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!
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.
Check if her school has any Wolfram licenses already, or if you can peruse administration to adopt it. Parents' opinion should mean a lot.
Mathematica/Cloud for Students - start playing with code, best approach. Millions of fun things to do. If you get this -- a perfect exploration starter is this free book Elementary Introduction to the Wolfram Language -- it has very simple exercises -- auto-graded.
Wolfram Language & Mathematica free on every Raspberry Pi! - the true spirit of tinkering with tiny cheap but mighty hardware and sophisticated programming
Self-sufficient kick-starter for beginners: Wolfram Programming Lab
Annual Wolfram High School Summer Camp. This is simply unparalleled experience of packing months/years of learning in just a few weeks under guidance of mentors. Here are the past years kids projects to take a look at, amazing. Early career kickstarter.
Student Ambassador and internships. You get to use tech for free by doing some good for others (volunteering, educating, publishing, developing, - basically starting the youngster's career early)
The Last but not least -- maybe should have been first -- play for free with Wolfram|Alpha -- a lot of data + computations are possible just with natural language queries. It would get her accustomed with the system that can help her future college experience, things like calculus, physics, chemistry, etc.
You might also want to check out Wolfram|Alpha Notebook Edition. It eases the learning curve by shifting focus to free-from input and Wolfram|Alpha intelligence and then leading to actual code and understanding how it works.
(Many other things you can explore on your own on Wolfram sites...)
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.
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:
Download a free Mathematica Trial and familiarize yourself with the basic functionality.
If you like it, download and install a free Wolfram Engine
The answer would be incomplete if I don't mention the pluses and 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.
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.