5 ms·

For someone self-studying mathematics: Do the exercises. Especially the hard ones. Struggle for hours. Don’t worry about solution manuals. It should be painful.

d4rkp4ttern 5y ago
Along the same lines: in a math textbook or math-heavy paper, try to prove the Lemmas or theorems yourself, when it’s sensible to attempt it. Probably more suitable in a textbook where they build up to a larger theorem starting from smaller lemmas — try to prove them yourself. Even if you don’t prove them the first time, on a re-read you can try to prove it yourself, as a way to test your understanding, and of course this also deepens your understanding.
caffeine 5y ago
This is good advice. But for me, the hours’ struggle is more useful if not contiguous. I get the best results from struggling with a given problem for no more than 1 hour continuously, and then going away and coming back sometime after my next sleep. By struggling I mean “not making visible progress” - if progress is happening then just keep rolling.
- mettamage 5y ago
  This sounds like how I approach leetcode. Leetcode feels a bit like math to me anyways. Coding isn't the hard part, understanding the algorithm in conjunction with the data structures is.
  - username90 5y ago
    Coding is the hard part if you are bad at coding but good at maths and algorithms. Writing accurate code for solving a hard problem in under 30 minutes requires you to be really good at coding.
nomy99 5y ago
This I think is the same thing as someone saying at the gym, don't stop until it hurts. People get injured and then never go to the gym again. How about look at the solution, understand the parts. Solve the problem. Revisit, revisit, revisit. This helped me breeze through engineering and also helped me professionally.
- username90 5y ago
  That is how people learn how to pass tests instead of learning the material. Passing tests is important in college, but if you want to learn on your own it doesn't matter.
  - deleted 5y ago
    [deleted]
  - nomy99 5y ago
    No. There are optimized paths to reach the same understanding
    - username90 5y ago
      Yes, but I'd argue that the path you took was a very suboptimal path to reach the same understanding since you almost surely didn't reach it. So now you'd have to redo almost everything in order to reach the same goal making it a very huge waste of time. Of course I cannot be sure of that, but I have seen so many people who learned the way you did and they had really poor understanding. In my experience only the people who try to challenge themselves actually gets there. Passing math classes requires almost no understanding at all btw, even getting good grades in them doesn't.
      - nomy99 5y ago
        No. You are over complicating things.
      - rattlesnake45 5y ago

d4rkp4ttern 5y ago

Along the same lines: in a math textbook or math-heavy paper, try to prove the Lemmas or theorems yourself, when it’s sensible to attempt it. Probably more suitable in a textbook where they build up to a larger theorem starting from smaller lemmas — try to prove them yourself. Even if you don’t prove them the first time, on a re-read you can try to prove it yourself, as a way to test your understanding, and of course this also deepens your understanding.

caffeine 5y ago

This is good advice. But for me, the hours’ struggle is more useful if not contiguous. I get the best results from struggling with a given problem for no more than 1 hour continuously, and then going away and coming back sometime after my next sleep. By struggling I mean “not making visible progress” - if progress is happening then just keep rolling.

mettamage 5y ago
This sounds like how I approach leetcode. Leetcode feels a bit like math to me anyways. Coding isn't the hard part, understanding the algorithm in conjunction with the data structures is.
- username90 5y ago
  Coding is the hard part if you are bad at coding but good at maths and algorithms. Writing accurate code for solving a hard problem in under 30 minutes requires you to be really good at coding.

nomy99 5y ago

This I think is the same thing as someone saying at the gym, don't stop until it hurts. People get injured and then never go to the gym again. How about look at the solution, understand the parts. Solve the problem. Revisit, revisit, revisit. This helped me breeze through engineering and also helped me professionally.

username90 5y ago
That is how people learn how to pass tests instead of learning the material. Passing tests is important in college, but if you want to learn on your own it doesn't matter.
- deleted 5y ago
  [deleted]
- nomy99 5y ago
  No. There are optimized paths to reach the same understanding
  - username90 5y ago
    Yes, but I'd argue that the path you took was a very suboptimal path to reach the same understanding since you almost surely didn't reach it. So now you'd have to redo almost everything in order to reach the same goal making it a very huge waste of time. Of course I cannot be sure of that, but I have seen so many people who learned the way you did and they had really poor understanding. In my experience only the people who try to challenge themselves actually gets there. Passing math classes requires almost no understanding at all btw, even getting good grades in them doesn't.
    - nomy99 5y ago
      No. You are over complicating things.
    - rattlesnake45 5y ago