The Classification of Closed Surfaces

In topology (an area of mathematics which can be viewed as an abstraction of geometry) one doesn't distinguish between spaces which can be continuously deformed into each other. Classification results are extremely sought for in mathematics but are rare. The topological classification of closed surfaces represents a classical but beautiful such result. We will introduce all relevant concepts and operations needed, and state this theorem in an intuitive way (no prior knowledge of topology will be assumed). This talk will be accessible to any undergraduate student interested in mathematics.