Geogebra is a free and multi-platform dynamic mathematics software

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Geogebra is highlighted as a valuable free, multi-platform dynamic mathematics software suitable for both learning and teaching, particularly for those unable to invest in advanced programs like Mathematica or Matlab. It is praised for its cross-platform capabilities and effectiveness in engaging students, especially for basic calculus and creating diagrams. For users seeking alternatives to Mathematica, Maxima is recommended, while Scilab and GNU Octave are noted as free and open-source alternatives to Matlab. The discussion emphasizes that different mathematical problems require distinct types of software solutions.
johndb
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Geogebra is a free and multi-platform dynamic mathematics software for learning and teaching. Looks pretty good to me if you can't afford an advanced software program like Mathematica or Matlab.
 
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I like Geogebra: cross platform, great fun for showing stuff to kids. Even does some very basic calc. Decent for quickly slapping together diagrams for other documents.
http://en.wikipedia.org/wiki/Geogebra

However, if you want an alternative to Mathematica, look at Maxima instead.
http://en.wikipedia.org/wiki/Maxima_(software)

Matlab has a few FOSS clones:
http://en.wikipedia.org/wiki/Scilab
http://en.wikipedia.org/wiki/GNU_Octave

Three very different problems need three very different types of program...
 
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