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I'm studying 3rd year maths at university and havent done that well in my first semester. I'll be starting 2nd semester next week on 4 maths subjects. I want to study through everything in my 3 maths subjects from 1st semester alongside 2nd semester. So I'll have 7 subjects in total to get through in 5 months. How can I efficiently use and divide my time to get through everything. Has anyone managed this before?

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closed as off-topic by John Douma, Shaun, José Carlos Santos, Kabo Murphy, Hans Lundmark Jan 4 at 8:26

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    $\begingroup$ Starting from scratch is usually a very difficult and sometimes very frustrating task for a student. The best, I think, is that details as much as possible your study method so we can say what you have to improve and what you are good at. $\endgroup$ – manooooh Jan 4 at 7:10
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    $\begingroup$ I took a fast track course to get into university with a lot of gaps in my math knowledge. I've not done so well in my maths subjects because I've been trying to teach myself the vocabulary of higher maths which is costing my study time. This is why I feel the need to start from the beginning of my subjects. $\endgroup$ – user606466 Jan 4 at 7:19
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    $\begingroup$ Thanks for expanding the question $\ddot\smile$. Have you ever tried to read a math book? What is your native language? What kind of mathematics are the ones that cost you the most? $\endgroup$ – manooooh Jan 4 at 7:22
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    $\begingroup$ Yes, I've read multiple maths books. I understand the structure of written mathematics better now. I am from Scotland. Ive been revising real analysis for such a long time that it's cost so much of my time for such little progress. The subjects from my last semester are Real analysis, abstract algebra and mathematical methods. In my second semester I'll be studying complex analysis, metric spaces, dynamical systems and mechanics. I'll keep upto date with the current subjects , but fit the other 3 in alongside. $\endgroup$ – user606466 Jan 4 at 7:35
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Unless your current subjects build on those you already took somehow, it might be more efficient to focus your present study efforts on your current courses, and then to review your past courses over the summer. Otherwise, that's just one hell of a workload and not worth the stress (plus it might get in the way of your other subjects and that and/or the stress might reflect on your grades).

Personally, it's also a matter of how you study - and that in itself might even depend on the courses themselves and your compatibility with them. For example, I find it's hard to really do "study time" for courses which are primarily proof-based in nature, e.g. real analysis. In those courses I personally find that the most you can do would be the following:

  • Know the absolute ins and outs of each theorem and definition taught in class
  • Do the homework, seeking help where necessary (e.g. from professors or MSE)
  • If your textbook has practice exercises, work those out too sometimes, if you're able; this helps with the previous in learning how to piece proofs together from the definitions/theorems you have, it's important to get comfortable using them in a course

If the course is more computationally-oriented - think your average calculus or linear algebra course, where's there more computations than proofs - I'd say the previous three apply, but also don't be afraid to try problems that aren't in the text (like make up your own integrals or functions to differentiate, if it were a calculus course, and check your answers somehow).

As for when to do your study time, it depends on your life and schedule and all that. Were I in your spot, I'd personally devote $30-60$ minutes every other day to one of the four subjects in the current semester, mostly focusing on the practice exercises I mentioned, since, hopefully, over time your repeated use of those definitions and results will help to ingrain them in your memory. But it all depends on how well you retain the material too; I tend to have a pretty good memory for this sort of stuff, and got by the past semester while mostly ignoring the third bullet point altogether (mostly because one course was so hard it would take up all my time in that respect anyways).

Sadly, there's too many variables between your own academic ability, lifestyle, and the courses to really give you a proper means of study. But the core point is that practice is essential. The last thing you need is to be using some technique for the first time on an exam.

But at the same time, also don't overdo it. Leisure time is important, and good for the mind. This is a big part of why I'm emphasizing that, if you don't need the material from your previous courses right now, you shouldn't bog yourself down by studying them on top of your present workload. This question slightly, if tangentially, touches on that matter.

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