Brief Introduction

This course introduces mathematical foundations for artificial intelligence through the lens of dynamical systems. Over four lectures, students will explore fixed points, stable and unstable manifolds, learning dynamics in multi-agent systems and games, complex and arithmetic dynamical systems, and applications of dynamical systems to machine learning.

The course will help students understand how dynamical systems connect with game theory, number theory, optimization, root finding, and machine learning.

Time

2026-07-14 ~ 2026-07-17  8:00 - 12:00

Lecturers

Trung Tuyen Truong, University of Oslo

Venue

Room 802, No.3 Teaching Building, Shanghai University of Finance & Economics

Application and Registration

No registration fee.

Program

Day 1: Foundations for Learning and Dynamics

Dynamical systems, fixed points, stable and unstable manifolds, and special results in dimension 2.

Day 2: Learning Dynamics in Multi-Agent Systems and Games

Fictitious play, gradient play, no-regret learning, and regret minimization.

Day 3: Complex and Arithmetic Dynamics

Complex dynamics, arithmetic dynamics, Julia sets, the Mandelbrot set, and examples from number theory.

Day 4: Applications in Optimization, Machine Learning, and Root Finding

Gradient descent as a discrete-time flow, Newton's method, Newton fractals, and applications to machine learning.