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.

- 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]

**Jupyter Example:**Notebook made in 2019 illustrating basic calculations, mathematical functions, plotting, and drawing lines. [Jupyter notebook] [PDF] [CoCalc]

- SageMath has a tutorial, installation instructions, other help resources.
- Sage Introductory Programming Tutorial
- CoCalc is a free way to run SageMath.