Transitioning from 'Read textbook to learn' to 'Read original paper/Read paragraphs of textbooks'

Question

I wanted to ask the following on Mathematics stack exchange, but checking the help centre, it appears that this site is more relevant: "Mathematical education, especially about teaching and pedagogy: Mathematics Educators"

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Throughout my undergraduate degree, it felt that for any course that I would need to study, I could find a textbook that covered all of the content needed and more - with this in mind, I would simply linearly work through the textbooks, and whenever I didn't understand something from one, I would move to another.

Now that I am in graduate school, this model of education does not seem to work. It seems that any textbook I find on more advanced topics only barely will touch on the thing I am interested, and will otherwise be largely off topic. Is a student meant to transition into a new state of study, where 1) I simply read a few paragraphs from this textbook, and a few from another, and so on?

2)Is it better that I give up on textbooks and simply look through the literature for the original papers? It seems that doing so would decrease the breadth of my study, but perhaps this is necessary.

Answer 1

The answers largely depend on which areas of math you're asking about and how close to the frontiers of research they are, but here's what I'd say in general.

1) I simply read a few paragraphs from this textbook, and a few from another, and so on?

If that's what works best for you, then by all means do it. In graduate school, especially after the first year or two in a PhD program, more of a focus is placed on independent learning, so it's really up to you how you do that.

2)Is it better that I give up on textbooks and simply look through the literature for the original papers?

Not necessarily. I would say learn from as many different sources as possible. Original papers are better if you're learning something closer to the frontiers of research. But if you're talking about, say, a graduate-level introduction to numerical analysis, then original papers may be overkill. Not that overkill is necessarily a bad thing in this context, but at the early stages of a graduate program you'll likely be more focused on passing qualifying exams, etc.

Answer 2

I'd say that it is not "linearly" vs. "nonlinearly" or "whole book" vs. "paragraphs" but rather you should change your focus when starting to read. When you transition to research, you should not start reading to learn some piece of theory, but to solve a problem or to understand a certain property. So the motivation should be different, and this usually leads to a different reading style. Also note that there are books that are not really meant to read cover to cover.