Part I. Introducing Discrete Dynamical Systems

0: Opening Remarks
1: Functions
2: Iterating Functions
3: Qualitative Dynamics
4: Time Series Plots
5: Graphical Iteration
6: Iterating Linear Functions
7: Population Models
8: Newton, Laplace, and Determinism

Part II. Chaos

9: Chaos and the Logistic Equation
10: The Buttery Effect
11: The Bifurcation Diagram
12: Universality
13: Statistical Stability of Chaos
14: Determinism, Randomness, and Nonlinearity

III. Fractals

15: Introducing Fractals
16: Dimensions
17: Random Fractals
18: The Box-Counting Dimension
19: When do Averages exist?
20: Power Laws and Long Tails
20: Introducing Julia Sets
21: Infinities, Big and Small

Part IV. Julia Sets and The Mandelbrot Set

22: Introducing Julia Sets
23: Complex Numbers
24: Julia Sets for f(z) = z2 + c
25: The Mandelbrot Set

Part V. Higher-Dimensional Systems

26: Two-Dimensional Discrete Dynamical Systems
27: Cellular Automata
28: Introduction to Differential Equations
29: One-Dimensional Differential Equations
30: Two-Dimensional Differential Equations
31: Chaotic Differential Equations and Strane Attractors

Part VI. Conclusion

32: Conclusion

VII. Appendices

A: Review of Selected Topics from Algebra
B: Histograms and Distributions
C: Suggestions for Further Reading