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.

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

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.