Mathematical Analysis

Mathematical analysis establishes the foundations upon which calculus is built. This book, based upon over six years of independent study outside the classroom, is a detailed and thorough introduction to the subject. The work begins with the preliminary definitions and facts of ordered sets, ordered groups, and ordered rings essential for the study, and then leads the reader through convergence, continuity, differentiability, and integrability with generalizations for each. The work includes a complete, detailed presentation of the construction of real numbers. The reader is assumed to have no previous knowledge of analysis. A background in modern algebra will be helpful, and previous exposure to calculus in some form is recommended. The book is not intended as a textbook and is suitable for someone pursuing mathematics as a hobby outside the classroom.