Foreword by David Bressoud.
201 p. 5-1/2 x 8-1/2 1963, 2007
ISBN: 978-0-226-80668-6 (ISBN-10: 0-226-80668-5) Spring 2007
When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique approach, Toeplitz summarized and elucidated the major mathematical advances that contributed to modern calculus.
Reissued for the first time since 1981 and updated with a new foreword, this classic text in the field of mathematics is experiencing a resurgence of interest among students and educators of calculus today.
Distributed for the Center for the Study of Language and Information.
140 p. 6 x 9
Series: (CSLI-STAD) CSLI-Studies in the Theory and Applications of Diagrams
Cloth ISBN: 978-1-57586-507-2 (ISBN-10: 1-57586-507-6) Spring 2007
Paper ISBN: 978-1-57586-508-9 (ISBN-10: 1-57586-508-4) Spring 2007
Twentieth-century developments in logic and mathematics have led many people to view Euclid’s proofs as inherently informal, especially due to the use of diagrams in proofs. In Euclid and His Twentieth-Century Rivals, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry.
TABLE OF CONTENTS
1. Background
2. Syntax and Semantics of Diagrams
3. Diagrammatic Proofs
4. Meta-mathematical Results
5. Conclusions
Appendix A: Euclid's Postulates
Appendix B: Hilbert's Axioms
Appendix C: Isabel Luengo's DS1
Appendix D: A CDEG transcript
References
Index
Subjects:
MATHEMATICS AND STATISTICS
PHILOSOPHY: General Philosophy
24 x 17 cm. Approx. 240 pages. Cloth.
ISBN 978-3-11-019556-9
Series: Radon Series on Computational and Applied Mathematics
Subjects: Mathematics / Numerical Mathematics
Language: English
to be published September 2007
This book contains four survey papers related to different topics in computational mechanics, in particular (1) novel discretization and solver techniques in mechanics and (2) inverse, control, and optimization problems in mechanics. These topics were considered in lectures, seminars, tutorials, and workshops at the Special Semester on Computational Mechanics held at the Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, in December 2005.
24 x 17 cm. Approx. 352 pages. Cloth.
ISBN 978-3-11-019449-4
Series: [de Gruyter Proceedings in Mathematics]
Subjects: Mathematics / Analysis
Mathematics / Geometry and Topology
Language: English
to be published September 2007
This volume contains contributions of principal speakers of a conference on Banach Spaces and their applications in analysis, held in May 2006 at Miami, Ohio, in honor of Nigel Kalton's 60th birthday. Its merit lies in the fact that it aims to encompass applications of Banach space methods in different areas of analysis, emphasizing versatility of the methods and underlying connections between seemingly distant areas of analysis.