Geometry and Topology
Instructor: Yu-Wei Fan ( Tsinghua University )
Course Introduction: How can we tell a coffee cup from a doughnut? Why can't some knots be untied, no matter how hard we try? This course introduces powerful mathematical tools that transform such geometric mysteries into algebraic problems we can solve. We'll discover how paths and loops in spaces reveal their fundamental structure through the concept of fundamental groups. Along the way, we'll explore a wide range of applications while developing both intuitive understanding and rigorous mathematical techniques.