Lecture plan
Week 1
Introduction, first programs; the Fibonacci sequence
Week 2
Chaos in a simple iterative map: the logistic map.
Week 3
Chaos in further iterative maps: numerical derivitives and graphs.
Week 4
Defining, constructing and measuring fractals. Fractals vs. "crossover"
Week 5
Fractal properties of iterated maps. Origin of universality in these
maps.
Week 6
Newton's Laws; orbits, numerical errors.
Week 7
Simulation of thermal equilibrium: the Monte Carlo method; detailed balance
the thermally excited oscillator, self avoiding walk.
Week 8
Measuring fractal properties of self-avoiding walks, diffusive growth,
phase transitions.
Week 9
Cellular automata