
Step-by-Step Math - kqr2
http://blog.wolframalpha.com/2009/12/01/step-by-step-math/
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Adrenalist
Priceless:

    
    
      This is pretty nice I would like to see the interface 
      enhanced so I could enter several math problems at once (for
      example: Chapter 7, problems 1-19 (odd)) and have the output
      in a printable / customizable format (ie a script font that
      looks like my handwriting).

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yummyfajitas
Suffice it to say, my students love this. Graded homework is now obsolete.

Of course, the department says graded homework must still be turned in...

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amichail
Give homework where the most interesting part is not something that Wolfram
Alpha can solve.

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dagw
I remember university teacher of mine had a collection of a few problems which
if you typed it into Mathematica would give an answer on a very different form
than what you would be likely to get if you solved by hand the 'normal' way.
Handy for giving you a heads up on who might be 'cheating'.

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roundsquare
Same is true here. Look at the solution to the quadratic in the beginning. I
suspect most students would use the quadratic formula and not complete the
square by hand.

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mkyc
Cheating is now easier. That's good, for two reasons:

1\. The steps are small and have clear documentation. Copying a wall of
numbers does nothing. Copying delimited steps while being told exactly what
they are helps. Actually, it's a lot like typical classroom instruction!

2\. Cheating from someone "smarter" allows rationalization. The class is hard,
you suck at math, they're smart. But here a dumb process spits out answers.
The typical response to this sort of narrow AI is "well, it's not that
difficult after all". This suggests that you don't need an abundance of
ingenuity to do rote math of this sort. And that's motivating, if you're
feeling daft.

The mediocre borrow and the great steal; if a novice learns from brute copying
then we shouldn't give a damn.

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pragmatic
Where was this when I was working through Calculus 2...

Kids have it easy these days.

Seriously, this is really cool.

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andreshb
Agreed, easily one of the most exciting things Ive seen recently.

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tudorachim
Aww, after I saw the integration examples I got my hopes up for a Show Steps
for this...

[http://www.wolframalpha.com/input/?i=integrate%5Bexp%28-t%28...](http://www.wolframalpha.com/input/?i=integrate%5Bexp%28-t%28t+a%5E2-u+b%5E2%2Bt+b%5E2%29%2F%28a%5E2+b%5E2%29%29%2C+t%5D)

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wtallis
NoScript filters that link as a potential XSS attack. I guess it doesn't like
brackets in URLs. That could be a problem for Wolfram if the noscript author
can't find a safe way to whitelist wolfram alpha links.

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redorb
on a limb: I would say the overlap of no-script to wolframalpha users is
minimal / WolframAlpha has other bigger problems to fix first.

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atamyrat
How is that noscript strips URLs with brackets is WolframAlpha's problem?

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wtallis
Mathematica (and thus Wolfram Alpha) is unusual in it's use of brackets to
enclose function arguments. Every other computer algebra system I've used has
been content with parentheses. And NoScript is pretty much the leading edge
for browser security, so if it thinks brackets are dangerous, they probably
are and other browsers could follow at any time. Wolfram Alpha's direct use of
Mathematica's notation in URLs seems a bit naive, and it wouldn't be the first
time Wolfram embarrassingly misunderstood the way the web works.

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cracki
how would brackets be dangerous? just because the author of noscript thinks
they are, doesn't make them so. he's definitely not infallible.

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ntoshev
Hmm, can I get Wolfram Alpha to compute a closed form solution of a recurrent
sequence - like the Fibonacci numbers?

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rbritton
Yes. e.g., <http://www.wolframalpha.com/input/?i=1%2C+1%2C+2%2C+3%2C+5>

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ludwig
It would be also be nice if the list of steps wasn't displayed all at once,
but more like a lazy evaluator (Show-Me-Next-Step?). That way you can let
Mathematica lead you for a bit, but then still be able to proceed on your own
without too much guidance.

Then again, knowing the answer ahead of time doesn't really hurt since
understanding the steps in between is what matters.

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hh
I have been looking at sage (sagemath.org) and sympy to see if I can use open
source math packages to do something like this for <http://www.mathmaster.org>
but I don't have any successes so far. Have you seen something like this
besides commercial software? They have a nice API but looking at the licensing
cost make me read no further.

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orblivion
Aren't they spreading themselves a little thin a little too early? Google can
afford to explore different areas, but I think these guys should first work on
an impressive engine for pulling together information on the web in a
meaningful way before looking at more niche things like resolving math. Unless
it somehow calls on the same AI base and was very little work to develop.

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jrockway
I am so glad this didn't exist when I was taking calculus. I would have never
learned anything :)

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andreshb
Why oh why did you not exist when I was still in school! I was born too
early...

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bioweek
How do you program something like that? I'm impressed.

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arohner
Let's treat this as an interview question:

First, I'll assume alpha works similar to a compiler. It parses the text, and
generates an AST for the input expression. Your goal is to replace the tree
with the 'best' possible equivalent AST. Best here is a fitness function, that
provides a score for a given AST. At first glance, we'll say the AST with the
smallest number of nodes is optimal.

Then, create a list of legal operations on a subtree. Try an operation, and
see if the AST gets better. Repeat.

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pwmanagerdied
As a personal exercise, I've been working on a basic math engine of my own
recently. It's not very difficult to break problems down into computer-
friendly steps, but if you approach them that way it's another challenge to
choose the steps you should pull out to show in human-friendly output.

Here's a screenshot of the output from a very simple example in the current
version: <http://imgur.com/hevar.png>. It uses LaTeX for the equations and
Flot for the graphs. It's a fun project to work on; it can be surprising how
far a program can get by just repeatedly applying some simple rules. :)

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genieyclo
This'll be perfect for precalc next semester

