The Elements of Cantor Sets: With Applications

A systematic and integrated approach to Cantor Sets and their applications to various branches of mathematicsThe 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 detailsA biography of Georg Ferdinand Ludwig Philipp Cantor, one of the most significant mathematicians of the last centuryChapter 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 SetsA wide spectrum of topics from measure theory to the Monty Hall ProblemAn 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.  Read more