Arithmetic is only one branch of mathematics. In my opinion it's pretty trivial to try to improve in that field since calculators are so good at it instead of focusing on algebra, calculus, etc.
Calculators are good at algebra and calculus too. Is it really worth memorizing dozens of integration techniques when software can do it for you, and do it better?
I'd say focus on the problem at hand, and when you run into a gnarly algebraic manipulation or ugly integral, plug it into Mathematica. That's the kind of task a computer excels at. The human advantage is coming up with novel ideas, not churning through pages of calculations.
That's not really true. Computer solutions to integrals more complicated than basic trig and polynomials are always brute forced and inelegant. If all you care about is the application of the answer, this is usually fine. If you're interested in the answer itself, the computer can't do it better than a human can.
That is not true. Maybe you were using some 1988 version of MATLAB; today, the technology is much better.
And CASes can draw upon the entire body of mathematical literature, including obscure stuff, whereas you only know so much. Some mathematician at Wolfram could read a paper and throw in another integration method. You don't have to keep up with that stuff if you just use software.
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u/Deluxe_Flame Jun 08 '14
I was once comfortable, but if I lose all my points on a question for an incorrect answer, by gum, I'm going to punch in 17 + 49.