1) 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

2) The following courses (all in Mandarin) were taught by Professor Chen-Yu Chi at National Taiwan University:

 - [Calculus 1][1] & [Calculus 2][2]. The topics in these courses are more like "advance calculus", not the usual calculus content. 
 - [Analysis 1][3] & [Analysis 2][4]. The topics include complex analysis, de Rham cohomology, functional analysis, Lebesgue integral, smooth manifold, measure theory, ODE, singular homology, topology.
 - [Algebraic Topology][5]. The main textbook is *Algebraic Topology* by Edwin H. Spanier. 


  [1]: https://www.youtube.com/playlist?list=PLVJXJebpO4PhAc21JW-cYbzT3sq4s7Qg8
  [2]: https://www.youtube.com/playlist?list=PLil-R4o6jmGihq7XzdNzb0d5hHqEJbr6L
  [3]: https://www.youtube.com/playlist?list=PLil-R4o6jmGhUqtKbZf0LIFKd-xN__g_M
  [4]: https://www.youtube.com/playlist?list=PLil-R4o6jmGhkuZPmKL_A5Y7N4HOsa1nX
  [5]: https://www.youtube.com/playlist?list=PLp24IEwWwtLJBhl1TvYjXF1-17q5lDpd3