4 ms·

I agree with the basic thrust of your comment, which as I interpret it boils down to saying it's unhelpful to throw book titles at a person without any context

by dsacco 9y ago

I agree with the basic thrust of your comment, which as I interpret it boils down to saying it's unhelpful to throw book titles at a person without any context or guidance. However, I disagree with this point: > If some 2-minute video gives you something actionable to do rather than going through a 2-hour chapter in textbook there is no point of going through 2-hour chapter. Knowledge is all about applying not learning the facts and saying it around to your friends I know it feels good but nothing comes out of it in real life. There are optimal and suboptimal ways to learn things, sure. But some things legitimately cannot be reduced from a complicated textbook chapter to a straightforward YouTube video. You can improve exposition, but that comes with its own time efficiency trade-offs, and you won't meaningfully simplify the material without compromising significantly in depth of coverage. In particular, even extremely good video series like 3Blue1Brown's Linear Algebra have neither the breadth nor the depth to replace the material in any given chapter of e.g. Axler's Linear Algebra Done Right. The exposition is certainly clear, and you can get a nice overview, but you're actually not learning enough to apply the mathematics if you watch a video on it. Ironically, such a video is much more likely to leave someone able to talk about the subject but woefully incapable of actually doing it. The videos that can be used for learning are mostly lectures. More importantly I think your conception of working through a chapter is incorrect. If you're spending a significant amount of time working through a textbook chapter, you're either 1) actively learning the material and doing the mathematics, not just passively reading it, or 2) you're not prepared for the material, and you're not learning efficiently. Finding a video to simplify the material doesn't resolve #2, it just disguises it. When you learn mathematics from a textbook, you should be applying the material by working through the exercises. You can't immediately jump into e.g. data analysis after learning linear algebra, and you certainly can't do so by watching a video on the subject. I'm fully with you that replying to these questions with textbook recommendations is unhelpful, but not because they're textbooks. Textbooks are great! The hard reality is that you can't simplify most mathematics into an easily, quickly digested format, especially if you want to apply it. There are simply too many prerequisites for most material and too many unknown unknowns that can leave glaring blind spots. "There is no royal road to geometry" is a saying for precisely this reason.

Chris2048 9y ago
> it's unhelpful to throw book titles at a person without any context or guidance Here's one reason it's unhelpful; After 4 or 5 people list a bunch of books, you now have a long list of books, and no way to know which to start with, unless there is a lot of overlap - you could just as well google/search amazon and look at ratings, which would give you far better results. Furthermore, many people tend not to read multiple math books on the same subject, so they just recommend what they know w/o having any knowledge of how that book fares against other suggestions. If they expand on either their own credentials, and reading on the matter, so you have the context of their knowledge; or give reasons why that book is good, this gives a better basis for comparison. As an aside; I like the coursera structure of following video lectures with content summaries of what was covered in the video. The advantage is 1) quick reference of material without having to search through a video; 2) if you already understand the topic, you can often just read the summary, and skip the video if you think you already know the material. Another aside; one problem with books versus videos is often books are long compendia of a field, where as videos are shorter. if you already know topic A and want to learn B, then there may already be a video on topic B, where as a book might cover B in some chapter. For these cases, it might be good to discuss individual chapters/sections of book, but that assumes you can ready them somewhat independently given prior knowledge.

by dsacco 9y ago

Chris2048 9y ago

> it's unhelpful to throw book titles at a person without any context or guidance Here's one reason it's unhelpful; After 4 or 5 people list a bunch of books, you now have a long list of books, and no way to know which to start with, unless there is a lot of overlap - you could just as well google/search amazon and look at ratings, which would give you far better results. Furthermore, many people tend not to read multiple math books on the same subject, so they just recommend what they know w/o having any knowledge of how that book fares against other suggestions. If they expand on either their own credentials, and reading on the matter, so you have the context of their knowledge; or give reasons why that book is good, this gives a better basis for comparison. As an aside; I like the coursera structure of following video lectures with content summaries of what was covered in the video. The advantage is 1) quick reference of material without having to search through a video; 2) if you already understand the topic, you can often just read the summary, and skip the video if you think you already know the material. Another aside; one problem with books versus videos is often books are long compendia of a field, where as videos are shorter. if you already know topic A and want to learn B, then there may already be a video on topic B, where as a book might cover B in some chapter. For these cases, it might be good to discuss individual chapters/sections of book, but that assumes you can ready them somewhat independently given prior knowledge.