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My daughter is a high school student and she likes science. In a couple of years she will go to university. I had a look at the Wolfram products (I used myself Mathematica when I was young) but I was unable to figure out what could be best suited for a student like her who is starting do some non trivial mathematics and physics. There are many tools, some looking very similar. Any suggestion? Can we start with something free? Thanks for any help!

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    $\begingroup$ You could by a Raspberry Pi (<100 Euros/Dollars). IIRC correctly, there is a free version of Mathematica for the Raspberry Pi for educational purposes. $\endgroup$ Sep 9 at 21:20
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    $\begingroup$ Some universities offer their students free Mathematica licenses. In between, if your daughter wants to start immediately, there is a student/schoolchild licence, that is cheaper. Another story, what will she learn. $\endgroup$ Sep 9 at 21:45
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    $\begingroup$ The student edition of Mathematica is one of the best gifts you could ever give to a student interested in STEM. Just the increased chances of admittance to a great university, or for a scholarship, will pay many many times your small investment. $\endgroup$ Sep 9 at 23:05
  • $\begingroup$ Consider pointing her towards Wolfram Cloud Open Access (also a Getting Started notebook here), which is basically Mathematica for free in your browser! (As far as I can tell, the interface and functionality is very similar to a desktop version of Mathematica.) $\endgroup$
    – thorimur
    Sep 9 at 23:46
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    $\begingroup$ 2/2 : by Shankar, especially the intro math chapter, but many like Griffiths), and relativity (i liked Spacetime and Geometry by Carroll, much of which is available for free as a pdf, and introduces a lot of the math). I've heard good things about One, Two, Three ... Infinity as an intro as well. other more exoteric/general-audience books i love, which are still very interesting and dive a little ways into things, include Chaos by James Gleick and Gödel, Escher, Bach by Hofstadter. not sure if this is any help, but hope it is! good luck! :) $\endgroup$
    – thorimur
    Sep 10 at 0:06
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There are probably many pathways, but a lot depends on the person and her teachers (perhaps you) and practically it is always about starting somewhere. The basis of everything in Wolfram universe is the Wolfram Language with its key power: enabling people to think computationally, meaning to converse with computer naturally, in code, exploring and having fun, asking it to do neat and useful things. Learning any new language is tough, but could be fun. So here are some potential starting points, more towards fun and practicality.

(Many other things you can explore on your own on Wolfram sites...)

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    $\begingroup$ It should be noted to get the best hardware spec‘d available raspberry pi, it makes life significantly better when using mma on it! $\endgroup$
    – morbo
    Sep 10 at 11:23
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    $\begingroup$ Wolfram Alpha should be much more prominently featured in this answer; it should be the last thing on the list, but the first. It's a very useful tool that anyone with an interest in mathematics can use (e.g. every high school student who's studying math, which is basically every high school student). Want to solve for the roots of a parabola? You could do it by hand with the quadratic equation... or you can just type the equation into Wolfram Alpha and have it solve it for you. $\endgroup$
    – nick012000
    Sep 10 at 16:34
  • $\begingroup$ @nick012000 thank you, addressed :-) $\endgroup$ Sep 10 at 16:41
  • $\begingroup$ I think Wolfram cloud open access should be featured in this answer, as it gives free access to the full wolfram language and Mathematica notebook interface via a standard web browser! (note the difference between this and the Mathematica/Cloud link.) I personally think it's the best option for OP, since 1) it's free 2) it's as powerful as Mathematica, except that computation is performed in the cloud 3) learning the wolfram language (or any PL) is, in my opinion, much more rewarding in the long run than querying wolfram|alpha! $\endgroup$
    – thorimur
    Sep 10 at 22:23
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Many years ago, I helped our niece with selecting a computer for college. As part my research on useful software for freshman college students, I discovered Mathematica and bought a home license to help her with her math class(es). Turns out she never used it. All her efforts went into studying for the math class instead.

My lesson learned, is that someone needs to show the student how to use Mathematica to help them with their lessons and homework if Mathematica isn't used or taught by their teacher in class. If you get Mathematica you'll likely need to figure how to teacher her how to use Mathematica for her homework. I recommend she takes the Daily Study Groups as they are an excellent way to learn Mathematica to supplement your tutelage. There are also many teaching resources at Wolfram U.

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I use online WolframAlpha. It’s inexpensive and very capable. It will let you store notebooks in the cloud, and do everything that is in high school math

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Let me recommend one more possibility. It is a free option that has full functionality of the Mathematica Engine, but lacks the Mathematica Front End. The Front End has to be provided externally, via e.g. Jupyter notebook.

The plan would be as follows:

  1. Download a free Mathematica Trial and familiarize yourself with the basic functionality.

  2. If you like it, download and install a free Wolfram Engine

  3. Follow the instructions here to install Jupyter notefbook on Windows, Linux or macOS.

  4. Enjoy!

The answer would be incomplete if I don't mention the pluses and minuses.

Minuses

A. Open Mathematica Notebook, type something and press F1--you get extensive documentation. Working with the Jupyter Front End you loose this possibility and have to look at the online documentation.

B. You cannot work with graphics and plots interactively.

Pluses

A. Learning Jupyter notebook will introduce you to lots of other interesting stuff. You will come in contact with python, which is another very popular programming language;

B. You will gain a programmer attitude to programming and will memorize more commands;

C. You will be more disciplined and more thoughtful in choice of notations.

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