#Math101 Session 40

Time：Oct. 22, 2026, 13:30-15:30

Location：Online via Tencent Meeting (ID: 927-712-396)

Speaker：Mr. Chen, Jiahou (Class of 2023)

Title：An invitation to differentiable manifolds

Abstract：This session offers a rigorous introduction to the foundational principles of differentiable manifolds. We begin by defining a topological manifold as a Hausdorff, second-countable space locally homeomorphic to R^n, grounding these topological axioms with classical examples such as spheres and tori. We then introduce differentiable structures by exploring the construction of coordinate charts, the smooth compatibility of transition maps, and the formulation of maximal atlases. This framework allows us to define smooth functions and mappings on manifolds by pulling back to local coordinate charts in R^n, thereby providing a bridge between standard multivariable calculus and modern geometric analysis.

（文：申爽/审核：郭千桥）