I am currently struggling my way through Probability and Statistics by DeGroot. I was reading it because it seemed to be the best introductory textbook I can find for probability and yet it still seems like there could be better ways to show the material sometimes. I’ve learned a good bit from it but I am feeling worried about gaining and retaining useful knowledge.
My current worries are about trade-offs. I do a few of the exercises at the end of the chapter, some I get right some I get wrong. For those I get wrong I usually try to see what I messed up, some equations seemed convoluted enough I’m not sure where to start to get to the correct answer.
So I get some right and I get some wrong. Am I able to move on to the next chapter now? What internal confidence / skill level should I have to where I can move on to the next chapter without worrying I might not know enough, while also not doing every single problem in the book. I know I will use probability for almost everything I do once I start making Machine Learning models, can I use that knowledge that I will be reinforcing these concepts in the future to accept a lower confidence level in my skill now? At the cost of off-loading that extra development into the future? Will I even need it as much as I thought in the future?
I don’t have a perfect mind either, no matter what level of competency my skills will decay over time unless reinforced through continuous practice, which I think will happen early-mid next year since that is when I plan to start going back into machine learning model creation. I assume more competency will decay slower / need less to time to get back to initial level. But any extra time put into building competency now leaves less time for building competency in programming.
So I am frustrated trying to find the balance between obtaining better confidence in skill vs time spent to obtain that confidence. If anybody else on LessWrong has self studied math books I would love your answer to this problem. I will continue to think about it as well, but it has been a nagging me for a while.
I am currently struggling my way through Probability and Statistics by DeGroot. I was reading it because it seemed to be the best introductory textbook I can find for probability and yet it still seems like there could be better ways to show the material sometimes. I’ve learned a good bit from it but I am feeling worried about gaining and retaining useful knowledge.
My current worries are about trade-offs. I do a few of the exercises at the end of the chapter, some I get right some I get wrong. For those I get wrong I usually try to see what I messed up, some equations seemed convoluted enough I’m not sure where to start to get to the correct answer.
So I get some right and I get some wrong. Am I able to move on to the next chapter now? What internal confidence / skill level should I have to where I can move on to the next chapter without worrying I might not know enough, while also not doing every single problem in the book. I know I will use probability for almost everything I do once I start making Machine Learning models, can I use that knowledge that I will be reinforcing these concepts in the future to accept a lower confidence level in my skill now? At the cost of off-loading that extra development into the future? Will I even need it as much as I thought in the future?
I don’t have a perfect mind either, no matter what level of competency my skills will decay over time unless reinforced through continuous practice, which I think will happen early-mid next year since that is when I plan to start going back into machine learning model creation. I assume more competency will decay slower / need less to time to get back to initial level. But any extra time put into building competency now leaves less time for building competency in programming.
So I am frustrated trying to find the balance between obtaining better confidence in skill vs time spent to obtain that confidence. If anybody else on LessWrong has self studied math books I would love your answer to this problem. I will continue to think about it as well, but it has been a nagging me for a while.