A Gateway to Modern Mathematics: Adventures in Iteration II is the concluding part of a two-volume work on iterations in the RMS series Little Mathematical Treasures. The books in this series address senior secondary school students who are interested in exploring mathematics a little beyond what the school curriculum offers.
Iterations is an exciting topic of study and should interest both the amateur as well as the professional. Many of the iterations in elementary mathematics offer scope for extended investigation. They are like a gateway to important themes of modern mathematics such as fractals and chaos and offer a route for experiencing the experimental and visually aesthetic side of mathematics.
The present work continues the study of iterations, started in Iteration I, but at a higher level. It examines the insights on iteration provided by differential calculus. Varioys approaches to the numerical solution of equations using iterations are studied. The book includes a brief account of two fascinating discoveries made in recent years-the theorems of Li and Yorke, and of Sakovskii. Julia sets of factional linear maps and quadratic maps, and some associated notions, including the famous Mandelbrot set are introduced.
Shailesh A Shirali