Syllabus

Instructors

• Agnès Beaudry — Mathematics 312 · Office hours: Mondays & Tuesdays, 11:00 am–12:00 pm
• Katherine E. Stange — Mathematics 308
• Jonathan Wise — Mathematics 204

Course plan

Four thematic units, each culminating in a concrete project:

Theory of LMs

How language models work: tokens, context, transformers, training — and the distinction between a model and the broaderAI system built around it.

Project: Build a small language model in Python

AI-assisted research

Using AI tools for mathematical work: vibe-coding, vibe-proofing, agents, and harnesses.

Projects: Vibe-coding visualizations; AI-assisted research paper; class-built harness

Formalization

Introduction to formalization languages — Lean — and proof assistants for verification.

Projects: Formalization of research paper; add formalization harness

Ethical practices

Issues surrounding AI in mathematical research: data sources, bias, resources, environmental cost, verification, responsibility, disclosure, reproducibility, attribution, and consequences for mathematicians.

Project: Class written guidelines for responsible AI use in research

Grading

Class participation comprises the full grade. All participating students receive an A.

Acceptable use of AI in this class

AI is acceptable for any assignment or project in this class and required for most.