I am a big fan of the working out analogy. In all cases you need to have a decent plan then execute-- basically this means showing up and putting in the work. If you do it right it should be a bit painful at times. And just like working out some people will progress more rapidly than you and have an easier time at it. So what? As long as your goal isn't to 'place' at the elite level, this is irrelevant. You really just need to show up and embrace the struggle. (For elite level tasks including grad school, its a bit more involved.)