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Math Typesetting, Mathematica, MathML

Xah Lee,

Here's a linear algebra notes i wrote in 1998, using Mathematica version 3, with much math typesetting. linearAlgebraNotes.nb. Mathematica 7 convert it to pdf very well. See: linearAlgebraNotes.pdf. Surprisingly, when converting to html, it actually generated a valid html with valid CSS. linearAlgebraNotes.html But further, it also exported to XML+MathML well: linearAlgebraNotes.xml (can be viewed with Firefox 3.6.12). Very well done!

A note about Mathematica's typesetting. Mma's typesetting capabilities is best on this earth. It was invented with Mathematica version 3 in 1996. It's not just a inert incomprehensible code as in TeX. For example, typing 1/Sqrt[x^2 + y^3], press a button, then it gets rendered into a 2-dimensional math notation. Yet, Mma understands it as a live math expression. When writing math, you don't need to learn some inane specialized formatting language. You just type as you code in a computer language. In a programing language, you can define functions. For example, in JavaScript f = function (x,y) {1/(x^2+y^3)}. Usually, the function name is limited to as a sequence of ascii chars. In other langs such as Haskell, you can define arbitrary operators. Again, the operator is limited to ascii chars, and basically just this binary form a ⊗ b. In Mathematica, you can define arbitrary 2-dimensional notations.

Also, whatever complex math expressions are automatically formatted, meaning, automatically wrapped. All these capabilities, i'd attribute to 2 very simple ideas:

Today, most mathematicians and engineers still use the extremely inane TeX/LaTeX. And much of open source offerings are based on TeX. MathML was a great idea (with much input from Wolfram Research), but it's a decade now and it's still practically not usable.

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