“This book could be used as a text for an undergraduate survey course of higher mathematics. It is an excellent reference for a graduate student, researcher or university instructor.” (American Mathematical Society, 1 March 2015)
“Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (Choice, 1 March 2014)
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.
From the Back Cover
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.
About the Author
ROBERT W. VALLIN, PhD, is Professor of Mathematics at Slippery Rock University. The recipient of numerous grants and awards, Dr. Vallin is also the author of over forty journal articles and has given many undergraduate and research talks on a variety of topics.
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