Contents

• Introduction
  • Overview of Module: From Simplicity to Simplicity in Complexity
  • Science and the Scientific Method
    • Examples
  • Summary
  • Appendix: A Mathematics Review
    • Calculus
    • Taylor Series
    • Exponential and Trigonometric Functions
  • Exercises
  • References
  
  
• The Physical Universe
  • Newtons Laws
  • Work, Energy and Power
  • Conservation Laws
    • Energy Conservation
    • Momentum Conservation
    • Angular Momentum Conservation
    • Parity Non-Conservation
  • Symmetry
  • Exercises
  • References
  
  
• From the Pendulum to Romeo and Juliet
  • The Simple Pendulum
  • The Double Pendulum
  • Romeo and Juliet
  • Decay Processes
  • Growth and Saturation
  • Exercises
  • References
  
  
• Emergence, Universality, Order and Disorder
  • Thermodynamics and Kinetic Theory
    • State Variables
    • The Ideal Gas
  • Statistical Mechanics
  • The Second Law
  • The First Law
  • Entropy for Open Systems
  • Phase Transitions and Symmetry Breaking
    • Second Order Transitions
  • Correlations
  • The Ising Model
  • Critical Opalescence
  • Summary
  • Exercises
  • References
  
  
• Dissipative Structures
  • Order in Nature
  • Vortices
  • Benard Cells
  • Non-Equilibrium Pattern Formation vs Equilibrium Phase Transitions
  • The Belousov-Zhabotinski Reaction
  • Turing Structures
  • Summary
  • Exercises
  • References
  
  
• Agent-Based Modelling and Self-Organisation
  • Game of Life
  • Termites
  • Boids
  • Ants
  • Herd Behaviour in Humans
  • Evolving Complex Networks
  • Summary
  • Exercises
  • References
  
  
• Modelling Non-Equilibrium Systems with Equations
  • Predator-Prey Systems
  • Modelling Epidemics and Revolutions
  • Modelling the Arms Race
  • Equations of War and Business
  • Summary
  • Exercises
  • References
  
  
• Artificial Societies
  • Exercises
  • References
  
  
• About this document ...