ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book explains what the images mean, how they are generated on the computer, and why they are important in mathematics. It deals with some very interesting, exciting, and beautiful topics in mathematics. The book discusses dynamical systems, the branch of mathematics that attempts to understand processes in motion. It shows that chaos occurs in elementary mathematical objects when they are regarded as dynamical systems. The book investigates the chaotic behavior of many other functions. And tools such as the Schwarzian derivative, symbolic dynamics, and bifurcation theory were shown to play an important role in understanding the behavior of dynamical systems. The images in the mathematical tour show quite clearly the great beauty of mathematical dynamical systems theory. Whereas the old masters had to rely solely on their imagination and their intellect, mathematicians have an invaluable additional resource to investigate dynamics: the computer.
