The Elements of Cantor Sets: With Applications

The Elements of Cantor Sets: With Applications

Author(s): Robert W. Vallin

Published Online: 2 AUG 2013 09:06PM EST

Print ISBN: 9781118405710

Online ISBN: 9781118548745

DOI: 10.1002/9781118548745

About this Book

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. 

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