The Elements of Cantor Sets

<p><b>A systematic and integrated approach to Cantor Sets and their applications to various branches of mathematics</b></p> <p><i>The Elements of Cantor Sets: With Applications</i> features a thorough introduction to Cantor Sets and applies these sets as a bridge between real analysis, probability, topology, and algebra.</p> <p>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.</p> <p><i>The Elements of Cantor Sets</i> provides coverage of:</p> <ul> <li>Basic definitions and background theorems as well as comprehensive mathematical details</li> <li>A biography of Georg Ferdinand Ludwig Philipp Cantor, one of the most significant mathematicians of the last century</li> <li>Chapter coverage of fractals and self-similar sets, sums of Cantor Sets, the role of Cantor Sets in creating pathological functions, <i>p</i>-adic numbers, and several generalizations of Cantor Sets</li> <li>A wide spectrum of topics from measure theory to the Monty Hall Problem</li> </ul> <p>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, <i>The Elements of Cantor Sets</i> is also appropriate as a useful reference for researchers and secondary mathematics education majors. </p>