### Lecture Description

In this video lecture, Prof. N.J. Wildberger talks about duality for polygons and the fundamental theorem of algebra.

We define the dual of a polygon in the plane with respect to a fixed origin and unit circle. This duality is related to the notion of the dual of a cone.Then we give a purely rational formulation of the Fundamental Theorem of Algebra, and a proof which keeps track of the winding number of the image of concentric circles about the origin.

### 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.