But I learn those without, and I do it faster than most anyway…</p>
<p>My point is that I can study at roughly 150% pace without doing problem sets and still getting excellent grades, is it worth the extra work to go upwards 250-300%? In a way I think so, so I take more courses than I can handle, but of course then my grades drop a bit since I still do not do the work. However that is not that bad since it is extremely easy to retake courses here so I can fix my grades when the material have grown on me.</p>
<p>Maybe you can help me structure my time? I think the problems is that I do not need to do it and that I have no experience of studying and that I haven’t done any exercises since sixth grade. I have checked the US curriculum and your requirements for diff majors, and I got roughly enough for both a maths major and a physics major at the end of my second year and I did study at half speed my first semester, doing your majors in four years is kind of a joke…</p>
<p>And now I just sound like a ****** anyway, go me
But these things really irk me, *** am I supposed to do…</p>
<p>I think at some point you have to stop thinking about grades and set your own personal standards regarding where you want to be in your studies. I watched some of my friends who were math champions and what not in high school go through an interesting cycle. They loved math before coming to college and then they get to college, stumble over the material, and suddenly lose their interest in math, because whatever interest in math they had was tied to their grades and ability to do math. I myself hated math in high school but got to college and suddenly math was my favorite subject. No, I don’t always get spectacular grades in math, but I’m willing to work hard and I want to know math so much more intimately than my peers do. Forget grades and focus on what you want to get out of the experience. </p>
<p>Another point is that life is short, really short. Every once in a while, I like to ask myself the question if I died today what would be my biggest regret. Then I would work harder on making that regret go away. It would suck if you had the ability to be a great mathematician but you wasted so much time working your way through the foundational material that you didn’t have enough time to make a lot of great contributions, even worse you died.</p>
<p>Sure, I prob. could’ve graduated in my freshman year if I wanted to with a math degree – in fact, the only thing stopping that would be breadth requirements. That’s not the point – a math degree as per any major outline is probably useless if you really want to get into the subject. It’s basic vocabulary. If you want to get to fun, interesting math, that’s a different story. </p>
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<p>You may not have studied advanced enough material, then. Everyone from Terence Tao and below recommends working some homework problems, even if they all say the skills for solving these are different from those used to solve research problems. “Faster than most” isn’t the point – if you’re more talented than most students around you, great, but most students are really not that serious about mathematics. You need to compare yourself to those who are, or otherwise, ask yourself if you really like the subject enough. </p>
<p>There is certainly theory out there that is so ridiculously abstract that even the top mathematicians in the world will tell you to go read the canonical textbook reference on the material + do virtually all the problems in the textbook before coming talking to them about, for instance, doing a Ph.D. in that field. I have felt like you do at times, but that was only when I hadn’t gotten to material that really challenged me. </p>
<p>Before I advise any further – what is your goal in studying math?</p>
It is more of a way to really understand physics, the better understanding of the mathematical concepts the easier it is to understand the more advanced parts of physics.</p>
<p>But in reality I don’t care much for physics either, I just have a slight urge to understand general concepts. But that is still better than nothing.</p>
<p>Anyway, abstract algebra and such is nice since it gives you a better understanding of mathematical objects, proof based calculus courses helps you solidify the basics while PDE/functional analysis are directly linked to the physics topics. I have already taken the undergrad level courses in those subjects but I plan to take the masters ones too just to get the hang of it. Now, anything more abstract than that is completely uninteresting to me.</p>
<p>Anyway, if I were going to get interested in maths it would probably come a day were I had to work with it (Got to to do research), but that’s not now. And since I have already started on grad level courses in physics the chances of me changing aren’t that big. I am also much better at physics than maths.</p>
<p>And I was a bit modest when I said that I do it faster than most, what I meant is that I do it faster than everyone I know. Still probably some which are faster but it can’t be common at all…</p>
