Here are video lectures from Taiwan Mathematics School; some of them were delivered in Mandarin: https://sites.google.com/view/tms-home/media-archive?authuser=0
The following courses (all in Mandarin) were taught by Professor Chen-Yu Chi at National Taiwan University:
- Calculus 1 & Calculus 2. The topics in these courses are more like "advance calculus", not the usual calculus content.
- Analysis 1 & Analysis 2. The topics include complex analysis, de Rham cohomology, functional analysis, Lebesgue integral, smooth manifold, measure theory, ODE, singular homology, topology.
- Algebraic Topology. The main textbook is Algebraic Topology by Edwin H. Spanier.