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]
Notebooks made during classes:
- Jupyter Example: Notebook made in 2019 illustrating basic calculations, mathematical functions, plotting, and drawing lines.
[Jupyter notebook]
[PDF]
[CoCalc]
Links to other SageMath resources:
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