SC - 966 | An Introduction to Analysis (Graduate Texts in Mathematics)

As its title indicates, this book is intended to serve as a textbook for an introductory course in mathematical analysis. In preliminary form the book has been used in this way at the University of Michigan, Indiana University, and Texas A&M University, and has proved serviceable. In addition to its primary purpose as a textbook for a formal course, however, it is the authors' hope that this book will also prove of value to readers interested in studying mathematical analysis on their own.

Indeed, we believe the wealth and variety of examples and exercises will be especially conducive to this end. A word on prerequisites. With what mathematical background might a prospective reader hope to profit from the study of this book? Our con­ scious intent in writing it was to address the needs of a beginning graduate student in mathematics, or, to put matters slightly differently, a student who has completed an undergraduate program with a mathematics ma­ jor. On the other hand, the book is very largely self-contained and should therefore be accessible to a lower classman whose interest in mathematical analysis has already been awakened.

1995 | ISBN 978-1-4612-6901-4 | ISBN 978-1-4612-0787-0 | ID: SC - 966

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SC - 1060 | Inconsistent Mathematics (Mathematics and Its Applications)

The theory of inconsistency has been growing steadily over the last two decades. One focus has been philosophical issues arising from the paradoxes of set theory and semantics. A second focus has been the study of paraconsistent or inconsistency-tolerant logics. A third focus has been the application of paraconsistent logics to problems in artificial intelligence. This book focuses on a fourth aspect: the construction of mathematical theories in which contradictions occur, and the investigation of their properties.

The inconsistent approach provides a distinctive perspective on the various number systems, order differential and integral calculus, discontinuous changes, inconsistent systems of linear equations, projective geometry, topology and category theory. The final chapter outlines several known results concerning paradoxes in the foundations of set theory and semantics. The book begins with an informal chapter which summarises the main results nontechnically, and draws philosophical implications from them. This volume will be of interest to advanced undergraduates, graduate students and professionals in the areas of logic, philosophy, mathematics and theoretical computer science.

1995 | ISBN 978-90-481-4480-8 | ID: SC - 1060

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