Introduction to Nonlinear Dynamics Unit 1

Nonlinear Dynamics: Mathematical and Computational Approaches is an (excellent) online course offered by Complexity Explorer. Unit 1 provided a general introduction to nonlinear dynamics and maps covering the following topics:

  1. Introduction to nonlinear dynamics
  2. Maps and difference equations
  3. Transients and attractors
  4. Parameters and bifurcations
  5. Field trip: Boulder Creek

Flexagons and the Math Behind Twisted Paper

Below I’ve collected my notes taken during the FutureLearn 3-week online course “Flexagons and the Math Behind Twisted Paper” presented by Dr. Yossi Elran of Davidson Institute of Science Education, Weizmann Institute of Science. This was a fascinating introduction to Flexagons and symbols to describe them, Möbius band, Catalan numbers and more. These are pretty rough notes at the moment, probably not very meaningful to those who haven’t taken this course.

KaTeX, Khan Academy's Math Typesetting Library

Khan Academy has published the fastest typesetting library for the web. IntMath’s KaTeX and MathJax comparison demo shows some impressive performance improvements. The demo page took 177 ms to process on my laptop. The MathJax version on the other hand took 4777 ms. The performance comes at a price that not everything is supported in KaTeX (yet). I wish aligned equations were supported, but I can live with it. Until I run across more serious problems I’ll happily use KaTeX instead of MathJax.

Zequals and the Art of Estimation

This Numberphile video is about Zequals which can be useful if you need to compute a quick estimate, for example to find out if your calculation is on the right track. The idea is to ruthlessly round every number to just one significant digit. For example: 3 * 7 = 21 zz 20 7 * 8 = 56 zz 60 436 * 68 zz 400 * 70 = 28000 zz 30000 The actual answer is 29648 and surprisingly close to the zequal-result.