Mental stagnation

For the discussion of math. Duh.

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crazyjimbo
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Mental stagnation

Postby crazyjimbo » Sat Jun 09, 2007 8:22 pm UTC

This thread's kind of related to the How Maths is Taught thread. It's also a bit of a moan.

I'm pretty good at maths, I understand the concepts I am taught fairly easily, and I can remember theorems and methods without trouble. I do well in my exams as a result.

But I don't feel like I'm *doing* maths. I'm just learning methods, and symbols and notation. I realised a while back, that I wasn't really thinking through what I was doing and I wasn't coming to any conclusions myself anymore. Everything was being spoon fed to me. This saddens me because I used to enjoy the creative thought processes I would go through and that 'epiphany feeling' when I worked something out. Now I'm stuck because I can't figure out how to get back to thinking for myself. I hope this is a passing phase, because next year I'll be going into my third year at university, and it should be the most interesting year yet.

So rant/moan over, has anyone else felt like this? Part of me wonders if I'm just not motivated enough, as I haven't found any areas that I really feel the desire to explore. Maybe some people could give me pointers on how to start exploring maths again.

EDIT: I hope I didn't come off as sounding too pathetic :?. Ah well, such is life :)

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Woxor
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Postby Woxor » Sat Jun 09, 2007 9:12 pm UTC

That's perfectly natural, and it will pass. Especially if you go on to graduate school (or graduate-level courses), your assignments themselves will become more challenging and you'll feel like you're learning more. I know that every time I manage to do ONE problem I've been assigned (I'm finishing my first year of grad school), I feel like a genius.

Unfortunately, there's a period between learning calculus and getting to the advanced stuff during which you might not have that same epiphany sort of feeling, because let's be honest, a lot of mathematics is boring details. But once those details are subconsciously natural to you, it gets awesome again. Just put up with it and study, and you'll get to that point. Even if you don't go to graduate school, your self-study can be pretty fun even with just a B.S. under your belt.

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EradicateIV
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Postby EradicateIV » Sat Jun 09, 2007 9:30 pm UTC

Woxor wrote:That's perfectly natural, and it will pass. Especially if you go on to graduate school (or graduate-level courses), your assignments themselves will become more challenging and you'll feel like you're learning more. I know that every time I manage to do ONE problem I've been assigned (I'm finishing my first year of grad school), I feel like a genius.


This is refreshing. I sometimes feel the same way but I know it's only bound to get better.

I mean, it's math! COME ON!
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SpitValve
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Postby SpitValve » Sat Jun 09, 2007 10:03 pm UTC

Out of interest crazyjimbo, what level of study are you at?

I found even in 1st year uni a good chunk of my calculus and physics stuff took some good thinking to nut out.

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3.14159265...
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Postby 3.14159265... » Sat Jun 09, 2007 10:25 pm UTC

Ok I JUST started liking the maths (1 year or so) and have been self-teaching number theory. IT IS FUCKIN GOREGOUS AWSOME

You people meant to tell me it will get boring some time during 3rd year?!?!?!
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crazyjimbo
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Postby crazyjimbo » Sat Jun 09, 2007 10:39 pm UTC

SpitValve wrote:Out of interest crazyjimbo, what level of study are you at?

I found even in 1st year uni a good chunk of my calculus and physics stuff took some good thinking to nut out.


I'm half way through an undergraduate degree. In terms of subjects I've covered, I've done some multivariable/vector calculus, some analysis (only real numbers), basic linear algebra, a bit of group theory etc. What I would consider to be the basics. I'm doing a scholarship thing this summer looking at differential forms.

Don't get me wrong, I'm not finding maths uninteresting, it just feels like I'm not the one doing the thinking. I just realised that I'm doing very little in the way of problem solving, because all of the problems I look at are solved by a method that we have been taught. It would be nice to look at some more open problems that I could explore, but I find it almost impossible to find this sort of thing.

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Spivak
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Postby Spivak » Sat Jun 09, 2007 11:56 pm UTC

You're just looking at the wrong exercises in my opinion. Just get a lot o the EXTREMELY DIFFICULT ones and you'll be fine. If even these ones bores you, well, you're a genius and you're not in the right course(is it an english word?).
Sorry for my bad grammar and my wrong ortography. I'm Brazilian, never left my country and I am too lazy to go to English classes. They bore me :(

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Woxor
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Postby Woxor » Sun Jun 10, 2007 3:44 am UTC

The idea of working on an open problem is SO tempting that it's probably an understatement to use the word "tempting" (I mean, who gets into mathematics to do what has already been done?), but you'll have to wait just a little bit longer before you can get a really good taste of that. There's just so much that has already been done at the intermediate level -- you need to learn more.

But before you start feeling too frustrated: the junior/senior level is where you finish passing over the big, tedious hump of undergraduate mathematics and start learning some basic advanced topics (analysis, algebra, some PDEs, complex analysis, etc.), which are a lot of fun just to learn and practice. The format of these and graduate courses is usually to assign a lot of difficult proofs for homework, so your creativity is tested more than your ability to regurgitate.


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