Quote:
Originally Posted by Jon Stratis
The big difference, from my perspective, is what needs to be done to find a solution - in Ether's problems, the only recourse is to actually understand the math involved and solve it yourself. This one is a standard mathematical item where the answer and derivation of the answer can be quickly and easily Googled.
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I disagree to some extent on this: one of Ether's recent quizzes was to calculate the integral of sqrt(x^2 + 4). Mathematica can do this with Integral[Sqrt[x^2 + 4], x] (or something similar) really quickly. But he asked for steps, which seems to mean you have to do it out by hand. Or not:
1. Use a free integral calculator like
Symbolab that gives the steps
2.
Wolfram Alpha ) has step by step solutions if you have the pro version (or the trial)
3. Mathematica has a Wolfram Alpha input (type == at the beginning of a line) that gives step by step solutions
Similarly, for the one about whether a series converges, Wolfram Alpha also has step by step solutions, and even with just the regular one, they tell you which test you can use to get the answer.
EDIT: Sorry if the wording made it sound like those quizzes aren't worth doing--they are, and they're really fun to do--or that they weren't well thought out--they are, and just how complicated the integral got should be proof of that... I was just saying that there are ways to get around the vast majority of math questions without actually doing them (if there wasn't, I'd probably never finish my math homework)
Math has really become about interpreting the problems and setting them up so a computer can do them rather than doing pure calculations. Yesterday my math teacher (I'm in multivariable) decided we needed more practice with integration in polar coordinates (\integral (stuff) r dr d\theta), so he gave us this quiz: Set up the polar integral to find the area of the region bounded by the lines x=0, x=6, y=0, and y=4.
The easy part of that question is finding the area, since it's just a rectangle. The hard part is setting up the integral, which isn't fun. The nice part is that I can use Wolfram Alpha to compute my integral to make sure it's correct.
It's like making design sketches: SolidWorks can do the math, but you need to know how to represent it or it's useless.
/off topic
Back to M1KRONAUT's quiz:
x = (2 + cos(0.5t))cos(t)
y = (2 + cos(0.5t))sin(t)
z = sin(0.5t)
In the future, if you create more math quizzes (and I hope you do--they're fun and CD can always do with more math

) consider making quizzes that require more interpretation of the question and can't be easily googled / wolfram alpha-ed. Consider something like these:
1. From my math teacher: Set up the polar integral to find the area of the region bounded by the lines x=0, x=6, y=0, and y=4. (no, I'm not cheating, I finished it already...) Or worse: Set up the integral in spherical coordinates to find the area of the cube bounded by the planes x=-1, x=1, y=-1, y=1, z=-1, and z=1.
2. The
birthday question or one that doesn't have as many videos explaining how to solve it... (I don't really get why it has been so difficult for many people to solve, but I guess I'm used to Singapore's math questions after using their workbooks for many years)
3. Any sort of word problems--in general, the type of questions that even Wolfram Alpha can't interpret. The types of questions that say "set up the ___" vs "solve ___" or even if they ask for a final answer, that require understanding the question before purely plugging in numbers.
EDIT: Look at some of Ether's math quizzes for inspiration on these. Even his "solve ___" ones can't easily be gotten on a CAS software / by googling it / from Wolfram Alpha, with the possible exception of the integral, which was interesting enough that I think it deserved to be one. Although I still believe that the first step of identifying
how to do it, rather than all the steps in the middle, is the hardest step that requires the most creativity. (Sorry Ether, I agree with you that we'll have to agree to disagree on this)