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I have finally decided to go more deep into math and cs, so to do that I will need proper tool, math tool. Could you please tell me what's the best open source math tool on the web today, since as far as I know majority of good math tools require you to pay for it, which is cool, but I am student and need some open source one and extra cash in my pocket. All are permitted to participate in choosing the best math tool.

Thanks in advance.

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    Specifying the type of math you plan on doing will help us give a more detailed response.2012-04-11
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    I agree with Austin. If you want to do "applied math," involving numerical computation/analysis, something like [octave](http://www.gnu.org/software/octave/) might be good. If you want to do "pure math" a computer algebra system like [GAP](http://www.gap-system.org/) might be good. If you're not sure, I would recommend [Sage](http://www.sagemath.org/) which combines the best open source packages in one platform.2012-04-11
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    A link to Sage: http://www.sagemath.org/2012-04-11
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    So it's Sage that you propose me to go with? And, yes I am not sure, basically all math involved would be best, if it's not possible then something more related to applied math would be OK too.2012-04-11
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    umm, octave is a good clone of mathcad, and its opensource, but really - mathematics, computer science are vast areas - need to be more specific - are you looking for software that is designed for educational purposes or software which aids in computation, problem solving etc.2012-04-11
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    What would you choose when you have been given the option to choose only one software, Sage or Octave?2012-04-11

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If you are at uni and can show digital image proving your enrollment. You can use Matlab under a student license. Also for statistics in particular R is quite famous and free i believe. Other software options maybe Ocatve but i have n't used that one before.

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    Yes, I have R already installed here, but it's more for statistics, rather than math. Also, I am a bit too lazy for going Matlab license, and I am not sure whether or not my faculty has a contract with Matlab Corporation.2012-04-11
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    You do n't need your faculty to contact them . I think they way i did it was download and install matlab when you need to activate it send the matlab guys a screen dump of you logged into your uni website showing that you are enrolled and undertaking classes this year and they would send you the key in a day or so. I think Matlab is a great tool and definitely worth the the effort, the direct competition to it is open source scilab which lacks documentation and some functionality. I went the scilab way and then converted to matlab. Good luck2012-04-11
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DMelt computational environment is free program (under GNU public license). It is Java, so it runs even on Linux/Mac. I use it for free since I do not do complicated staff, but when you need to do something sophisticated, you need to setup a membership.