stonecold3169
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- Jan 30, 2001
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Originally posted by: DrPizza
Originally posted by: RabidMongoose
abstract algebra was weird, but I did well in it even though I still don't know what it was about
lmao, I skipped a week or so of classes, with the prof's permission, to experiment and find out what it was like to struggle in a math class - so I could understand what my students would be experiencing when they struggled in math.
All I can say about that experience is that it made that class a major pita. I was so lost that I didn't know where to begin with questions. I still managed to get an A - so, like RabidMongoose, I "did well in it even though I still don't know what it was about"
I started from scratch during the summer after the course was over and went through everything again until I did understand it.
Otherwise, the hardest math I've done was independent research in understanding extra-dimensional objects by looking at their intersections with 3-d space. Daily headaches as I thought about it and worked on it. Or to put it this way, imagine you live on a line and can only comprehend 1 dimension. You only see a projection of a 2 dimensional image (such as a triangle) on your line. Spin the 2-dimensional image. View how its projection (a line) changes length as the 2-d object is spinning. Now, attain the ability to think in 2-d while you live in your 1-d universe. Figure out what the object looks like.
Now, you can move on to a 2-dimensional plane of existence. This is when I realized I could be more creative. Rather than just looking at a projection of a 3-d object on my two-dimensional space, I could even move the 3-d object through my 2-d space and view the 2-d intersection. ex) if a sphere could move through a piece of paper, its intersections (as it moved through) would start as a point and grow into a circle with a diameter equal to that of the sphere, then decrease back to a point before winking out of existence.
Taking this another step, I wrote a program on Mathematica so that I could view movies of 4-dimensional objects passing through 3-dimensional space. I attempted to train my mind to be able to grasp the shapes of 4-dimensional objects. I think I saw God or something... it gave me horrible headaches.
Otherwise, Real Analysis was one of the more difficult math classes to get an A in... tough prof.
Actually, if you've ever taken Abstract Linear Algebra, you spend a great deal of time looking at the projections of multidimensional objects transformed onto different sized planes (you actually touch on it in Abstract algebra as well, but you are never really told why at that point).
I agree with the point earlier that math is challenging and not hard... at least until you get into analysis, and then it becomes a freaking artform.
The hardest course I ever took on the undergrad level was complex anaylsis 2, which consisted of using proofs and theory to build solid proofs of what you guys did in calc 2 and why you did it. The class was a nightmare.