Izu Vaisman's Books

Foundations of Three-Dimensional Euclidean Geometry

By: Izu Vaisman

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Foundations of Three-Dimensional Euclidean Geometry

By: Izu Vaisman

This book presents to the reader a modern axiomatic construction of three-dimensional Euclidean geometry in a rigorous and accessible form. It is helpful for high school teachers who are interested in the modernization of the teaching of geometry.

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Page Count

287

Publisher

CRC Press

Published Date

ISBN 10

1000110494

ISBN 13

9781000110494

Cohomology and Differential Forms

By: Izu Vaisman

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Cohomology and Differential Forms

By: Izu Vaisman

This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romania's University of Iasi, the treatment is suitable for advanced undergraduates and graduate students of mathematics as well as mathematical researchers in differential geometry, global analysis, and topology. A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the Čech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.

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Page Count

305

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486804836

ISBN 13

9780486804835

Analytical Geometry

By: Izu Vaisman

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Analytical Geometry

By: Izu Vaisman

This volume discusses the classical subjects of Euclidean, affine and projective geometry in two and three dimensions, including the classification of conics and quadrics, and geometric transformations. These subjects are important both for the mathematical grounding of the student and for applications to various other subjects. They may be studied in the first year or as a second course in geometry.The material is presented in a geometric way, and it aims to develop the geometric intuition and thinking of the student, as well as his ability to understand and give mathematical proofs. Linear algebra is not a prerequisite, and is kept to a bare minimum.The book includes a few methodological novelties, and a large number of exercises and problems with solutions. It also has an appendix about the use of the computer program MAPLEV in solving problems of analytical and projective geometry, with examples.

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Page Count

300

Publisher

World Scientific

Published Date

ISBN 10

981023158X

ISBN 13

9789810231583

A First Course in Differential Geometry

By: Izu Vaisman

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A First Course in Differential Geometry

By: Izu Vaisman

This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.

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Page Count

186

Publisher

CRC Press

Published Date

ISBN 10

1000146405

ISBN 13

9781000146400

Lectures on the Geometry of Poisson Manifolds

By: Izu Vaisman

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Lectures on the Geometry of Poisson Manifolds

By: Izu Vaisman

This book is addressed to graduate students and researchers in the fields of mathematics and physics who are interested in mathematical and theoretical physics, differential geometry, mechanics, quantization theories and quantum physics, quantum groups etc., and who are familiar with differentiable and symplectic manifolds. The aim of the book is to provide the reader with a monograph that enables him to study systematically basic and advanced material on the recently developed theory of Poisson manifolds, and that also offers ready access to bibliographical references for the continuation of his study. Until now, most of this material was dispersed in research papers published in many journals and languages. The main subjects treated are the Schouten-Nijenhuis bracket; the generalized Frobenius theorem; the basics of Poisson manifolds; Poisson calculus and cohomology; quantization; Poisson morphisms and reduction; realizations of Poisson manifolds by symplectic manifolds and by symplectic groupoids and Poisson-Lie groups. The book unifies terminology and notation. It also reports on some original developments stemming from the author's work, including new results on Poisson cohomology and geometric quantization, cofoliations and biinvariant Poisson structures on Lie groups.

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Page Count

210

Publisher

Birkhäuser

Published Date

ISBN 10

3034884958

ISBN 13

9783034884952

Cohomology and Differential Forms

By: Izu Vaisman

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Cohomology and Differential Forms

By: Izu Vaisman

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Page Count

305

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486804836

ISBN 13

9780486804835

A First Course in Differential Geometry

By: Izu Vaisman

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A First Course in Differential Geometry

By: Izu Vaisman

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Page Count

186

Publisher

CRC Press

Published Date

ISBN 10

1000146405

ISBN 13

9781000146400

Symplectic Geometry and Secondary Characteristic Classes

By: Izu Vaisman

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Symplectic Geometry and Secondary Characteristic Classes

By: Izu Vaisman

The present work grew out of a study of the Maslov class (e. g. (37]), which is a fundamental invariant in asymptotic analysis of partial differential equations of quantum physics. One of the many in terpretations of this class was given by F. Kamber and Ph. Tondeur (43], and it indicates that the Maslov class is a secondary characteristic class of a complex trivial vector bundle endowed with a real reduction of its structure group. (In the basic paper of V. I. Arnold about the Maslov class (2], it is also pointed out without details that the Maslov class is characteristic in the category of vector bundles mentioned pre viously. ) Accordingly, we wanted to study the whole range of secondary characteristic classes involved in this interpretation, and we gave a short description of the results in (83]. It turned out that a complete exposition of this theory was rather lengthy, and, moreover, I felt that many potential readers would have to use a lot of scattered references in order to find the necessary information from either symplectic geometry or the theory of the secondary characteristic classes. On the otherhand, both these subjects are of a much larger interest in differential geome try and topology, and in the applications to physical theories.

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Page Count

225

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475719604

ISBN 13

9781475719604

Lectures on the Geometry of Poisson Manifolds

By: Izu Vaisman

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Lectures on the Geometry of Poisson Manifolds

By: Izu Vaisman

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Page Count

210

Publisher

Birkhäuser

Published Date

ISBN 10

3034884958

ISBN 13

9783034884952

Foundations of Three-Dimensional Euclidean Geometry

By: Izu Vaisman

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Foundations of Three-Dimensional Euclidean Geometry

By: Izu Vaisman

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Solve jigsaw puzzle

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Page Count

287

Publisher

CRC Press

Published Date

ISBN 10

1000110494

ISBN 13

9781000110494

Book's by Izu Vaisman

Foundations of Three-Dimensional Euclidean Geometry

Foundations of Three-Dimensional Euclidean Geometry

Cohomology and Differential Forms

Cohomology and Differential Forms

Analytical Geometry

Analytical Geometry

A First Course in Differential Geometry

A First Course in Differential Geometry

Lectures on the Geometry of Poisson Manifolds

Lectures on the Geometry of Poisson Manifolds

Cohomology and Differential Forms

Cohomology and Differential Forms

A First Course in Differential Geometry

A First Course in Differential Geometry

Symplectic Geometry and Secondary Characteristic Classes

Symplectic Geometry and Secondary Characteristic Classes

Lectures on the Geometry of Poisson Manifolds

Lectures on the Geometry of Poisson Manifolds

Foundations of Three-Dimensional Euclidean Geometry

Foundations of Three-Dimensional Euclidean Geometry

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