Why don't educators and modern math text books use programming languages instead of mathematical notation?<p>As a programmer, I tend to absorb mathematical concepts by writing programs. With the recent emphasis on programming literacy, and the fact that much math ends up expressed in a computer program, why don't educators use programming languages instead of mathematical notation? Mathematical symbols are often difficult to represent without special editors. Modern languages (Python, Ruby, arguably R) can be used to notate algorithms in a few lines of code that replace "pseudocode" type illustrations.
Formal (math) notation has been around forever and it will probably stay that way. Using it to specify software is a recent application, but the meanings of symbols and their relationships are well established. Programming language syntax rules change, math does not. Also, math is more concise, more precise, and easier to analyze (prove that something is possible/impossible) than a programming language.<p>P.S. Check out Using Z (usingz.com). It is fantastic.
Some responses might involve analogies with musical notation. Knowing the notation allows you to read the modern literature and also great documents of the past. But it would seem that an awful lot of math could be applied with out having that depth of understanding. Guitar tableture serves as a suitable proxy for guitarists...