AlgTop1: One-dimensional objects

This is a continuation of the series of Algebraic Topology videos. Previous post was AlgTop 0.

Professor Wildberger is an interesting speaker. He holds some unorthodox views, for instance he doesn’t believe in “real numbers” or “infinite sets”. Nevertheless, his videos are excellent and educational. Highly recommended to watch!

The basic topological objects, the line and the circle are viewed in a new light. This is the full first lecture of this beginner’s course in Algebraic Topology, given by N J Wildberger at UNSW. Here we begin to introduce basic one dimensional objects, namely the line and the circle. However each can appear in rather a remarkable variety of different ways.


Featured book:

Divine Proportions: Rational Trigonometry to Universal Geometry

Author: NJ Wildberger

This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included.

Algebraic Topology Video by Professor N J Wildberger

This is the Introductory lecture to a beginner’s course in Algebraic Topology given by N J Wildberger of the School of Mathematics and Statistics at UNSW in 2010.

This first lecture introduces some of the topics of the course and three problems.

If you are curious about how to make the interesting flap of paper (Problem 1), the solution can be found here. 🙂


Featured book:

Divine Proportions: Rational Trigonometry to Universal Geometry

Author: N J Wildberger

This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included.