**Contents**

**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