Language, Math, and Mind

Winter 2019 quarter

Taught by

Rachel Hastings
linguistics, mathematics
  • UG

Language and mathematics represent two areas of human cognition characterized by significant complexity and abstraction. In this program we will study linguistics and mathematics, as well as the cognitive structures associated with each of these areas of abstract thought and knowledge. We will analyze language structure, including the study of phonology (speech sounds), morphology (word structure), syntax (sentence structure), and semantics (linguistic meaning). We will also study mathematics, with the goal of illuminating the nature of mathematical thinking. Topics in math will be drawn in part from introductory logic and proofs, number systems, and elementary set theory. Although there is no particular math prerequisite, students should be ready and willing to engage in focused mathematical thinking. To facilitate the participation of all students, part of our work will involve collaborative learning in small groups of students with similar math background. Additionally, students will spend time working in groups with diverse math experience, with a focus on communicating mathematical ideas to a broader audience.

Alongside our studies of linguistics and mathematics, we will engage in seminar reading and discussion relating to cognitive processes associated with language and mathematical thinking. We will explore such questions as: How does the human mind handle abstraction? What is the role of metaphor in language and math? Can particular aspects of language and math be identified as learned or innate? How do children learn language skills (such as speaking and reading) and mathematics (such as numerical and spatial reasoning)? How do math and language vary across cultures?

The work for this program will include solving math problems, writing proofs, studying abstract principles of grammar, analyzing linguistic data to identify structure and unconscious rules of grammar, and reading and writing about cognition and mental structure. Students will also participate with a small group in a final project involving library research and a final presentation. Anticipated credit equivalencies for the program include introductory linguistics, mathematical reasoning, and seminar/project in cognitive studies.

Program Details

Fields of Study

consciousness studies linguistics mathematics

Preparatory For

mathematics, languages, linguistics, and cognitive studies.


Winter Open

Location and Schedule

Campus Location


Time Offered


Online Learning

Hybrid Online Learning < 25% Delivered Online