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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

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.
    - throwlaplace 7y ago
      > you won't actually be able to do the math but i'm not a mathematician. i don't need to be able to do math anymore than i need to be able to do history (while reading serious history books). >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. no i didn't. that's precisely why i used the word "exposed". >violent agreement we don't agree but i'm not being violent. but my responses are short and yours are long. i do not see the exercises as essential for anyone other than practicing mathematicians. i have read a great many serious math books (i just recently finished Tu's Manifolds book and am now reading Oksendal's SDEs). i read them without doing absolutely any exercises but following the rest of the guidelines in the post i responded to. the experience is gratifying because i learn about new objects and new ways of thinking about objects i've already learned about. that's absolutely the only thing that matters to me. but let me ask you something >That, to me, implies learning to do, not learning about. here's a fantastic explanation of the topological proof of Abel-Ruffini https://www.youtube.com/watch?v=zeRXVL6qPk4 https://www.youtube.com/watch?v=zeRXVL6qPk4 would you say that I don't understand that proof if i haven't done any exercises related to it? and therefore would you say I didn't learn any math by having watched that video?
- l_t 7y ago
  > 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. This is a great point and example of the problem with a one-size-fits-all strategy. For some books, exercises are an essential part of comprehension. For others, not so much. > 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. My experience is that by taking excellent notes and asking why, you engage with the material to a similar degree, if not a greater degree, than by doing exercises. (Once again, depending on the book, as you mentioned.) > Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it. I would argue that's the point. Usually self-taught math is about self-growth. Getting new ideas, being exposed to new concepts, recognizing patterns. Being able to actually "do it" on-the-spot is beside the point (and is the quickest level of skill to evaporate once you stop focusing on that material, anyway.)

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.
  - throwlaplace 7y ago
    > you won't actually be able to do the math but i'm not a mathematician. i don't need to be able to do math anymore than i need to be able to do history (while reading serious history books). >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. no i didn't. that's precisely why i used the word "exposed". >violent agreement we don't agree but i'm not being violent. but my responses are short and yours are long. i do not see the exercises as essential for anyone other than practicing mathematicians. i have read a great many serious math books (i just recently finished Tu's Manifolds book and am now reading Oksendal's SDEs). i read them without doing absolutely any exercises but following the rest of the guidelines in the post i responded to. the experience is gratifying because i learn about new objects and new ways of thinking about objects i've already learned about. that's absolutely the only thing that matters to me. but let me ask you something >That, to me, implies learning to do, not learning about. here's a fantastic explanation of the topological proof of Abel-Ruffini https://www.youtube.com/watch?v=zeRXVL6qPk4 https://www.youtube.com/watch?v=zeRXVL6qPk4 would you say that I don't understand that proof if i haven't done any exercises related to it? and therefore would you say I didn't learn any math by having watched that video?
l_t 7y ago
> 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. This is a great point and example of the problem with a one-size-fits-all strategy. For some books, exercises are an essential part of comprehension. For others, not so much. > 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. My experience is that by taking excellent notes and asking why, you engage with the material to a similar degree, if not a greater degree, than by doing exercises. (Once again, depending on the book, as you mentioned.) > Ignore the exercises if you want, but you almost certainly will end up knowing about the math, but not able to do it. I would argue that's the point. Usually self-taught math is about self-growth. Getting new ideas, being exposed to new concepts, recognizing patterns. Being able to actually "do it" on-the-spot is beside the point (and is the quickest level of skill to evaporate once you stop focusing on that material, anyway.)