The “standard” way of reading a textbook (a math textbook or something) is, at least I imagine, to read it in order. When you get to exercises, do them until you don’t think you’d get any value out of the remaining exercises. If you come across something that you don’t want to learn, skip forwards. If you come across something that’s difficult to understand because you don’t fully understand a previous concept, skip backwards.
I almost never read textbooks this way. I essentially read them in an arbitrary order. I tend to start near the beginning and move forwards. If I encounter something boring, I tend to skip it even if it’s something I expect to have to understand eventually. If I encounter something I have difficulty understanding because I don’t fully understand a previous concept, I skip backwards in order to review the previous concept. Or I skip forwards in the hopes that the previous concept will somehow become clear later. Or I forget about it and skip to an arbitrary different interesting section. I don’t do exercises unless either they seem particularly interesting, or I feel like I have to do them in order to understand the material.
I know that I can sometimes get away with the second method even when other people wouldn’t be able to. If I were to read a first-year undergraduate physics textbook, I imagine I could read it in essentially any order without trouble, even though I never took undergraduate physics. But I tend to use this method for all textbooks, including textbooks that are at or above my level (Awodey’s Category Theory, Homotopy Type Theory, David Tong’s Quantum Field Theory, Figure Drawing for All It’s Worth).
Is the second method a perfectly good alternative to the “standard” method? Am I completely shooting myself in the foot by using the second method for difficult textbooks? Is the second method actually better than the “standard” method?
This is how I read too, usually. I think it’s one of those things that works better for some people but not others. I’ve tried reading things the standard way, and it works for some books, but for other books I just get too bored trudging through the boring parts.
BTW, I’ve also been reading HoTT, so if you want to talk about it or something feel free to message me!
On one hand, it’s a good sign that you have a keen sense of what you need to know, how and where to look for it, and at what pace. On the other hand, authors who know more about a subject than you do must have had their reasons to choose the order in which they present their material. I’d say keep listening to your gut on what is important to read, but at least try to get acquainted with the other topics you’re choosing not to go deeply into.
So, I read textbooks “wrong”.
The “standard” way of reading a textbook (a math textbook or something) is, at least I imagine, to read it in order. When you get to exercises, do them until you don’t think you’d get any value out of the remaining exercises. If you come across something that you don’t want to learn, skip forwards. If you come across something that’s difficult to understand because you don’t fully understand a previous concept, skip backwards.
I almost never read textbooks this way. I essentially read them in an arbitrary order. I tend to start near the beginning and move forwards. If I encounter something boring, I tend to skip it even if it’s something I expect to have to understand eventually. If I encounter something I have difficulty understanding because I don’t fully understand a previous concept, I skip backwards in order to review the previous concept. Or I skip forwards in the hopes that the previous concept will somehow become clear later. Or I forget about it and skip to an arbitrary different interesting section. I don’t do exercises unless either they seem particularly interesting, or I feel like I have to do them in order to understand the material.
I know that I can sometimes get away with the second method even when other people wouldn’t be able to. If I were to read a first-year undergraduate physics textbook, I imagine I could read it in essentially any order without trouble, even though I never took undergraduate physics. But I tend to use this method for all textbooks, including textbooks that are at or above my level (Awodey’s Category Theory, Homotopy Type Theory, David Tong’s Quantum Field Theory, Figure Drawing for All It’s Worth).
Is the second method a perfectly good alternative to the “standard” method? Am I completely shooting myself in the foot by using the second method for difficult textbooks? Is the second method actually better than the “standard” method?
This is how I read too, usually. I think it’s one of those things that works better for some people but not others. I’ve tried reading things the standard way, and it works for some books, but for other books I just get too bored trudging through the boring parts.
BTW, I’ve also been reading HoTT, so if you want to talk about it or something feel free to message me!
On one hand, it’s a good sign that you have a keen sense of what you need to know, how and where to look for it, and at what pace. On the other hand, authors who know more about a subject than you do must have had their reasons to choose the order in which they present their material. I’d say keep listening to your gut on what is important to read, but at least try to get acquainted with the other topics you’re choosing not to go deeply into.