Stanford University Mathematics Camp - Program 2: Algebraic Topology

SUMaC welcomes an elite group of talented current 10th- and 11th-grade students from around the world for three weeks of intensive online study in advanced mathematics. Program II centers on algebraic topology, a major area of current mathematics research. Topology is the study of the properties of shapes that remain unaffected by deformations. For example, a sphere made out of rubber can be deformed into the shape of a cube. While it may appear that a sphere and a cube don't have that much in common, it turns out that they are topologically equivalent and in a way that can be made precise mathematically. This course will explore different ways of analyzing topological properties of shapes using algebraic concepts, such as the notion of group.