# SageMath in this course

SageMath is a software package for doing mathematics which is built on top of Python. It is free and open source, which is a significant advantage over commercial mathematics software.

We'll predominantly use SageMath to visualize dynamical systems and to conduct experiments.

## Course documents on SageMath:

• Starting up with CoCalc
• Orbits and Rotations: A notebook demonstrating orbits in the context of rotations of the circle. [Jupyter notebook] [PDF] [CoCalc]
• Periodicity: A notebook demonstrating periodic orbits on the doubling map of the circle, and demonstrating how to draw cobweb plots. [Jupyter notebook] [PDF] [CoCalc]
• Homeomorphisms of $\mathbb R$: A notebook describing the dynamical behavior of homeomorphisms of $\mathbb R$. [Jupyter notebook] [PDF] [CoCalc]
• Topological Conjugacy 1: A notebook demonstrating topological conjugacy in the context of homeomorphisms of $\mathbb R$. [Jupyter notebook] [PDF] [CoCalc]
• Bifurcations in homeomorphisms of $\mathbb R$: A notebook demonstrating one of the simplest examples of a bifurcation. [Jupyter notebook] [PDF] [CoCalc]
• The Logistic Family: Demonstrates varying the parameter μ from 1 up through a little beyond 3, where the family undergoes a bifurcation. [Jupyter notebook] [PDF] [CoCalc]
• Conjugacy in the Logistic Family: Demonstrates that the maps with parameter μ in the interval (1, 2) are all topologically conjugate on $[0,1]$. [Jupyter notebook] [PDF] [CoCalc]