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I've tried a few things recently that help with that: 1. Don't do exercises unless you want to. Completionism is a trap. 2. Take notes. Rewrite things in your

by l_t 7y ago

I've tried a few things recently that help with that: 1. Don't do exercises unless you want to. Completionism is a trap. 2. Take notes. Rewrite things in your own words. Imagine you're writing a guide for your past self. 3. Ask questions. Anytime you write something down, pause and ask yourself. Why is this true? How can we be sure? What does it imply? How could this idea be useful? 4. Cross-reference. Don't read linearly. Instead, have multiple textbooks, and "dig deep" into concepts. If you learn about something new (say, linear combinations) -- look them up in two textbooks. Watch a video about them. Read the Wikipedia page. _Then_ write down in your notes what a linear combination is. Anyway, everyone's different of course, but these practices have been helping me get re-invigorated with self-learning math. Hope they help someone else out there. I welcome any feedback! (edit: formatting)

throwlaplace 7y ago
this is excellent execellt advice. seriously anyone interested in learning math, chancing on this comment, should write it down. i wish i could upvote many more times. i have a bachelors in pure math and am 10 years out. i have time and again revisited things and didn't make good substantive progress until i came to these same exact conclusions. especially the part about skipping the exercises. if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them. a lot of exercises are a hazing ritual or imagined by the author to be a dose of bitter medicine (i'm looking at you electrodynamics by jd jackson) since they mistakenly believe all readers are formal students. the most important exercise is to mull over and consider what you're reading/learning. naturally dovetails in to asking question: what happens if i remove a hypothesis from a theorem, what happens if i add one, is there an analogy to another object/group/measure/etc, etc. also read multiple books (http://libgen.is/ http://libgen.is/ is your very very good friend and generous friend). a lot of math authors (no matter how esteemed they are) are terrible writers or make mistakes (look up errata for previous editions of your favorite book). the only thing i'd add is to learn to use LaTeX to take notes - it is much easier and faster and neater.
- ColinWright 7y ago
  > this is excellent execellt advice ... especially the part about skipping the exercises. if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them I think this is deeply mistaken. In a well-chosen book, such as the ones in the submitted article, doing the exercises is not to test your memorisation, it's to develop your understanding. Math is not a spectator sport. Reading about math is fine, but it will not take root and develop unless you engage with it, and the exercises are the way to do that. Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it.
  - jjgreen 7y ago
    This, 100 times. Mathematical understanding can only be obtained by doing, fighting with the concepts, causing that pain that you get behind the eyes. Just reading the text will give you a surface knowledge, maybe enough to impress at interviews or parties, but nothing more ...
  - throwlaplace 7y ago
    >Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it. Isn't that literally exactly what I said? > if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them
    - ColinWright 7y ago
      The submission and this entire thread is about learning math. That, to me, implies learning to do, not learning about. Yes, you said: > if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them There's ground in the middle, and this thread is about that. This thread is not about learning for tests and qualifications, nor is it about "being exposed", it's learning how to do the math. And for that you need to do the exercises. You don't need to do all of them, you don't need to be completionist about it, but if you don't do the exercises, if you don't actually do the math then you won't actually be able to do the math. Specifically, you said (quoting again): > if you're ... just interested in learning ... There's a difference between learning about and learning to do. If you meant just "learning about" then you are at odds with the entire thread. True, in that case you don't need to do the exercises, but I don't think that's what people are talking about here. I think people are talking about being able to do the math. And if you meant "learning to do" then in my opinion you are wrong, and one needs to do a large slab of the exercises. Otherwise it's fairy floss, and not steak. My apologies if all this seems overkill, but there's a real danger of talking past each other and being in violent agreement, and I wanted to state explicitly and clearly what I mean, and why I thought you said something different.

by l_t 7y ago

throwlaplace 7y ago

this is excellent execellt advice. seriously anyone interested in learning math, chancing on this comment, should write it down. i wish i could upvote many more times. i have a bachelors in pure math and am 10 years out. i have time and again revisited things and didn't make good substantive progress until i came to these same exact conclusions. especially the part about skipping the exercises. if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them. a lot of exercises are a hazing ritual or imagined by the author to be a dose of bitter medicine (i'm looking at you electrodynamics by jd jackson) since they mistakenly believe all readers are formal students. the most important exercise is to mull over and consider what you're reading/learning. naturally dovetails in to asking question: what happens if i remove a hypothesis from a theorem, what happens if i add one, is there an analogy to another object/group/measure/etc, etc. also read multiple books (http://libgen.is/ http://libgen.is/ is your very very good friend and generous friend). a lot of math authors (no matter how esteemed they are) are terrible writers or make mistakes (look up errata for previous editions of your favorite book). the only thing i'd add is to learn to use LaTeX to take notes - it is much easier and faster and neater.

ColinWright 7y ago
> this is excellent execellt advice ... especially the part about skipping the exercises. if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them I think this is deeply mistaken. In a well-chosen book, such as the ones in the submitted article, doing the exercises is not to test your memorisation, it's to develop your understanding. Math is not a spectator sport. Reading about math is fine, but it will not take root and develop unless you engage with it, and the exercises are the way to do that. Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it.
- jjgreen 7y ago
  This, 100 times. Mathematical understanding can only be obtained by doing, fighting with the concepts, causing that pain that you get behind the eyes. Just reading the text will give you a surface knowledge, maybe enough to impress at interviews or parties, but nothing more ...
- throwlaplace 7y ago
  >Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it. Isn't that literally exactly what I said? > if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them
  - ColinWright 7y ago
    The submission and this entire thread is about learning math. That, to me, implies learning to do, not learning about. Yes, you said: > if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them There's ground in the middle, and this thread is about that. This thread is not about learning for tests and qualifications, nor is it about "being exposed", it's learning how to do the math. And for that you need to do the exercises. You don't need to do all of them, you don't need to be completionist about it, but if you don't do the exercises, if you don't actually do the math then you won't actually be able to do the math. Specifically, you said (quoting again): > if you're ... just interested in learning ... There's a difference between learning about and learning to do. If you meant just "learning about" then you are at odds with the entire thread. True, in that case you don't need to do the exercises, but I don't think that's what people are talking about here. I think people are talking about being able to do the math. And if you meant "learning to do" then in my opinion you are wrong, and one needs to do a large slab of the exercises. Otherwise it's fairy floss, and not steak. My apologies if all this seems overkill, but there's a real danger of talking past each other and being in violent agreement, and I wanted to state explicitly and clearly what I mean, and why I thought you said something different.