A systematic and integrated approach to Cantor Sets and their applications to various branches of mathematics
The Elements of Cantor Sets: With Applications features a thorough introduction to Cantor Sets and applies these sets as a bridge between real analysis, probability, topology, and algebra.
The author fills a gap in the current literature by providing an introductory and integrated perspective, thereby preparing readers for further study and building a deeper understanding of analysis, topology, set theory, number theory, and algebra.
The Elements of Cantor Sets provides coverage of:
- Basic definitions and background theorems as well as comprehensive mathematical details
- A biography of Georg Ferdinand Ludwig Philipp Cantor, one of the most significant mathematicians of the last century
- Chapter coverage of fractals and self-similar sets, sums of Cantor Sets, the role of Cantor Sets in creating pathological functions, p-adic numbers, and several generalizations of Cantor Sets
- A wide spectrum of topics from measure theory to the Monty Hall Problem
An ideal text for courses in real analysis, topology, algebra, and set theory for undergraduate and graduate-level courses within mathematics, computer science, engineering, and physics departments, The Elements of Cantor Sets is also appropriate as a useful reference for researchers and secondary mathematics education majors.