I'm just starting graduate school (master in mathematics) and there we have absolute freedom in choosing the number of courses that we can attend each term. In consequence, I'm wondering what is the best strategy when taking courses:

  1. To take three courses and broaden fast my knowledge of mathematics but doing less problems on every course, or
  2. To take two courses and slow my rate of knowledge of mathematics but make a lot of more problems on every course.

I should say that I'm considering the first strategy because I want to get as soon as possible to research activities (mainly because I have seen that all graduate students are getting fast to research activities and end up their masters degree with at least one article and it is known that this is important if you want a place in the best doctoral programs in the world).

So, in terms of education and pedagogy and so on, what is the best strategy?

Thanks in advance.

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    $\begingroup$ Probably either approach is wrong if it is followed dogmatically. The question is what is helping you to grow mathematically? Also, equally important, what activity is helping you gain a better connection to the math community. If you intend to stay at your school, or even if this is just one possibility, it is important to take courses with the professor who is doing the sort of math which you wish to study. In short, courses are not just about studying, they are also about building relationships with fellow students and professors ideally. $\endgroup$ – James S. Cook Jul 18 '18 at 14:08
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    $\begingroup$ I'm voting to close this question as off-topic because it relates to learning mathematics rather than teaching it. $\endgroup$ – G. Allen Jul 21 '18 at 22:41
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    $\begingroup$ I'm voting to close this question as off-topic because it is more a question about academia or mathematics than teaching mathematics $\endgroup$ – kcrisman Oct 10 '19 at 1:44

Academia in general, and Mathematics in particular, tends to reward specialization over generalization. Not in every case, but doctoral studies are typically very deep and narrow. If that is your goal, then focus on the parts of math that you enjoy and have strength in.

On the other hand it is good to have a lot of mathematical interests at your current state so that you have a lot of ways you can jump into research. The further you move along, the more will be the pressure to specialize. Once you hold a doctorate you are pretty free to make your own path.

The other consideration is about how hard you want to work right now, and how much risk you want to accept of getting in over your head with a heavy work load and subjects that are different enough from what you already know that you have a non-trivial learning curve.

There is no reason why you need to make a decision now and stick to it for all time. If you are taking really new courses, fewer is likely better (safer). If you are already somewhat comfortable with the new material and want to work really hard (all the time), then plunge in.

But better that you should consider your strengths (and any weaknesses) and find a way to excel.

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