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. 🙂
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.
3 thoughts on “Algebraic Topology Video by Professor N J Wildberger”
I’m interested to know what’s meant by increasing accuracy in practical problems in a context like this. Would you know of anyone who’s reviewed the book in enough detail that it’s explained?
Thanks for the reply! For more information on the book, you can refer to http://web.maths.unsw.edu.au/%7Enorman/book.htm
There are also sample chapters for download!