# InfoCoBuild

## The Algebraic Topology: A Beginner's Course

The Algebraic Topology: A Beginner's Course (UNSW). Taught by Professor N. J. Wildberger, this course provides an introduction to algebraic topology, with emphasis on visualization, geometric intuition and simplified computations. Algebraic topology is one of the most dynamic and exciting areas of 20th century mathematics, with its roots in the work of Riemann, Klein and Poincare in the latter half of the 19th century. This course introduces a wide range of novel objects: the sphere, torus, projective plane, knots, Klein bottle, the circle, polytopes, curves in a way that disregards many of the unessential features, and only retains the essence of the shapes of spaces. And it also has some novel features, including Conway's ZIP proof of the classification of surfaces, a rational form of turn angles and curvature, an emphasis on the importance of the rational line as the model of the continuum, and a healthy desire to keep things simple and physical.

 Introduction

 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 Lecture 27 - Covering Spaces Lecture 28 - Covering Spaces and 2-oriented Graphs Lecture 29 - Covering Spaces and Fundamental Groups Lecture 30 - Universal Covering Spaces Lecture 31 - An Introduction to Homology Lecture 32 - An Introduction to Homology (cont.) Lecture 33 - Simplices and Simplicial Complexes Lecture 34 - Computing Homology Groups Lecture 35 - More Homology Computations Lecture 36 - Delta Complexes, Betti Numbers and Torsion