Mathematical Foundations in AI

Modern AI rests on a small set of mathematical ideas. This course develops four of them — linear algebra, probability, stochastic processes, and optimization — and shows how each underpins today's AI systems. We study how linear algebra describes the computations inside neural networks, how probability and stochastic processes model data, uncertainty, and sequential decision-making, and how optimization turns these models into algorithms that learn. Throughout, theory is paired with applications in deep learning, reinforcement learning, and large language models, giving students the mathematical tools to understand, analyze, and improve modern AI methods.

Peking University · MELON Research Group