Week 3: September 14 - 18

Deterministic Dynamical Systems

This week we study "deterministic dynamical systems". These are systems which develop over time, where the current state completely determines the future.

Week 3 Notebook

Mayfly Model

The example we use is the "Mayfly model", a discrete-time model of mayfly population dynamics. This model is developed in class, and we begin to explore the behavior of the model using a numerical simulation.

Large numbers of mayflies often mature together within a short period of time, leading to swarms so thick that they blanket roads, buildings, and show up on radar.

IPython Notebook

• IPython "magics": %pylab inline

Python

• xrange
• break
• continue
• pow
• Labeling plots

Quiz 2

• Lists
• append
• List indexing and slicing
• List concatenation
• plot
• range
• for loops
• IPython magics
Sample Quiz 2

Assignment 2: Are There any Non-Prime C-Numbers?

A "C-number" was defined in class as an integer n > 1 such that bn mod n = b for all integers 1 < b < n.

Activity:

• Find out if any non-prime C-numbers exist.

Tools:

• Develop a way to check if an integer is a C-number.
• Develop a way to check if an integer is prime.