### Lecture Description

In this video lecture, Prof. N.J. Wildberger talks about the Borsuk Ulam theorem: a continuous map from the sphere to the plane takes equal values for some pair of antipodal points. This is then used to prove the Ham Sandwich theorem (you can slice a sandwich with three parts (bread, ham, bread) with a straight planar cut s so that each slice is cut cut in two. Also, we give an application to the continuum: the plane is different (not homeomorphic) 3 dimensional space.

### Course Index

- Introduction to Algebraic Topology
- One-dimensional Objects
- Homeomorphism and the Group Structure on a Circle
- Two-dimensional Surfaces: The Sphere
- More on the Sphere
- Two-dimensional Objects: The Torus and Genus
- Non-orientable Surfaces: The Mobius Band
- The Klein Bottle and Projective Plane
- Polyhedra and Euler's Formula
- Applications of Euler's Formula and Graphs
- More on Graphs and Euler's Formula
- Rational Curvature, Winding and Turning
- Duality for Polygons and the Fundamental Theorem of Algebra
- More Applications of Winding Numbers
- The Ham Sandwich Theorem and the Continuum
- Rational Curvature of a Polytope
- Rational Curvature of Polytopes and the Euler Number
- Classification of Combinatorial Surfaces (Part I)
- Classification of Combinatorial Surfaces (Part II)
- An Algebraic ZIP Proof
- The Geometry of Surfaces
- The Two-holed Torus and 3-Crosscaps Surface
- The Two-holed Torus and 3-Crosscaps Surface
- Knots and Surfaces (Part I)
- Knots and Surfaces (Part II)
- The Fundamental Group
- More on the Fundamental Group

### Course Description

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.