Topology: The Nature of Shape and Space

Advanced—Fall

Topology, a modernized version of geometry, is the study of the fundamental, underlying properties of shapes and spaces. In geometry, we ask: How big is it? How long is it? But in topology, we ask: Is it connected? Is it compact? Does it have holes? To a topologist there is no difference between a square and a circle and no difference between a coffee cup and a donut because, in each case, one can be transformed smoothly into the other without breaking or tearing the mathematical essence of the object.  This course will serve as an introduction to this fascinating and important branch of mathematics. Conference work will be allocated to clarifying course ideas and exploring additional mathematical topics. Successful completion of a yearlong study of Calculus is a prerequisite and completion of an intermediate-level course (e.g., Discrete Mathematics, Linear Algebra, Multivariable Calculus, or Number Theory) is strongly recommended.