The World of Mathematics

Term 3, Wed. Periods 4–5 (co-taught) · Niigata University

Syllabus

Note

This class is held online via Zoom.

Course contents (Orita’s part)

1. Euler numbers and polyhedra — Euler’s polyhedron formula
2. Euler numbers and wind flows — the Poincaré–Hopf theorem
3. Euler numbers and critical points of functions — Morse’s theorem
4. Euler numbers and the curvature of surfaces — the Gauss–Bonnet theorem