Free course


Free statement of participation on completion

Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this free course, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the classification theorem of compact surfaces.

Course learning outcomes

After studying this course, you should be able to:

  • explain the terms surface, surface in space, disc-like neighbourhood and half-disc-like neighbourhood
  • explain the terms n-fold torus, torus with n holes, Möbius band and Klein bottle
  • explain what is meant by the boundary of a surface, and determine the boundary number of a given surface with boundary
  • construct certain compact surfaces from a polygon by identifying edges
  • explain how a surface in space can be regarded as a topological space.

You can start this course right now without signing-up. Click on any of the course content sections below to start at any point in this course.
If you want to be able to track your progress, earn a free Statement of Participation, and access all course quizzes and activities, sign-up.

Course content