Introduction to Ergodic Theory
(MATH 307K – 2026–2027 Fall)

• Syllabus
• Poincaré's recurrence theorem
• Kac's recurrence theorem
• von Neumann's ergodic theorem
• Birkhoff's ergodic theorem (proof 1)
• Birkhoff's ergodic theorem (proof 2)
• Mixing
• Topological transitivity
• Minimality and almost periodicity
• More on topological recurrence
• Probability measures on compact metric spaces
• ...
• Assignment 1
• Assignment 2
• Assignment 3