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UNSW - The Algebraic Topology: A Beginner's Course

UNSW - The Algebraic Topology: A Beginner's Course. This is a collection of video lectures on Algebraic Topology given by UNSW's Professor NJ Wildberger. This is a beginner's course in algebraic topology suitable for advanced undergraduates, or those with mathematical maturity and some familiarity with abstract algebra (mostly group theory). It features a visual approach to the subject that stresses the importance of familiarity with specific examples. And it also introduces 'rational curvature', a simple but important innovation.

Lecture 01 - Introduction to Algebraic Topology

Lecture 02 - One-dimensional Objects

Lecture 03 - Homeomorphism and the Group Structure on a Circle

Lecture 04 - Two-dimensional Surfaces: the Sphere

Lecture 05 - More on the Sphere

Lecture 06 - Two-dimensional Objects: the Torus and Genus

Lecture 07 - Non-orientable Surfaces: the Mobius Band

Lecture 08 - The Klein Bottle and Projective Plane

Lecture 09 - Polyhedra and Euler's Formula

Lecture 10 - Applications of Euler's Formula and Graphs

Lecture 11 - More on Graphs and Euler's Formula

Lecture 12 - Rational Curvature, Winding and Turning

Lecture 13 - Duality for Polygons and the Fundamental Theorem of Algebra

Lecture 14 - More Applications of Winding Numbers

Lecture 15 - The Ham Sandwich Theorem and the Continuum

Lecture 16 - Rational Curvature of a Polytope

Lecture 17 - Rational Curvature of Polytopes and the Euler Number

Lecture 18 - Classification of Combinatorial Surfaces I

Lecture 19 - Classification of Combinatorial Surfaces II

Lecture 20 - An Algebraic ZIP Proof

Lecture 21 - The Geometry of Surfaces

Lecture 22 - The Two-holed Torus and 3-crosscaps surface

Lecture 23 - Knots and Surfaces I

Lecture 24 - Knots and Surfaces II

Lecture 25 - The Fundamental Group

Lecture 26 - More on the Fundamental Group