Chapter One - Introduction

   Section       Title                                  Page 
    1.1    Dynamical Systems                              1	
    1.2    Sequences                                      6
    1.3    Series                                        13
    1.4    Programming the TI-83                         18
    1.5    Infinite Sequences and Series                 25

Chapter Two - Fractals

   Section      Title                                   Page 
    2.1    What is a Fractal?                            33
    2.2    Similarity Dimension                          43
    2.3    Boxcount Dimension                            54

Chapter Three - Orbit Analysis

   Section     Title                                    Page 
    3.1    Deterministic Chaos                           65
    3.2    Fixed Points                                  71
    3.3    Periodic Points                               81
    3.4    The Attraction Criterion for Fixed Points     87
    3.5    The Attraction Criterion for Cycles           93

Chapter Four - The Road to Chaos

   Section    Title                                    Page 
    4.1    The Logistic Function                         97
    4.2    Period Doubling                              110
    4.3    Universality                                 117
    4.4    The Properties of Chaos                      125

Chapter Five - Functions of Complex Numbers

   Section    Title                                   Page
    5.1    A Review of the Basics                      135
    5.2    Graphing Complex Numbers                    141
    5.3    Polar Form                                  146
    5.4    Complex Functions                           154

Chapter Six - Julia and Mandelbrot Sets

   Section    Title                                   Page
    6.1    What is a Julia Set?                        159
    6.2    Filled Julia Sets                           166
    6.3    Unfilled Julia Sets                         173
    6.4    Properties of Julia Sets                    178
    6.5    The Mandelbrot Set                          187
    6.6    Properties of the Mandelbrot Set            195

Chapter Seven - The Mathematics of Chaos

   Section    Title                                   Page
    7.1    Differentiation                             203
    7.2    The Quadratic Route to Chaos                208
    7.3    The Mandelbrot Structure                    214
    7.4    The Doubling Function                       220

Chapter Eight - The Meaning of Chaos

   Section    Title                                   Page
    8.1    Chaos and the Sciences                      231
    8.2    Chaos and the Humanities                    241
    8.3    Chaos and Philosophy                        251

Bibliography                                           261
							

Answers to Selected Exercises                          265


Index                                                  279