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I'm asking this question mostly looking for advice as a student, but I also thought this could be an interesting discussion subject for this SE comunnity.

A word of explanation first: I'm a first year undergraduate student of mathematics in Poland, and the "program" is organised so that before the start of the 2nd year one chooses in what "aspect" of mathematics they want to specialise. There's stuff like theoretical, applied, mathematics in economy and some other things I'm not really considering. Based on the specialisation chosen, you're going to be attending a certain set of classes until the end of the undergraduate stage.

Now, theoretical mathematics is definitely the most interesting one for me, but at this university it's also by far the hardest specialisation. In previous years, it got about ~12 of the best students total, out of over 100 in other specialisations and the classes one takes after choosing are indeed very demanding. The question is, how beneficial would it really be to choose something this demanding. The way I see it, it certainly has a lot of benefits, attending difficult classes with the best students in the given year would certainly be very educating. On the other hand, it'd be very time-consuming, leaving little place for one to keep learning additional things, outside of the standard curriculum.

How much does a student actually benefit from attending classes at a significantly higher level than normal, at the expense of their freedom in choosing what branches of mathematics they could study on their own(which would be possible if an easier and less time-consuming specialisation was chosen)?

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    $\begingroup$ Talk to students who were faced with the same decision: ideally, both current and graduated. For those who have finished the program (whether the theoretical track or applied or economic): Are they satisfied with their choice? Would they have done things differently? Why? And, of course: What are they doing now? $\endgroup$ – Benjamin Dickman May 13 '14 at 22:25
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Warning: personal preference-based answer:

I tend to do much better at challenging things that I enjoy than easy things I find uninteresting, and as an undergraduate/postgraduate student I wouldn't have dreamed of picking something dull because it was easy - I would have been seriously demotivated.

For example, I'd rather spend three hours writing a program that works something out automatically than two hours working it out myself.

My job is difficult and stressful, but it's fun, and there's no way I would swap it for something routine.

University is a great time of life to devote yourself wholeheartedly to learning; later on you will not be so free.

You're in a dilemma between doing the interesting thing as the main thing or when you have spare time. I'd choose it as the main thing.

The more you can find out about what each route will be like, the better you will be placed to make this decision.

Caveats: I'm not you, you might have different priorities in life; for example, I find many people prioritise money higher than I do. You have to make your own decision - it's a mistake to not work out what you believe is best for you.

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Very hard to answer, as this depends sensibly on your interests and aptitudes. If you are really interested in the "demanding" track, by all means try it. If you don't, you could end up regretting it all your life. It can't be that you can't switch in the middle if you find out it isn't for you. And I doubt any courses you take that aren't needed in the end will be completely useless...

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  • $\begingroup$ Well, I am interesting in the more demanding track, and I enjoy pure mathematics a lot more than any applied stuff that will be involved in other specialisation. But I also like to pick a branch that I'll study on my own, and that's something I might not have enough time to do if I choose that specialisation. I'm wondering if that freedom of choice is actually important, or if maybe it's better to just stick to the curriculum and follow it without branching out based on my whims. $\endgroup$ – Ormi May 13 '14 at 21:29
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    $\begingroup$ @Ormi. I'd go for my principal interest. You can fill out later, I hope you have a long life before you. It's not that you'll be doing what you study all your life. And I'm sure you'll find ways to pursue side subjects somehow if you show sufficient talent to interest your teachers $\endgroup$ – vonbrand May 13 '14 at 22:33

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