For something in my field, I "speed read" it. (In quotes because I have no idea if this is how actual speed reading works.) I.e. set aside one or two blocks of 4 hours or so and commit to finishing the book in that window.

I usually don't retain a ton, but the big benefit is that I know where to find the relevant sections when I need them in the future, and have some sort of big-picture view of how they fit together.

I read these kind of books front to back while trying to program the examples and graphs for myself. It's slow going in all but I've gotten great rewards from only a few books. (These would be 4 in 14 (!) years Strang linear algebra, Greene econometric analysis, Gelman Bayesian statistics and McKay information theory). For me, build once, never forget just works. The thing is, I never feel the need to refresh earlier work after this. Even if I look at my code from a decade ago it just clicks. Did some MOOCs on the side and while I passed those quite well, I didn't retain as much as from the struggle above.

Possibly a controversial opinion but my belief is that you can effectively measure the usefulness of a non-fiction work (text book, academic paper, article, tutorial, etc) by asking if you learnt anything from it.

One. Simple. Thing. Is. Enough.

Freedom from the pressure to fully understand everything from a book (or even from a single chapter) has allowed me to learn a lot more in recent years, and in a far more enjoyable manner.

So for me, I read the book quickly or academic paper almost as if it is a fiction. Generally not going back or pausing. Sometimes even faster. (I have found this gives me a better overview of the entire content, comapred to meticulously starting slowly at the first chapter and eventually getting stuck.) I do this until, a particular section stands out and really piques my interest. This is typically either because: (i) it is coincidentally relevant to something I have been recently working on, or (ii) the author's description of a topic is written in just the right way that things 'just click' and I have a newer or deeper understanding of the topic. Often these scenarios give me the intrinsic motivation to spend a longer time on that topic.

In this way, I often read the same book/paper many times over, during a period of a few months, and each time I learn something new. In some ways, this strategy is similar to what some people call the wedge approach which is a balance between the debate of being a studying wide or deep. That is, study a lot of things broadly, several things moderately, and a few things very deeply.

The corollary to this idea comes from my teaching experience. Teachers know that the best learning comes when the difficulty is just at the edge of a student's ability. Not too easy. Not too hard. This is the power of incremental learning. So it makes sense you only have to find one thing in the text book that is just at the edge of what you already know, and learn about that.

So often when I need to do something for work, I apply this +1 technique. I learn what I need to do for my project and then just 'one bit more'. All those 'one bit more' explorations add up to quite a lot over time.

Hope that helps. ;)

For mathematics: The most important part is the problems. You can actually start at the problems, and read the sections until you can answer the problems. Most people avoid the problems because they take time and require them to actually think about the content (it's painful). So my advice: Pick the problems you find interesting and see if you can find solutions to them from the content of the book and learn that well. That would be the most optimised form of studying mathematics. Note: You do not need solution sets to do this.

>At the risk of sounding quite silly, how do people read these textbooks

literally just front to back. I did maths in university and when I started to work for a few years I didn't get too do much of it so I just got into the habit to put half an hour a day aside to work through whatever books I find interesting.

I actually enjoy it much more now than I did in uni given that I can do it at my own pace now and for fun.

Depends on the person, their interest and the textbook. I've read a few college textbooks over the years in areas I'm interested in. Some, I just read specific sections/chapters. Others, the whole thing. I don't generally do the exercises unless I'm not comfortable that I've got the material down. I usually find out pretty quickly if that's the case, since I typically apply the knowledge shortly after reading.

I read textbooks recreationally, in addition to genre fiction. I purposely try to read broadly across multiple topics, but have a horrible habit of getting hooked and doing deep dives in particular areas. In my case, I think it stems from enjoying reading college history textbooks (from my mother) and music theory textbooks (father) starting at about 10 years old. I enjoy the dry non-narrative and technical writing.

From my experience, the solution is to find a book that matches your current knowledge and goal; which usually means finding a combination of books. Also, if you do not have the necessary prerequisite you'll need to find a mentor who can fill you in.

About exercise, I do not think you are meant to solve them all. The most important thing is to get the main idea from chapter to chapter.

Statistical Rethinking is very easy to read (at least compared to most textbooks).

I think a good conceptual foundation is the difference between someone who throws buzzword solutions at a problem to see what sticks, and someone who can make a good tweak to get working a standard-ish idea that doesn’t quite work out of the box. Without understanding these concepts it is easy to get stuck spinning in loops on a complicated problem — where tweaking to improve one thing messes with another thing.

I won’t claim Bayesian is the only conceptual framework, but I found it particularly intuitive and straightforward — and gives you a lot of flexibility. Refer an earlier discussion on Bayesian approaches a few days ago.

I don't get this fear of math. You're talking about probability theory here. It literally _is_ mathematics. Why would someone want to study applied probability theory but try and dodge the foundation of the entire discipline? Sigh.

It says above that quote: "These are satirical, but real"

I don't think this is true having read some of the later chapters and not knowing measure theory. And if you don't trust me, Gelman doesn't know measure theory either (https://statmodeling.stat.columbia.edu/2008/01/14/what_to_le...) and he wrote the book...

There's little that can be said about Dirichlet processes without measure theory; fundamentally speaking they are random measures. That said, the vast majority of the book presupposes no measure theory.