Title of the course: Geometry and Calculus in Spheres
Instructor: Dr. Evgeny Malkovich
Institution: METU NCC
Dates: 31 August – 6 September 2026
Prerequisites: Basic knowledge of differential and integral calculus, analytical geometry (derivatives, 2d integrals, surfaces, dot- and cross-products, Gram matrix…)
Level: Graduate, advanced undergraduate, beginning undergraduate
Abstract: In this course will study some interesting facts about the geometry and topology of the spheres. We will start with well-known facts on the circumference of a circle and the area of the spheres. And we will try to finish explaining how 3d-sphere S^3 (i.e. unit quaternions) generates the rotations of 3d space. Also the following topics will be discussed: Jordan curve theorem, Dido’s problem, Platonic solids, Euler characteristic, Girard’s theorem for spherical triangles, Poincare-Hopf theorem and is it possible to brush a hedgehog?
Language: English