MODELS,MATHEMATICS AND MACHINE LEARNING in Fall 2026 (MA1099FB2)

Humans across cultures have developed ways of representing ideas about quantity, space, and relationships in order to understand and act in the world. These ways of thinking, which we now call mathematics, are part of a broader human activity of building and sharing models.

In this course, you will explore how such models are created and used, with a focus on mathematical models. We begin with our own experiences, then examine how different cultures have represented number, geometry, and relationships. Along the way, we work with diagrams, number systems, and simple structures such as graphs to model situations.

We investigate how explanations become justifications and proofs, and how algorithms provide procedures for solving problems within a given model. You will implement algorithms from everyday contexts (eg. a recipe), from mathematics (like Egyptian multiplication and division), and from computing (such as sorting a list).

We then turn our attention to machine learning: models that are not only built, but trained. You will experiment with simple neural networks to see how such systems learn from data. Throughout, you will engage in hands-on activities, collaborative work, and reflection on your own learning as a process of building and revising models.