Self-study methods for advanced math books and papers

AI Thread Summary
Studying advanced math books and papers often presents challenges due to the lack of exercises for practice. Many participants highlight that understanding the content itself can be a significant exercise, especially with monographs from publishers like AMS or Springer, which typically do not include exercises. Effective study methods include reading the material thoroughly, reflecting on the concepts, and revisiting complex sections multiple times to reinforce understanding. Concrete examples of advanced math topics are requested to provide context for the discussion, emphasizing the need for clarity in the types of materials being studied. Overall, the focus is on deep comprehension through repeated engagement with the text rather than traditional problem-solving exercises.
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How to study advanced math books and papers? Advanced math books don't have exercises to practice. What study methods do you use?
 
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flamengo said:
How to study advanced math books and papers? Advanced math books don't have exercises to practice. What study methods do you use?

What advanced math? Please give concrete examples.

Usually understanding the math in a research paper is already an exercise itself!
 
Give a look at most monographs(like the ones in AMS or Springer bookstores). There are no exercises in them.
 
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read...think...repeat.
 
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flamengo said:
Give a look at most monographs(like the ones in AMS or Springer bookstores). There are no exercises in them.

Again, concrete examples?
 

Thread 'Self Learning Math/Physics'

Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
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Thread 'What should I do if I found a paper with same result as mine?'

Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...
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