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Choosing math courses is one of the most important aspects of being a math major, though these choices are often quite difficult. Upon entering Princeton, many math majors do not know which areas of math to explore. Even for those who have decided this question, it is often not apparent which courses to take and in what order. Moreover, there are always questions of which courses it is feasible to take simultaneously, which courses overlap in material covered, what knowledge does one need before taking a course, and many others.
The goal of this course guide is to provide information to help math majors make these decisions. Before this course guide was compiled, the available sources of information were the registrar's Course Offerings and the math department's undergraduate courses page. These two are important information sources, and every math major should consult them. This course guide supplements these sources by bringing in the student's perspective. All of the information presented here is taken from the experiences math majors have had taking these courses.
Princeton's Math Department is often lauded as one of the very best in the world. Now you can see how they approach the study of the subject there.
(Score: 3, Interesting) by bzipitidoo on Sunday December 04 2016, @05:06AM
I got a lot of math in my education. Calculus in high school. But I didn't feel that I really understood calculus and opted to take the college level calculus classes, even though I had earned a B in Calculus I with my AP exam score. I thought they might be better taught at the college level. Nope! Was a big mistake. I ended up with a C in Calculus I thanks to the graduate student they had teaching that class being an inexperienced, nitpicking ass. Lost a whole letter grade on a test for forgetting to put dx/dy on all my correct answers. He just mechanically took 2 points off each time I made that same mistake.
Then the school got me with another hole in the rules. My SAT scores were good enough that I didn't have to take any freshman math before Calculus. But, weirdly the school did NOT give us credit. By the time everyone in my major was done with the required math, we'd all had the same amount of math, but most of my classmates had 15 hours of credit, and I had only 12. An advisor told me to take trig, but I rejected his lame advice, and a good thing too, as I would not have gotten credit had I followed it. I was forced to take a more advanced math class, and picked differential equations.
Anyway, my experience was that math teaching is focused too much on trivia, too much rote learning through drills. Definitely not enough understanding, so that students learn where and how to apply it. For instance, what distinguishes an analytic proof from a geometric one? What's the distinction between an irrational number and a transcendental number, and why do we care? Why is "Squaring the Circle" so hard? Transforms such as Laplace and Fourier are pretty useful and cool. And FFT, don't forget FFT. But math classes tend to dwell on the tedious details of how to do them, rather than when to use them and what to do with them. That's particularly annoying now that we have smartphones that can handle the details.
(Score: 2) by fubari on Sunday December 04 2016, @08:41PM
agree r.e. understanding / depth of concept coverage.
And yeah I've had TA's like you describe.
I'm re-studying all the math I've forgotten. My first time around (pre-internet, yeah I'm that old :-) ) the drill was to hurry to keep up and cram for tests (being un-interesting was just icing on the cake-of-apathy... couldn't compensate for that).
As for depth, I've been pleased working through the stuff on Khan Academy; I find myself wishing it had been around when I was starting out.
If the kids over at Khan Academy keep working I wouldn't be surprised if they keep going deeper and further... but for now they haven't gotten into linear algebra or the same.