I program, and am also presently working my way through some math books. I find that I often have to backtrack to look up pieces of notation like variables and operators. Unfortunately, this is very problematic. Greek and Latin letters give no indication of where they came from and are not usable search terms, even knowing the full context in which they appeared. Many authors have their own bits of idiosyncratic notation, often combinations of subscripting and line art generated by TeX macros. Since expanding equations out to their definitions is so difficult, I sometimes don’t bother to investigate when one looks odd, which as you might expect leads to big trouble later when errors in understanding creep by.
This is not nearly as big a problem for me when reading code, however, because there every variable and nonstandard operator has a descriptive name wherever it’s used, and documentation is never more than a few hotkeys away. The same thing could be done for math. Suppose you took a typical higher math book, and replaced every single-letter variable and operator with an appropriate identifier. For me, this would make it much more readable; I would gain a better understanding in less time. However, I don’t know the effect size or how broadly this generalizes.
Do other people have this problem? Might this issue deter some people from studying math entirely? Has anyone tried the obvious controlled experiment? How about with an experimental group specifically of programmers?
Dense Math Notation
I program, and am also presently working my way through some math books. I find that I often have to backtrack to look up pieces of notation like variables and operators. Unfortunately, this is very problematic. Greek and Latin letters give no indication of where they came from and are not usable search terms, even knowing the full context in which they appeared. Many authors have their own bits of idiosyncratic notation, often combinations of subscripting and line art generated by TeX macros. Since expanding equations out to their definitions is so difficult, I sometimes don’t bother to investigate when one looks odd, which as you might expect leads to big trouble later when errors in understanding creep by.
This is not nearly as big a problem for me when reading code, however, because there every variable and nonstandard operator has a descriptive name wherever it’s used, and documentation is never more than a few hotkeys away. The same thing could be done for math. Suppose you took a typical higher math book, and replaced every single-letter variable and operator with an appropriate identifier. For me, this would make it much more readable; I would gain a better understanding in less time. However, I don’t know the effect size or how broadly this generalizes.
Do other people have this problem? Might this issue deter some people from studying math entirely? Has anyone tried the obvious controlled experiment? How about with an experimental group specifically of programmers?