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I'm a mature student enrolling at a Maths degree course soon at the university. I'd like to be able to use some software package to help me visualize equations, graphs, play around with variables with some sort of sliders, watch the results, use that to help me understand Maths better.

Not interested in "real world" stuff for now (realistic simulations for engineering purposes and stuff like that). Just a good piece of software that I can use to better understand and manipulate and visualize mathematical principles; but at the same time something user friendly enough to allow me to concentrate more on the maths side of things, rather than spending all of my limited time fighting with the software to achieve the most menial of tasks.

I understand there's always a learning curve involved when picking up a new piece of software, I'm not afraid of that. But different packages will have different curve steepnesses...

Don't care if it's commercial or open source software.

I've been reading about Mathematica, Maple, Matlab and something called Sage. Looks like these are the main players in this market.

Any opinions on which software should I invest in to help me with my studies? Again, mostly to visualize and understand Maths. No need for anything more elaborate for now, although no problem if the potential for growth is already there.

Thanks!

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  • $\begingroup$ Matlab/Mathematica are your friends. $\endgroup$ – Shahar Mar 23 '14 at 22:25
  • $\begingroup$ i would go for something along the lines of Geogebra or Geometer's Sketchpad. The strengths are the ability to drag a diagram around, see how things change when you alter conditions. I learned with actual graph paper, actual compass and straightedge. The thing that is clearest to me about today's students is that they cannot actually see much of anything, no practice with drawing. Similar with 3-d visualization, i used to make models of polyhedra and so on. I am, of course, very old. $\endgroup$ – Will Jagy Mar 23 '14 at 22:25
  • $\begingroup$ I agree that both of these are worth looking at, and Geogebra is free. And...I agree, I'd probably construct the Euler line using a pencil , paper , straightedge and compass , (or perhaps download a document that had the results I needed). I love the diagrams in a journal like Forum Geometricorum and may put in the time to learn one of these eventually. $\endgroup$ – Alan Mar 23 '14 at 22:40
  • $\begingroup$ Now that i think of it, I do recommend zometool.com and those sets with the bar magnets and little steel balls. To some extent the things you can build readily are directed by the design of the toy, but the better ones still allow some flexibility. amazon.com/CMS-Magnetics%C2%AE-Magnetic-Building-Sets/dp/… $\endgroup$ – Will Jagy Mar 23 '14 at 22:40
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    $\begingroup$ Wow, that's what I need , a method of constructing Zonohedra! $\endgroup$ – Alan Mar 23 '14 at 22:41
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If you happen to own a Macintosh, the application named Grapher ( it's inside the utilities folder) seems to be a great application for visualizing results. It is very easy to start out with and can produce some very involved visualizations.

SAGE is free but it's visualization capabilities depend on getting Gnuplot to work correctly. I haven't gotten results equal to the commercial packages (the three Ms). Mathematica has so much support that I would probably recommend it above Maple and Matlab. Although , to some extent this will depend on getting a hands on copy to play with. Although I once owned a copy of Matlab and have it running on a much older machine I can't get a newer version to play around with, cost is prohibitive for me. So Maple is number two, I'm still learning it. Your results will certainly vary. Try SAGE first, maybe you'll have better luck with the Graphics package.

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  • $\begingroup$ Thank you, @Alan Yes I use a Mac, and I find the Grapher application very useful. Although it looks a bit limited and doesn't allow some kind of interactive interface that I can "touch and drag" to see changes in real time. I'm not a particularly smart or fast guy, so I think a tool like that would probably help me visualize and understand the concepts better. But I will play around with the trial versions of most of them, for sure. Regarding Matlab prices, the Home edition is marked at 105€/$145: mathworks.com/pricing-licensing/… $\endgroup$ – Toscano Mar 23 '14 at 22:47
  • $\begingroup$ Really, I'll take a look at it, I mean I own an old copy, but I'll take a look at the pricing, I really thought it was out of reach. Thanks! $\endgroup$ – Alan Mar 23 '14 at 22:52
  • $\begingroup$ Bought a copy of Matlab today, thanks for the heads up! $\endgroup$ – Alan Mar 25 '14 at 3:40
  • $\begingroup$ You're welcome, @Alan Who would have thought that I'd be able to help someone on my first post here? ;) $\endgroup$ – Toscano Mar 26 '14 at 16:38

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