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Comment by elcapitan | Hacker News Reader

Method-wise it could be helpful to get a (lightweight) computer algebra software and learn how to use it and how to explore knowledge using it. One thing you won't have when you're out on your own is a method to just try out stuff and verify that it is correct, or to get better visualizations quickly. Often you will get stuck with something and need a different angle (which teachers or other students could normally provide). Then you can just open the software and play with it.

One place to do that for free on a basic level would be Wolfram Alpha: https://www.wolframalpha.com/examples/math/

Edit: (I mean this in addition to the learning resources like books and videos)

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Personally, I wouldn't recommend Wolfram Alpha, or anything proprietary. If you have some programming knowledge (as OP is likely to), Sympy and Matplotlib are much more capable and controllable (and free!).

I think if you're building up skills and knowledge, it should be towards something you have control over and can use in any situation without worrying about licences, cost, etc. At my university, we teach undergrad engineers Matlab, and it just seems like an expensive clunky dead end to me (though their numerical methods knowledge should be transferable).

I think for starting from scratch these software library interfaces (that is what they are) create way more problems than they solve, if OP is not experienced enough to use them. That doesn't mean they can't get around to use them finally, but for exploring a space a tool like Alpha that is both evaluating as well as explaining seems much more useful. Interacting with Sympy and Matplotlib seems like something you would do when you have already a solid understanding of what you want to achieve.

I'm not so sure. I use Sympy, Matplotlib, Numpy, etc. even when I am just exploring, and have little idea what I want to achieve.

I do use and recommend http://desmos.com, which is proprietary (but pretty limited and easily translated to Python). It doesn't lock features behind a paywall like Wolfram Alpha.

I was just guessing from OPs post saying that they don't even have basic highschool math knowledge, from which I would assume that translating mathematical concepts into concepts in Python would probably create more difficulties than necessary, whereas in Alpha you can just dump an equation and then get an interpretation. Matplotlib in particular is kind of an expert interface for a library, at least when I last checked it out.

Desmos looks interesting.

I use Desmos all the time when teaching. It's accessible to students with no programming knowledge, and the killer feature is that I can just give students a link so they can interact with a demo I've made.

For example:

Quadratic through 3 points (drag the points around): https://www.desmos.com/calculator/tf1f80zgug

Pythagoras's Theorem (drag the sliders): https://www.desmos.com/calculator/dbjxbeuzk7

Why shearing preserves area (drag the slider): https://www.desmos.com/calculator/1vykaqf7je

At my university we also use Matlab a lot. However, I've found that Octave is a very suitable replacement for all packages except Simulink, which is widely used for Control. The alternative here would be Scilab/Xcos.

I also use python/sympy/matplotlib/scipy/jupyter a lot and it's absolutely great -- highly recommend to the OP.

> Personally, I wouldn't recommend Wolfram Alpha, or anything proprietary. If you have some programming knowledge (as OP is likely to), Sympy and Matplotlib are much more capable and controllable (and free!).

If one doesn't mind proprietary, though, and wants even more capable and controllable, Mathematica on a Raspberry Pi is pretty cool, and is free (beer) and is included in the default install of Raspbian.

For an open source option: http://www.sagemath.org/

This is good advice, and Wolfram Alpha is magical!

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