I am going to start my first year of a research-oriented master program on computational math. I have found some topics about how to read books/papers, such as this and this on math stack exchange. Though they are indeed great advice, I think they are mainly for students studying pure math.
From what I know, unlike pure math students, applied math students usually don't spend the first year reading certain textbook (such that Evans' PDE book). Instead, applied math students start by reading certain papers, and if they don't understand some concepts, they refer to certain books/papers, read specific sections which can solve the problem and proceed the original paper. And they spend a lot of time implementing numerical schemes. Hence I got a feeling that applied math students may not have enough time to systematically build up a solid theoretical background (such as functional analysis) by finishing an advanced textbook, taking their own notes and solving exercises, which I think may not be good in the long run.
May I know whether my understanding is correct? As graduate students/ researchers on numerical analysis, did you spend some time reading a entire (or a large part of) pure math book? May you share your experience about how to balance reading textbooks and doing research with me?
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