I would recommend learning JavaScript first, as it is supported in all major browsers and does not require the installation of additional plugins, so it seems to be the perfect candidate for your "maximum possible audience" requirement.
In terms of supporting high-level math, you will most likely want to find a good library to use. I donβt know all your needs, but a simple search for the "Matrix Algebra" JavaScript library came up with this as the first result that looks promising,
If you do not find a library that meets all your needs, you can build mathematical functions that you will need yourself. This may sound like a hunch, but keep in mind that all higher-level functions are built on the basis of lower-level functions, and since JavaScript is a functional language, it is well suited to create this type of functionality. However, I do not know your programming knowledge, level of commitment to the project, or the complexity of the functions that you will need. Thus, if this proves a cumbersome task, and Java handles everything you need, then the applet is a good second option.
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