birkhäuser boston birkhäuser boston apr 2001 (8 Ergebnisse)

Buch. Zustand: Neu. Neuware -The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 630 pp. Englisch.

Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world.Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world.A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 288 pp. Englisch.

Buch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -The topic of this book is the theory of state spaces of operator algebras and their geometry. The states are of interest because they determine representations of the algebra, and its algebraic structure is in an intriguing and fascinating fashion encoded in the geometry of the state space. From the beginning the theory of operator algebras was motivated by applications to physics, but recently it has found unexpected new applica tions to various fields of pure mathematics, like foliations and knot theory, and (in the Jordan algebra case) also to Banach manifolds and infinite di mensional holomorphy. This makes it a relevant field of study for readers with diverse backgrounds and interests. Therefore this book is not intended solely for specialists in operator algebras, but also for graduate students and mathematicians in other fields who want to learn the subject. We assume that the reader starts out with only the basic knowledge taught in standard graduate courses in real and complex variables, measure theory and functional analysis. We have given complete proofs of basic results on operator algebras, so that no previous knowledge in this field is needed. For discussion of some topics, more advanced prerequisites are needed. Here we have included all necessary definitions and statements of results, but in some cases proofs are referred to standard texts. In those cases we have tried to give references to material that can be read and understood easily in the context of our book.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 372 pp. Englisch.

Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The topic of this book is the theory of state spaces of operator algebras and their geometry. The states are of interest because they determine representations of the algebra, and its algebraic structure is in an intriguing and fascinating fashion encoded in the geometry of the state space. From the beginning the theory of operator algebras was motivated by applications to physics, but recently it has found unexpected new applica tions to various fields of pure mathematics, like foliations and knot theory, and (in the Jordan algebra case) also to Banach manifolds and infinite di mensional holomorphy. This makes it a relevant field of study for readers with diverse backgrounds and interests. Therefore this book is not intended solely for specialists in operator algebras, but also for graduate students and mathematicians in other fields who want to learn the subject. We assume that the reader starts out with only the basic knowledge taught in standard graduate courses in real and complex variables, measure theory and functional analysis. We have given complete proofs of basic results on operator algebras, so that no previous knowledge in this field is needed. For discussion of some topics, more advanced prerequisites are needed. Here we have included all necessary definitions and statements of results, but in some cases proofs are referred to standard texts. In those cases we have tried to give references to material that can be read and understood easily in the context of our book. 372 pp. Englisch.

Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world.Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world. 288 pp. Englisch.

Buch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -'Categorical Perspectives' consists of introductory surveys as well as articles containing original research and complete proofs devoted mainly to the theoretical and foundational developments of category theory and its applications to other fields. A number of articles in the areas of topology, algebra and computer science reflect the varied interests of George Strecker to whom this work is dedicated. Notable also are an exposition of the contributions and importance of George Strecker's research and a survey chapter on general category theory. This work is an excellent reference text for researchers and graduate students in category theory and related areas.Contributors: H.L. Bentley \* G. Castellini \* R. El Bashir \* H. Herrlich \* M. Husek \* L. Janos \* J. Koslowski \* V.A. Lemin \* A. Melton \* G. Preuá \* Y.T. Rhineghost \* B.S.W. Schroeder \* L. Schr'der \* G.E. Strecker \* A. ZmrzlinaSpringer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 298 pp. Englisch.

Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers. 630 pp. Englisch.

Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -'Categorical Perspectives' consists of introductory surveys as well as articles containing original research and complete proofs devoted mainly to the theoretical and foundational developments of category theory and its applications to other fields. A number of articles in the areas of topology, algebra and computer science reflect the varied interests of George Strecker to whom this work is dedicated. Notable also are an exposition of the contributions and importance of George Strecker's research and a survey chapter on general category theory. This work is an excellent reference text for researchers and graduate students in category theory and related areas. Contributors: H.L. Bentley \* G. Castellini \* R. El Bashir \* H. Herrlich \* M. Husek \* L. Janos \* J. Koslowski \* V.A. Lemin \* A. Melton \* G. Preuá \* Y.T. Rhineghost \* B.S.W. Schroeder \* L. Schr'der \* G.E. Strecker \* A. Zmrzlina 298 pp. Englisch.