How to make sure one understands each and every detail while reading a textbook/research paper without leaving any gaps?

Question

I am a physics Master's student. I have good grades, with CGPA above 9(/10)(However, all courses in my university are graded on a curve so the actual marks are significantly lower than 90%). This has been my marks throughout my undergraduate and graduate courses and I was happy because this was above average. Also, my summer projects in UG were usually computational and any difficulty I had in theoretical aspects I attributed it to my inexperience in advanced Physics.

However, recently I have started to work on pure theoretical project and while reading for the project I realized that I consistently miss some details from each topic. I understand the general idea, can re-derive most of the equations(with some effort) however when I discuss things with my professor or when I read further topics I realize that I have missed certain key-details. This is exactly similar to the case of me missing a few key questions in my exams and getting that 9 grade point instead of 10(or at-least I think so). I was not worried about this before but now I realize that there is some flaw in the way I study (but I do not know what).

Since I want to apply for Physics PhD I realized that I will need to have solid concepts and it would be best to correct my mistakes but I do not know how or even what could be the reason for my imperfect understanding.

Any direct suggestion would help or even certain general guidelines on what I can do.

Things I've tried recently -

1) I've started to written down almost everything I read. This is slightly laborious but is certainly helping. It also helps me to gloss over the things I read previously when I come back the next day.

2) I completely avoid smartphone when I'm library/study room so that I won't get distracted. Not sure if it helps me solve the above problem but certainly helps me study better in general.

3) I've tried to read the topics from several sources. The books I am reading is somewhat like a collection of research papers and hence does not have a exercises. So I though reading from various sources might help get better ideas but it's not really helping because most other sources are too high level as an introductory text. But this will probably help me in cases where it's practical to do this.

4) Somewhat similar to point (1)- I am trying reread, whenever I can, what I've done until that point. But not sure how much this will help me in filling the gaps.

Answer 1

I will give a separate answer for textbooks and for scholarly papers. The difference is that textbooks normally come with exercises to help solidify the understanding of the material.

For a scholarly work in a technical field, however, a proven method is to read the paper three times, but with a different focus each time.

The first reading is something like a deep skim. You are looking for an overall, not a detailed, understanding at that point. Take notes as you go, but don't just try to copy things. The notes should capture the main points of the paper. What was the methodology, what are the main conclusions. But also take notes about what you don't get from this reading.

Wait bit, a day or so, before the next reading so that the ideas have a chance to settle in your mind.

The second reading is deep. Here you are trying to follow the arguments of the paper in detail. Use the notes from the first reading to guide you. Think about how the paper extends the field. Think about what it does that is new and interesting. Take notes also. The notes include those things you don't yet understand. Different colored note cards are very useful for different kinds of notes.

The third reading, again after a short wait, is to solidify the second, if needed, but also to look for ways that the paper can be extended. What future research does the paper suggest, explicitly or implicitly. Again, refer to your older notes and take new ones.

Then, after the third reading, summarize your notes. What is most interesting about the paper? What is incorrect in it? What are the important things to retain?

Note that not every paper requires this deep understanding, but those that relate to your own research probably do.

For textbooks, you can do the above, but it may not be necessary for two reasons. First, a scholarly paper is directed at a small group of specialists and you may not yet have the skill and experience to understand it quickly, but the textbook is supposed to be written for people still learning. So, it should be more accessible, using more complete arguments, say. But you can also, intersperse your readings with the exercises. Ideally you should be able to do every exercise in the book. (There are exceptions, in which research problems are hidden in the "exercises", but these are rare.) If you don't have an obvious solution to an exercise, seek feedback on your attempt. Even if you don't have time to do every exercise, you should read them. Think about how you would attack that exercise.

Time is obviously an issue if you adopt/adapt this method. One way to handle that is to make sure that you don't waste time, not that you spend longer hours. If you take notes on notecards and paper then you aren't tied to your desk. If you have periods of inactivity, say on a long commute by bus, make sure that you always have a copy of the current paper and a few note cards. Even if there are only a few moments, waiting in a line to buy coffee, you can review your note cards and jot down a few ideas if they come.

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There is a learning theory behind all this. Deep learning requires reinforcement. You don't "learn" something by reading or seeing it once. Feedback from exercises is also an important element, but harder to get for papers. One way to do that is to read a paper as part of a study group and have a discussion after, say, the second reading. Discussions with the professor for students can also work if it is available.

Answer 2

Related to your first point, but instead of just writing down whatever you read, you could summarize the material and write down the important points. You could also write them in the form of a blog post (not necessarily public), where you explain the key ideas to the reader. Combining multiple sources (point 3) would be even better -- you might end up creating a valuable resource that helps others too.

This should help in evaluating your understanding and finding gaps, if any, after which you could re-read the relevant parts. It may particularly help by forcing you to explain and think over any inadvertent jumps in reasoning you might have made (something that appears deceptively obvious may not be so, for example). In addition to all this, getting occasional feedback from someone familiar with the subject area would also be useful.

However, sometimes gaps in understanding might be inevitable, if the explanation in the paper is truly ambiguous. In such a scenario, after making an initial effort, you could discuss with senior colleagues or contact the authors directly.