>>9578223I'm the Arizona comp ling guy from earlier. One big part of comp ling is natural language processing (NLP), which is how you take raw text and extract information from it to help you do cool stuff with it down the line. Like you might want to separate all the words in a corpus of text and get their parts of speech or syntactic information, that kind of thing. Then you can use that processed text for applications like machine learning, for example teaching a model to distinguish spam emails from legit emails using language data.There's also speech recognition/synthesis, which of course is what you see in Amazon's Alexa, Siri, Cortana, etc.
Anyway that's just an example. I recommend looking at Jurafsky and Martin's "Speech and Language Processing", that's a very popular book and it goes over a ton of stuff (not just speech like the title implies). Even just skimming the table of contents will give you some ideas. Another good book is Manning and Schütze's "Foundations of Statistical NLP"; it seems to overlap party with Jurafsky and Martin, but it was helpful anyway.
Oh and math-wise I'd say the list of topics is basic calculus, linear algebra, probability/stats, and logic. But you don't need very deep knowledge of them, assuming you're focusing on applied stuff instead of reading hard theoretical research.