Step-by-Step Math

http://blog.wolframalpha.com/2009/12/01/step-by-step-math/

by kqr2 • 17 years ago

132 32 17 years ago

blog.wolframalpha.com

ludwig• 17 years ago

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.

yummyfajitas2• 17 years ago

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...

timwiseman• 17 years ago

There have always been ways to cheat at basic school work, if nothing else by grabbing someone who did know how to do it and copying theirs. This does add one more way, but it can also be constructive if struggling to learn something.

amichail• 17 years ago

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

dagw• 17 years ago

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'.

DougBTX• 17 years ago

Assume learning by doing, and Alpha's ability to solve any introductory problem, and you are screwed.

pmichaud• 17 years ago

I've been offering these kind of calculators for a while to students... but the department doesn't require a grad their homework. Is this college? What college department requires that sort of thing?

yummyfajitas2• 17 years ago

It is a college:

http://www.math.nyu.edu/courses/Calculus/2009/Fall/122/hw.ht...

kingkawn• 17 years ago

You'll be able to tell who those kids are because they'll die on the exam.

pwmanagerdied• 17 years ago

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. :)

tudorachim• 17 years ago

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...

wtallis2• 17 years ago

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.

redorb2• 17 years ago

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

pragmatic• 17 years ago

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

Kids have it easy these days.

Seriously, this is really cool.

andreshb2• 17 years ago

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

Adrenalist• 17 years ago

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).

genieyclo• 17 years ago

This'll be perfect for precalc next semester

andreshb2• 17 years ago

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

hh• 17 years ago

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.

ntoshev• 17 years ago

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

rbritton• 17 years ago

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

gnosis• 17 years ago

Also see: http://www.research.att.com/~njas/sequences/

bioweek• 17 years ago

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

arohner• 17 years ago

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.

mkyc• 17 years ago

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.

jrockway• 17 years ago

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

orblivion• 17 years ago

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.

Step-by-Step Math

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