I'm a wannabe mathematician, whose master's thesis is (by the looks of it) going to focus on a certain "compiler", used to produce learning materials from a subset of $\LaTeX$, in the context of mathematics education. I'm of course going to have to talk about the compilation process in general, and was planning to discuss the mathematical abstractions related to it (this being a master's thesis in mathematics), and then use those to describe the compiler.
I have no experience in the field whatsoever, however, and was wondering whether the concepts of regular expressions and languages, automata and the like are actually used to model (and|or) describe the functionality of compilers in a professional setting. Is it typical (even in the industry) to use these methods of modelling compilers, or are there better alternatives available?
I simply stumbled upon these basic concepts in a certain course handout, and they seem useful, but I want to be certain.