Timeline for What is the best way to read advanced textbooks in Pure Mathematics (PhD Level)? [closed]
Current License: CC BY-SA 4.0
24 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26 at 13:12 | history | closed |
Sam Hopkins YCor abx Andy Putman Daniele Tampieri |
Not suitable for this site | |
| Nov 26 at 9:08 | review | Close votes | |||
| Nov 26 at 13:12 | |||||
| S Nov 26 at 9:05 | history | bounty ended | Arnold | ||
| S Nov 26 at 9:05 | history | notice removed | Arnold | ||
| Nov 26 at 9:05 | vote | accept | Arnold | ||
| Nov 23 at 2:33 | comment | added | Timothy Chow | Related: How to read an article and make it actually useful? and When is one 'ready' to make original contributions to mathematics? | |
| Nov 22 at 19:56 | comment | added | Daniel Asimov | Yes, always read actively. With a pen or pencil and a pad of paper, so you can try to check anything in the book that seems less than obvious. Also, look ahead and at the table of contents, so you have an idea of where you've been and where you are going. | |
| Nov 22 at 18:56 | answer | added | Alec Rhea | timeline score: 3 | |
| Nov 22 at 8:28 | history | edited | gmvh | CC BY-SA 4.0 |
Corrected punctuation
|
| Nov 22 at 8:24 | answer | added | gmvh | timeline score: 4 | |
| S Nov 20 at 12:13 | history | bounty started | Arnold | ||
| S Nov 20 at 12:13 | history | notice added | Arnold | Improve details | |
| Oct 27 at 17:33 | comment | added | Malkoun | Another advice is maybe, try to learn actively, by always asking some questions, and try to have a deeper understanding of the theorems. Also it is ok to ask "stupid" questions. Those usually help getting your understanding of the basic facts at a good level. | |
| Oct 27 at 17:30 | comment | added | Malkoun | Commenting a bit on the approach part of your post, it is of course very important to know the relevant definitions, so that's good, but I personally do not think that memorizing entire proofs is very helpful. However, understanding the basic ideas used in proofs is very important, as those can often be reused elsewhere. I don't think math books are to be read "linearly", so to speak. And definitely do talk to some more experienced mathematicians, especially those who could potentially be thesis advisors. | |
| S Oct 27 at 16:54 | history | suggested | J. W. Tanner |
Added relevant tags
|
|
| Oct 27 at 15:11 | review | Suggested edits | |||
| S Oct 27 at 16:54 | |||||
| Oct 27 at 13:05 | comment | added | an_ordinary_mathematician | I think that sometimes even more important than remembering statements by heart is remembering some key ideas in the proofs, because they become new tools in your toolbox. Another thing that helps is to try to make variations of the theorems in the book and try to prove or disprove them. Self study is hard but it is essentially the only way from the PhD and on wards. Also try to discuss with other mathematicians as much as you can. | |
| Oct 27 at 12:50 | comment | added | Carl-Fredrik Nyberg Brodda | @non-euclideangeometry I don’t think your indirect, slightly cryptic comments are very helpful to OP at all. Could you rephrase them in a more direct way? | |
| Oct 27 at 10:08 | comment | added | Arnold | @non-euclideangeometry"To op, good luck btw getting it out of them, especially if you actually achieve it." What the 2 "it " means? | |
| Oct 27 at 9:04 | comment | added | no upstairs | Don't you know I'm just joshin' them. It's fine to be proud. To op, good luck btw getting it out of them, especially if you actually achieve it. @NateRiver profscam may be relevant reading. | |
| Oct 27 at 8:37 | comment | added | Z. M | Doing a PhD is not passively reading books. There are way more mathematics than one can assimilate during a lifespan, let alone PhD. It is more about guided investigation: you basically learn what your advisor suggests, and see that, with this limited learning, you are still capable of proving something nontrivial. This is highly personal: different advisors have different opinions. | |
| Oct 27 at 8:05 | comment | added | Nate River | @non-euclideangeometry could you elaborate on the second part? What is the relevance of the PhD student status specifically? | |
| Oct 27 at 7:36 | comment | added | no upstairs | Very carefully. And let me reiterate: you're a phd student. | |
| Oct 27 at 7:04 | history | asked | Arnold | CC BY-SA 4.0 |