With the help of an answer on Quora, I've written a paragraph explaining how mathematics can be used in linguistics:

The usefulness and type of mathematics varies greatly depending on the subfield within linguistics. Here are a few kinds of math commonly used in linguistics: * STATISTICS: Statistics is needed for anybody who ever wants to publish, since statistical methods are needed to validate research results. Additionally, a mastery of summary statistics would help one describe and better understand observations and trends within an area of study. * DIFFERENTIAL EQUATIONS & MULTIVARIABLE CALCULUS: The Fast Fourier Transform, Kalman Filters, and Autoencoding are all used in signal processing (advanced phonetics, speech recognition). This tends to be pretty specialized stuff, since it begins to deal with the acoustics of human speech, and involves a lot of number crunching. * DISCRETE MATHEMATICS: Useful in language modeling, including formal grammars, language representation, and historical linguistic trends. * SET THEORY: Set theory can be used to model the word classes, semantic classes, natural phonemic classes, and the allophonic variations of each phoneme in a language. * LOGIC: Reason and logic are the foundation for pragmatics, the study of implicature, so it follows that a good mathematical understanding of logic would aid someone in studying pragmatics. To an extent, logic can also model syntax and semantics (Truth Conditions, De Morgan's Laws, References, etc.) * GRAPH THEORY: Trees can be useful for modeling syntax trees, semantics taxonomies, language family trees, and etymology trees. Weighted graphs can model the lexical similarity between different languages, and lattice graphs can be used for optimality theory. * FINITE-STATE TRANSDUCERS: Context-sensitive rewriting rules of the form a → b / c _ d, used in linguistics to model phonological rules and sound change, are computationally equivalent to finite-state transducers, provided that application is non-recursive, i.e. the rule is not allowed to rewrite the same substring twice. In morphological parsing, inputting a string of letters into a Finite-State Transducer (FST), will output a string of morphemes. Weighted FSTs have applications in natural language processing, including machine translation, and in machine learning. * ELEMENTARY ALGEBRA: Nearly every field in linguistics uses algebra. From the corpus linguist looking to add up collocates to the German linguist looking to describe the subsets of populations who modify syllable-final voiced consonants. * MACHINE LEARNING, AI: Sentiment analysis, isogloss description, and vowel boundaries all tend to be very fuzzy problems that have a plenitude of data, but no clear mathematical function to describe them. Linguists use neural nets, support vector machines, and Bayesian functions to describe these boundaries to maximize predictive accuracy.