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.