Calculus

[in abyssia]

They say you truly learn your algebra skills until you take a calculus class. And it is true. I've learned some cool wacky algebraic manipulations in my CAL II class. Hard stuff man.

PLease, share your stories

[Chessnut]

You don't truly see the power of calculus until you have handled Fourier transforms and differential equations (beams bending, heat distribution, cable vibration/dampening, stress, etc.). It's fairly amazing how well you can understand the physical universe with these tools. Linear algebra is definitely more abstract, which, in my opinion, makes it more difficult. Using the word "algebra" has little meaning to me, as many mathematical concepts can be used to arrive at a solution. From what I have learned, the conclusion is more important than the method to arrive at the conclusion. Then again, I'm in engineering, so I'm likely biased. We aren't given the opportunity to see many derivations, which can be very beautiful.

I'd rather not force this into a thread about personal thoughts though (seems rather menial).

[druidakoda]

Have you had any analysis? That's the really heavy stuff. Very hard/different at first but once you grasp the concepts it's truly astounding and you'll feel much safer about using calculus in the presumptuous way it gets taught. It's an odd thing that in mathematical education you start with assumptions and then dig deeper and deeper down to the truth behind it.

I find algebra easier to understand myself, though later on it stops resembling what the layman thinks of algebra at all. I've just finished group theory just now and though all the ideas are quite straightforward, there are so many it's hard to keep track of them and you never know when some small result you learned a month ago will become an integral part to a current problem. Then eventually you learn about these big theorems (e.g. Sylow's Theorems) that incorporate so much and so varied an amount of information in their proofs that it's awe inspiring how someone had the insight to construct them.

From what I have learned, the conclusion is more important than the method to arrive at the conclusion. Then again, I'm in engineering, so I'm likely biased. We aren't given the opportunity to see many derivations, which can be very beautiful.

The conclusion is important, but the proof is necessary for the conclusion to be important. I understand why in engineering this is not regarded as important because, well, it's not mathematics. We're the creatures in behind the walls making sure you guys don't wreck the place. You're the creatures making the walls, making sure we have a home.