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I'm taking courses of math at university level, it's kind of the equivalent of master degree in mathematics, I'm from Argentina. The way to learn mth in my university is this: We attend lectures, we also do exercises, we also read at home. This question is about this: How do you "store" the exercises you solve? I have solved, many, many problem sets (as every math student in the world) I will describe my current system, I would be interested in knowing other systems you employ and what you think it's the best. My current method is I print the problem sets, I number the pages of my notebook, when I solve an exercise I write on a notebook, then I write the page number (and the notebook number, because I have tens of notebooks) ritght on the problem statement, on the problem set page.

This method is good, but there are books I don't print, and there are exercises on these books, and I can't write the books, because they are virtual ebooks. This is frustrating because, I will not remember I have solved that exercise.

I need a system that keeps track of every exercise, including books i don't print.

Santropedro
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  • I store the problems I have solved in my head. I don't label any of them in any way. I forget a lot of them, but that just gives me more exercise to work on :) – Servaes Aug 27 '15 at 02:18
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    I feel you are overthinking it. Often you forget how you solved a problem, and you will stumble upon it again and it will be good for you to work on it from scratch. I moved to a different continent, and I couldn't bring all my old notebooks. Imagine how awful it would be if all my knowledge was in there... – Silvia Ghinassi Aug 27 '15 at 02:21
  • I admire you both like to work. I'm similar to you! Many times, even if I have stored a exercise, instead of peaking the solution I recreate it again in my head. This is fun. But sometimes, Instead of loosing time having fun, it's better to peak on my own solution to see what's the way I look at it, and don't loose any time. Then I can move to more important difficult problems. – Santropedro Aug 27 '15 at 02:23
  • I totally know how important is to memorize and understand problems and theories, to internalize theories. But I realized it's even better to not only have them in mind but in text. Memory will always have some thoughs fall trought the cracks. – Santropedro Aug 27 '15 at 02:29
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    This can actually be harmful to you as you may keep rehashing the same ideas and find it hard to think of new ones. At least that is what would happen to me. Maybe your mind works differently. – Matt Samuel Aug 27 '15 at 02:31
  • Note: I'm new on the site. I deleted my own answer because actually it was intended to be a comment, but I had a mouse slip. – Santropedro Aug 27 '15 at 03:17

2 Answers2

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Well, the simplest solution is just to write up your homework in LaTeX and keep the files in well-organized folders. This also has the advantage of making you quick at LaTeX and giving your professors something far nicer to grade.

That said, I have years' worth of old LaTeX documents on old hard drives and I've never seen that it was worth it to go back and look at them. The main benefit you get by doing exercises is increased understanding, and either you gain that and don't need to go back or going back and reading a solution doesn't help that much.

(I guess I should actually mention that have seen exceptions -- several of my professors have handwritten solutions from their grad school days to a couple of particular texts in their drawers, but I think they use these largely because it's very technical stuff that you don't really use in your day-to-day work.)

Daniel McLaury
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  • This worked for me. I wrote up all my homework in advanced courses in LaTeX and the professors loved it and I never looked at it again. – Matt Samuel Aug 27 '15 at 02:36
  • Why latex and not pen and paper? I have the solution is my notebook, it's hand written. I need a way to "link" it to the book, in a way that is accesible from the book. – Santropedro Aug 27 '15 at 02:37
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    @Santropedro Haven't you answered your own question? Computers can do automatic searches. No matter what method you use with pen and paper, you still have to flip through the pages. – Matt Samuel Aug 27 '15 at 02:38
  • But yes, folders is to me, a good idea. Probably folders and txt files with page number of my notebook – Santropedro Aug 27 '15 at 02:39
  • Yes, I don't like your solution because I have handwritten exercises of books and no intention whatsoever of latexing them. I now realize i just had to do a txt file and keep that file in a special folder of solved problems. – Santropedro Aug 27 '15 at 03:15
  • With this approach, I think you will learn more TeX than mathematics. – BruceET Aug 27 '15 at 15:30
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First, about questions in electronic form. If necessary, you should be able to print a problem or get a screen-shot of it, and save your written answer.

However, more generally, I think you need to learn to prioritize what you keep. Often, several problems on roughly the same topic will be assigned. Is it really necessary to save every one?

Ideally, for each problem, you should be able to figure out its purpose and connection with topics, methods, etc. you are studying. I think it is extremely valuable to try to do this for each problem in any case. But that can also be a guide to to which problems to save.

Be especially on the lookout for problems for which the solution appears to involve a novel method or 'trick', maybe even one that is not discussed anywhere in the text. The second time you encounter the same 'trick' it is a trick you've seen before. The third time it's not a trick any more but a 'technique'. Make sure to save the version that most clearly displays the technique.

In some mathematical fields, the material covered in the text pretty clearly points the way to solving the problems. In these fields, I think you'll need to save fewer worked problems. In other fields, a big part of problem solving is interpreting the theory so it can be applied to advance another theory or so that you can work a practical 'story' problem. (Some parts of calculus and probability theory come instantly to mind.)

At some point you will have to prioritize, and that may be an advantage. Thinking hard about the essence of a problem and whether it's worth saving will help fix it in mind so you will remember the point of it. Perhaps more important, you will have less to save, and it will be easier to retrieve the important things you have saved.

Finally, I think you should consider some sort of computer cataloging system for all the stuff you are saving. That can be done very efficiently. If you don't know how to retrieve what you save, there's no point saving it.

BruceET
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  • Sounds good. Im right now writing almoat all problems I solve in handwritten style in notebooks. So, I kind of don't need to choose problems. But still, that seems important for the understanding... thanks. – Santropedro Aug 27 '15 at 02:43
  • The TeX idea mentioned in another Answer and some Comments may be very useful, provided you get good enough at TeX that you can do it quickly and don't fuss endlessly about getting the most elegant version of TeX. – BruceET Aug 27 '15 at 02:52
  • It will not be useful for me, as I understand my own notes. Probably some day google invents a math search that searches digital documents to find math queries, like how to calculate the quotient of a group and it redirects you to that exercise you did two months ago. Tex also would be very portable, and easy to store on the cloud, also easy to read for other people if I share it.It obviously has advantages. I'll consider it. – Santropedro Aug 27 '15 at 03:13
  • No doubt Google in particular and the Internet in general is a valuable resource, and will likely become even more so. However, as a mathematician, a huge part of your success, value, proficiency, and satisfaction will be determined by how much in inside your head. – BruceET Aug 27 '15 at 03:18