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I'm only a lowly master's student so I don't have a good hold of all literature, and pragmatics & discourse aren't really my forte, so I think I'd rather refer you to a great resource: the Handbook of Linguistics, editors Aronoff and Rees-Miller. If you don't have hold of basic linguistics theory and concepts, you may give An Introduction to Language by Fromkin, Rodman, Hyams a go. For deepening on Chomskyan syntax, which has roots in mathematical / logical approaches, I suggest Syntactic Structures Revisited by Howard Lasnik, which is a truly wonderful pedagogical achievement, given the excess complexity of Chomskyan theory. In any case tho, if you are familiar with basics of linguistics, the Handbook is _the_ resource to familiarise yourself with latest research and history of ideas of any subdiscipline of linguistics.

Trying to talk about it a bit myself, I think I should start with saying that I don't really know methodology in pragmatics, but it and discourse analysis (DA) are pretty close to each other. Discourse analysis is an umbrella term for many research methodologies, and it's a hugely multidisciplinary field, so it's hard to pin it down. Tho suffice to say the concerns of DA inside of linguistics is separate from that in literary studies and the Foucauldian tradition, which tend more towards philosophical approaches. DA in Linguistics is more exact in general and focused on extents of written or aural or signed text and conversations. One of the most common tools is transcriptions peculiar to DA. There on we investigate different properties like structure, pauses or intonation in how they relate to different pragmatic goals, like turn taking in speech and signaling coherence, deixis, etc., in more "purer" DA research, and other strands of research like Critical Discourse Analysis or Feminist Discourse Analysis may then extrapolate how these reflect power relations or social preconceptions. This probably overlaps a lot with pragmatics---and a lot of theoretical and analytical tooling like speech act theory or Gricean maxims are shared---but AFAIU DA is more interested in textual (i.e. speech, not necessarily written) context here, whereas pragmatics in more mechanical and semiotic workings---tho I doubt subfields of linguistics are as distinct as some of the literature makes them seem to be. In any case, a more concrete method that's used a lot in DA (or other subfields) is corpus analysis, where large, often annotated corpora is used in order to test what constituents are found together.

Talking about your interest in math here, you may or may not find what you want in this. On the one hand, language is an incredibly flexible mechanism and almost everything, from words to farts to where one looks at has semiotic and discourse-relevant content, and this is something that conflicts a lot with more logically / mathematically motivated approaches like Chomskyan grammar. Simply put, language is hard to pin down, because unlike say in physics, chemistry, or astronomy, your subject matter is an extremely diverse, constantly changing beast that's produced with animals with extreme agency. But OTOH universe, biology, or materials are messy in their own ways and mathematical approaches have been useful in these pursuits. So it depends on where you come to it from, really.

As to the article you linked I'd say it falls under the umbrella of computational semantics which is an area I'm totally alien to (FWIW I'm more partial to usage based grammar and sociolinguistics). It does use corpora but that's not exclusive to discourse analysis (in fact its a methodology that began around the 90s and is used across all subdisciplines of linguistics today, maybe bar phonetics). There's an over reliance on the concept of the "word" as some basic elementary unit here, which is not really the case. There being a word to express something in a language or not is not really a barrier or obstacle to expressing it in any language. The study feels like it could really make use of another linguist among its authors. There are disciplines that explore language contact and variation, second language education, and translation in itself, which could have a word or two here.