A Gateway to Modern Mathematics: Adventures in Iteration 1 (Little Mathematical Treasures) by Shailesh A Shirali

This book is about iterative processes, i.e., processes that are done repetitively (“reiterated”); such processes often result in sequences which are rich in patterns, making them ideal for investigation. It is written for the student who loves to tinker around with numbers and equations, and with mathematical ideas in general; tinker around just as a child, does when he or she wanders into a wooded region and begins to explore the many marvels and mysteries that are to be found in undisturbed places. The world of mathematics too is full of wonders but, sadly, many children never see them at all, or even suspect that they exist. The fact that mathematics is a living science and that one can make discoveries and actually contribute to the growth of the subject is hardly ever pointed out at the school level. And yet, the actual fact is that mathematics is alive, and not merely a collection of formulas and theorems dating from Greek and Vedic times. New discoveries are constantly being made in the subject every year; new areas of research develop constantly. Problems dating from many centuries get solved; alongside this, new questions get asked, new problems posed.