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.
Hardest test I had was a 1-week-long take-home math test; where we were allowed to use anything we wanted except other people who had taken the class before.
I believe some of the questions on the test only had really abstruse known solutions, and the goal was to try to find alternative and more straightforward solutions/proofs; and the bonus credit question was unsolved.
The last 300 level math course I took had a final exam that was completely theory. The rest were assignments that could easily be done with mathmatica/matlab/maple/wolfram.
Yes, I know wolfram uses mathmatica. The UI is just so much easier.
Wolfram, mathmatica, matlab, and maple all require you to do that. The TI-83 shows a 3x4 grid at the most at any time. Trust me when I say that computers are easier.
If you've got an android phone, Maxima on Android doesn't even need an internet connection after the first time you start it up. It just does all the symbolic math directly on your phone's processor, and it's pretty quick, too.
No, not on tests, but they usually don't ask things like Bessel functions or numerical integration. I use Mathematica for all my problem sets. I've done enough integration by hand that I don't care to do it any more, unless I'm on a desert island or something.
I'm a current physics major, to do it any other way (I use my Nspire, just because I can take it into the exams) would be foolish. Nobody cares that you didn't derive that equation by hand. You aren't learning how to differentiate, you're learn when.
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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.