springer basel springer basel nov 2014 (2 Ergebnisse)

Buch. Zustand: Neu. Neuware -Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel¿s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage.The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging.This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students inrelevant disciplines.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 316 pp. Englisch.

Buch. Zustand: Neu. Neuware -Bartel Leendert van der Waerden made major contributions to algebraic geometry, abstract algebra, quantum mechanics, and other fields. He liberally published on the history of mathematics. His 2-volume work Modern Algebra is one of the most influential and popular mathematical books ever written. It is therefore surprising that no monograph has been dedicated to his life and work. Van der Waerden¿s record is complex. In attempting to understand his life, the author assembled thousands of documents from numerous archives in Germany, the Netherlands, Switzerland and the United States which revealed fascinating and often surprising new information about van der Waerden. Soifer traces Van der Waerden¿s early years in a family of great Dutch public servants, his life as professor in Leipzig during the entire Nazi period, and his personal and professional friendship with one of the great physicists Werner Heisenberg. We encounter heroes and villains and a much more numerous group in between these two extremes. One of them is the subject of this book.Soifer¿s journey through a long list of archives, combined with an intensive correspondence, had uncovered numerous details of Van der Waerden¿s German intermezzo that raised serious questions and reproaches.Dirk van Dalen (Philosophy, Utrecht University)Professor Soifer¿s book implicates the anthropologists¿ and culture historians¿ core interest in the evolution of culture and in the progress of human evolution itself on this small contested planet.James W. Fernandez (Anthropology, University of Chicago)The book is fascinating. Professor Soifer has done a great service to the discipline of history, as well as deepening our understanding of the 20th century.Peter D. Johnson, Jr. (Mathematics, Auburn University)This book is an important contribution to the history of the twentieth century, and reads like a novel with an ever-fascinating cast of characters.Harold W. Kuhn (Mathematics, Princeton University)This is a most impressive and important book. It is written in an engaging, very personal style and challenges the reader¿s ability of moral and historical judgment. While it is not always written in the style of ¿objective¿ professional historiography, it satisfies very high standards of scholarly documentation. Indeed the book contains a wealth of source material that allows the reader to form a highly detailed picture of the events and personalities discussed in the book. As an exemplar of historical writing in a broader sense it can compete with any other historical book.Moritz Epple (History of Mathematics, Frankfurt University)Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 504 pp. Englisch.