A Guide to Real Variables (Dolciani Mathematical Expositions)

The purpose of __A Guide to Real Variables__ is to provide an aid and conceptual support for the student studying for the qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness, topology and the like. All the basic examples like the Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated. The book contains over 100 examples, and most of the basic proofs. It illustrates both the theory and the practice of this sophisticated subject. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too. A Guide to Real Variables provides aid and conceptual support for the student studying for the qualifying exam in real variables. Beginning with the foundations of the subject, the text moves rapidly but thoroughly through basic topics like completeness, convergence, sequences, series, compactness, topology and the like. All the basic examples like the Cantor set, the Weierstrass nowhere differentiable function, the Weierstrass approximation theory, the Baire category theorem, and the Ascoli-Arzela theorem are treated. The book contains over 100 examples, and most of the basic proofs. It illustrates both the theory and the practice of this sophisticated subject. Graduate students studying for the qualifying exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too. Steven Krantz is well-known for his skill in expository writing and this volume confirms it. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize A Guide to Real Variables is an aid and conceptual support for students taking an undergraduate course on real analysis. It focuses on concepts, results, examples and illustrative figures, rather than the details of proofs, in order to remain a concise guide which students can dip into. The core topics of a first real analysis course are covered, including sequences, series, modes of convergence, the derivative, the integral and metric spaces. The next book in this series, Folland's A Guide to Advanced Real Analysis is designed to naturally follow on from this book, and introduce students to graduate level real analysis. Together these books provide a concise guide to the subject at all levels, ideal for student preparation for exams.