In this video lecture, Prof. N.J. Wildberger introduces the central theorem in Algebraic Topology: the classification of two dimensional combinatorial surfaces. We use cut and paste operations to reduce any combinatorial surface into a standard form, and also introduce an algebraic expression to encode this standard form.
In this course, Prof. N.J. Wildberger gives 26 video lectures on Algebraic Topology. This is a beginner's course in Algebraic Topology given by Assoc. Prof. N J Wildberger of the School of Mathematics and Statistics, UNSW. It features a visual approach to the subject that stresses the importance of familiarity with specific examples. It also introduces 'rational curvature', a simple but important innovation. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.