The goal of this course is to equip you with conceptual and mathematical tools to analyze and formally model language.

Humans use complex language, and this is one of the fundamental characteristics of our species. In this course, you will learn how to think mathematically by analyzing the structure underlying the languages we all speak and use to reason. We will learn concepts from formal language theory, discrete mathematics, set theory, and basic logic to explore and understand puzzling properties of language that we encounter in everyday contexts. Although the concepts we’ll use require attention to detail, we’ll see that not only are they very powerful, but also intuitive to work with. This course is an excellent opportunity to learn about symbolic, mathematical tools that have virtually no numbers, but have the power and precision to model accessible and intriguing data in the domain of natural human language.

This simple finite state machine characterizes some simple phrases in English

using sets to represent the meaning of a phrase like 'red car'

This representation of the world using Naive Set Theory allows us to model the meaning of some simple phrases in English

This course satisfies a General Education math requirement for certain majors.

Most recent syllabus

All past syllabi for this course