One very useful feature is that any concept or word has links to related concepts & words - synonyms, antonyms, misspellings included. You might define a language that lets you talk about relationships between objects, and try to pattern match (for searching). The ability to modify a search, and suggested modifications, could help. Google does a little of this, but is hardly a model of usability for newcomers. Possible test cases for a matcher: Lookups on subexpressions within expressions, equations, inequalities. Finding subdiagrams within geometry proofs. I suggest abandoning the distinction between student/teacher for purposes of access. The costs are high. Rich ----- Quoting Joshua Zucker <joshua.zucker@gmail.com>:
On Fri, Sep 9, 2011 at 3:31 PM, <rcs@xmission.com> wrote:
While we're on the subject of math-related databases, I'll mention another collection we need: Worked Problems & Puzzles. Mathists generate and solve a lot of problems. Most of these are not profound enough to publish. It would still be worthwhile to collect them, to smooth the path for followers. Collecting is the easy part; the hard task is organization & making it searchable. For example, some of the geometry problems we've discussed over the years: How to make them searchable beyond adding keywords? Searching for "ellipse intersection" is too unspecific.
I'm very interested in helping create or maintain something like this, although my particular interest is in problems suitable for the K12 audience, which has only some overlap with the problems that Rich is thinking of here.
So far I don't have any better ideas than tagging things with keywords, some from a pre-cooked list of standard topics and others subject to creation on the spot by the problem contributor. So if anyone knows anything about how to organize a useful database along these lines, please let me know!
You can look at http://www.mathcircles.org/content/problem-list for a beginning effort in this direction.
--Joshua Zucker
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