A Gateway to Modern Mathematics: Adventures in Iteration I is the first
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. This book, which is at an elementary level, introduces the
idea of iteration. It also explores various associated notions like
fixed points, orbits, cycles, limit points, convergence, solution of
equations and cob-webbing. It contains a large number of illustrative
examples from the world of arithmetic, algebra and geometry. Students
preparing for the mathematical Olympiads will benefit from a study of
the book, and teachers who run mathematics clubs will find here a rich
source of material.
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