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This course explores the concepts of the Klein bottle and projective plane in Algebraic Topology. By investigating the five Platonic solids and using Euler's formula, students will learn about the relationships between vertices, edges, and faces. The course employs a triangulation argument and delves into the concept of flowing down a sphere. The intended audience for this beginner's course includes individuals interested in foundational issues in mathematics and seeking a new approach to Algebraic Topology.
