Real Analysis

Mathematical analysis is the largest branch of mathematics with numerous subject areas. This book focuses on analysis using the set of real numbers as the metric space under study. It is based upon over a decade of independent study outside the classroom and provides a detailed and thorough introduction to the subject. The work leads the reader through the definition and properties of real numbers, convergent sequences and series, continuous functions, differentiable functions, power series and integrable functions. It concludes with an exposition on natural functions. An appendix establishing the uniqueness of real numbers is also included. Throughout this development, the topics are presented with an emphasis on theory over application. The reader is assumed to have no previous knowledge of real analysis, although some experience with abstract algebra which includes ordering and some familiarity with calculus will be helpful. The book is not intended as a textbook and is suitable for someone pursuing the study of real analysis as a hobby outside the classroom.