[math-fun] Mathematics as Hypertext ... and a Logic Assistant
I'm contemplating two projects for final-year CS students to do: 1) Thinking of mathematics as (partly comprising) a set of: Theorems with Preconditions and Proof(s), Generalisation theorem-theorem relationships, Theorem-(used in/by)-Proof relationships Counterexamples ... I see this information forming a database with an application 'projecting' this information to a web-interface which allows one to navigate around 'theorem space'. This seems well-suited to the web, and the opportunities of multimedia (graphics, animation, video, sound) is just a bonus - perhaps helped also by the XML-style language MathML. I'm thinking of asking a CS student to create such a system. Question is - is there anything out there of this kind already? 2) The intended system is a 'Logic Assistant'. A user-student would be trying to prove something using the formal means of a logic with already-known results and rules of inference. The system would either know the proof (as provided data) or be trying to work it out too [and I think there are systems for this 'out there' but I don't know about them]. The student would start with say 100 points and lose a few points for every 'atom' of hint provided by the system. The system would be able to manage hints, compare what the student proposed with the right answer, and general be an assistant/mentor/tutor in the learning process. Same question as for '1' really - is there anything out there of this kind already? Thanks in advance for any inputs - Guy Haworth, Univ of Reading, UK
For your "math browsing" project, the closest thing I know of would be MediaWiki (used by WikiPedia) which has some math display capabilities. However, the state of math-on-the-web still seems primitive to me. A year or two back I wrote up some web pages about using math on the web: http://www.myphysicslab.com/web_math.html Another possibility is a commercial package like Mathematica (it has some hypertext linking capability). But I don't know how you would deliver the results to a wide audience. If you find something better please let me know! --erikn On Mar 27, 2006, at 3:28 PM, Guy Haworth wrote:
I'm contemplating two projects for final-year CS students to do:
1) Thinking of mathematics as (partly comprising) a set of: Theorems with Preconditions and Proof(s), Generalisation theorem-theorem relationships, Theorem-(used in/by)-Proof relationships Counterexamples ...
I see this information forming a database with an application 'projecting' this information to a web-interface which allows one to navigate around 'theorem space'.
This seems well-suited to the web, and the opportunities of multimedia (graphics, animation, video, sound) is just a bonus - perhaps helped also by the XML-style language MathML.
I'm thinking of asking a CS student to create such a system. Question is - is there anything out there of this kind already?
2) The intended system is a 'Logic Assistant'. A user-student would be trying to prove something using the formal means of a logic with already-known results and rules of inference. The system would either know the proof (as provided data) or be trying to work it out too [and I think there are systems for this 'out there' but I don't know about them].
The student would start with say 100 points and lose a few points for every 'atom' of hint provided by the system. The system would be able to manage hints, compare what the student proposed with the right answer, and general be an assistant/mentor/tutor in the learning process.
Same question as for '1' really - is there anything out there of this kind already?
Thanks in advance for any inputs - Guy Haworth, Univ of Reading, UK
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On 3/28/06, Erik Neumann <erikn@myphysicslab.com> wrote:
However, the state of math-on-the-web still seems primitive to me. A year or two back I wrote up some web pages about using math on the web:
One thing you didn't mention is AsciiMathML: ( http://www1.chapman.edu/~jipsen/asciimath.html ) It's a javascript parser that converts TeX math formulas to mathml. IE users need to download a free plugin for mathml, though.
If you find something better please let me know! --erikn -- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike
* Mike Stay <mike@math.ucr.edu> [Mar 29. 2006 11:10]:
[...]
One thing you didn't mention is AsciiMathML: ( http://www1.chapman.edu/~jipsen/asciimath.html ) It's a javascript parser that converts TeX math formulas to mathml. IE users need to download a free plugin for mathml, though.
Doesn't work with any of Mozilla/Firefox/konqueror for me... Let's mentions tex2mail (perl script coming with pari/gp): % tex2mail --linelength=99 --noindent < srctransc/log.tex / +-+ 2 \ 5 7 11 13 1 | 1+\|3 x+x | x x x x ------ log | ----------- |=x - -- - -- + --- + --- +...= +-+ | +-+ 2 | 5 7 11 13 - 2 \|3 \ 1-\|3 x+x / / 12k+1 12k+5 12k+7 12k+11 \ \~~ oo| x x x x | = > | + ------ - ------ - ------ + ------- | /__ k=0\ 12k+1 12k+5 12k+7 12k+11 / (Note the glitch with \infty at sum symbol) The input is \begin{eqnarray} \frac{1}{2\,\sqrt{3}}\,\log\left(\frac{1+\sqrt{3}\,x+x^2}{1-\sqrt{3}\,x+x^2}\right) & = & x - \frac{x^5}{5} - \frac{x^7}{7} + \frac{x^{11}}{11} + \frac{x^{13}}{13} \pm \ldots = \\ & = & \sum_{k=0}^{\infty}{\left( + \frac{x^{12k+1}}{12k+1} - \frac{x^{12k+5}}{12k+5} - \frac{x^{12k+7}}{12k+7} + \frac{x^{12k+11}}{12k+11} \right)} \end{eqnarray} Using UTF-8 could produce quite beautiful results.
On 3/29/06, Joerg Arndt <arndt@jjj.de> wrote:
* Mike Stay <mike@math.ucr.edu> [Mar 29. 2006 11:10]:
[...]
One thing you didn't mention is AsciiMathML: ( http://www1.chapman.edu/~jipsen/asciimath.html ) It's a javascript parser that converts TeX math formulas to mathml. IE users need to download a free plugin for mathml, though.
Doesn't work with any of Mozilla/Firefox/konqueror for me...
It has to be a version that has MathML support. The versions here at school have it, but I don't know if it's part of the main version or if you have to select that feature somewhere when downloading. -- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike
participants (4)
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Mike Stay