Introduction to Analysis Theorems and Examples

This book focuses on the theoretical aspects of calculus. The book begins with a chapter on set theory before thoroughly discussing real numbers, then moves onto sequences, series, and their convergence. The author explains why an understanding of real numbers is essential in order to create a foundation for studying analysis. Since the Cantor set is elusive to many, a section is devoted to binary/ternary numbers and the Cantor set.  The book then moves on to continuous functions, differentiations, integrations, and uniform convergence of sequences of functions. An example of a nontrivial uniformly Cauchy sequence of functions is given. The author defines each topic, identifies important theorems, and includes many examples throughout each chapter. The book also provides introductory instruction on proof writing, with an emphasis on how to execute a precise writing style.

Set Theory.- Real Numbers.- Sequences and Series.- Continuous Functions.- Differentiations.- Integrations.- Sequences and Series of Functions.

Hidefumi Katsuura is Professor Emeritus at the San Jose State University Department of Mathematics and Statistics, where he began teaching in 1984. He earned his Ph.D. in Mathematics with a focus on topology from the University of Delaware. He is the author of over thirty articles on a variety of topics. His current research interest is three-dimensional geometry.