Geometry V

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Geometry V

Robert Osserman
Geometry V Book PDF

Author : Robert Osserman
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 54,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662034842

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Geometry V by Robert Osserman Pdf

Few people outside of mathematics are aware of the varieties of mathemat ical experience - the degree to which different mathematical subjects have different and distinctive flavors, often attractive to some mathematicians and repellant to others. The particular flavor of the subject of minimal surfaces seems to lie in a combination of the concreteness of the objects being studied, their origin and relation to the physical world, and the way they lie at the intersection of so many different parts of mathematics. In the past fifteen years a new component has been added: the availability of computer graphics to provide illustrations that are both mathematically instructive and esthetically pleas ing. During the course of the twentieth century, two major thrusts have played a seminal role in the evolution of minimal surface theory. The first is the work on the Plateau Problem, whose initial phase culminated in the solution for which Jesse Douglas was awarded one of the first two Fields Medals in 1936. (The other Fields Medal that year went to Lars V. Ahlfors for his contributions to complex analysis, including his important new insights in Nevanlinna Theory.) The second was the innovative approach to partial differential equations by Serge Bernstein, which led to the celebrated Bernstein's Theorem, stating that the only solution to the minimal surface equation over the whole plane is the trivial solution: a linear function.

Euclid

Shoo Rayner
Euclid Book PDF

Author : Shoo Rayner
Publisher : Unknown
Page : 54 pages
File Size : 54,9 Mb
Release : 2017-11-02
Category : Juvenile Nonfiction
ISBN : 1908944366

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Euclid by Shoo Rayner Pdf

Geometry is brought to life as Euclid explains principles of Geometry to his friends. With jokes and lots of illustrations, discover the beauty of geometry and, before you know it, you too will soon be a friend of Euclid! Shoo Rayner adds humour and simplicity to a tricky subject. A perfect introduction.

The Wonder Book of Geometry

David Acheson
The Wonder Book of Geometry Book PDF

Author : David Acheson
Publisher : Oxford University Press
Page : 240 pages
File Size : 53,7 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9780192585370

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The Wonder Book of Geometry by David Acheson Pdf

How can we be sure that Pythagoras's theorem is really true? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet? David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.

Two-Dimensional Conformal Geometry and Vertex Operator Algebras

Yi-Zhi Huang
Two Dimensional Conformal Geometry and Vertex Operator Algebras Book PDF

Author : Yi-Zhi Huang
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 45,9 Mb
Release : 1997-07-15
Category : Mathematics
ISBN : 0817638296

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Two-Dimensional Conformal Geometry and Vertex Operator Algebras by Yi-Zhi Huang Pdf

The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc­ tures of conformal field theories. Much of the recent progress has deep connec­ tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in [Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac­ Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on. He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a "big and important problem. " On the one hand, the theory of vertex operator algebras and their repre­ sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.

Diophantine Geometry

Marc Hindry,Joseph H. Silverman
Diophantine Geometry Book PDF

Author : Marc Hindry,Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 766 pages
File Size : 54,9 Mb
Release : 2000-03-23
Category : Mathematics
ISBN : 0387989757

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Diophantine Geometry by Marc Hindry,Joseph H. Silverman Pdf

This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

Algebraic Geometry

K. Lonsted
Algebraic Geometry Book PDF

Author : K. Lonsted
Publisher : Springer
Page : 664 pages
File Size : 46,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540350491

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Algebraic Geometry by K. Lonsted Pdf

Not long ago, conducting child assessment was as simple as stating that "the child gets along with others" or "the child lags behind his peers." Today's pediatric psychologists and allied professionals, by contrast, know the critical importance of using accurate measures with high predictive quality to identify pathologies early, form precise case conceptualizations, and provide relevant treatment options. Assessing Childhood Psychopathology and Developmental Disabilities provides a wide range of evidence-based methods in an immediately useful presentation from infancy through adolescence. Noted experts offer the most up-to-date findings in the most pressing areas, including: Emerging trends, new technologies, and implementation issues. Interviewing techniques and report writing guidelines. Intelligence testing, neuropsychological assessment, and scaling methods for measuring psychopathology. Assessment of major pathologies, including ADHD, conduct disorder, bipolar disorder, and depression. Developmental disabilities, such as academic problems, the autism spectrum and comorbid pathology, and self-injury. Behavioral medicine, including eating and feeding disorders as well as pain management. This comprehensive volume is an essential resource for the researcher's library and the clinician's desk as well as a dependable text for graduate and postgraduate courses in clinical child, developmental, and school psychology. (A companion volume, Treating Childhood Psychopathology and Developmental Disabilities, is also available to ensure greater continuity on the road from assessment to intervention to outcome.)

Geometry - Intuition and Concepts

Jost-Hinrich Eschenburg
Geometry Intuition and Concepts Book PDF

Author : Jost-Hinrich Eschenburg
Publisher : Springer Nature
Page : 168 pages
File Size : 42,5 Mb
Release : 2022-10-31
Category : Mathematics
ISBN : 9783658386405

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Geometry - Intuition and Concepts by Jost-Hinrich Eschenburg Pdf

This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified. The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions. This book is a translation of the original German 1st edition Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

Elementary Differential Geometry

Barrett O'Neill
Elementary Differential Geometry Book PDF

Author : Barrett O'Neill
Publisher : Academic Press
Page : 422 pages
File Size : 44,6 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483268118

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Elementary Differential Geometry by Barrett O'Neill Pdf

Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.

Tensor Geometry

Christopher T. J. Dodson,Timothy Poston
Tensor Geometry Book PDF

Author : Christopher T. J. Dodson,Timothy Poston
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 46,8 Mb
Release : 2009-11-23
Category : Mathematics
ISBN : 354052018X

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Tensor Geometry by Christopher T. J. Dodson,Timothy Poston Pdf

This treatment of differential geometry and the mathematics required for general relativity makes the subject accessible, for the first time, to anyone familiar with elementary calculus in one variable and with some knowledge of vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the many illustrations presenting figures of three and more dimensions as closely as the book form will allow.

Complex Projective Geometry

G. Ellingsrud
Complex Projective Geometry Book PDF

Author : G. Ellingsrud
Publisher : Cambridge University Press
Page : 354 pages
File Size : 42,6 Mb
Release : 1992-07-30
Category : Mathematics
ISBN : 9780521433525

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Complex Projective Geometry by G. Ellingsrud Pdf

A volume of papers describing new methods in algebraic geometry.

Asymptotic Formulae in Spectral Geometry

Peter B. Gilkey
Asymptotic Formulae in Spectral Geometry Book PDF

Author : Peter B. Gilkey
Publisher : CRC Press
Page : 312 pages
File Size : 46,6 Mb
Release : 2003-12-17
Category : Mathematics
ISBN : 9780203490464

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Asymptotic Formulae in Spectral Geometry by Peter B. Gilkey Pdf

A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computi

Handbook of Differential Geometry, Volume 1

F.J.E. Dillen,L.C.A. Verstraelen
Handbook of Differential Geometry Volume 1 Book PDF

Author : F.J.E. Dillen,L.C.A. Verstraelen
Publisher : Elsevier
Page : 1067 pages
File Size : 52,5 Mb
Release : 1999-12-16
Category : Mathematics
ISBN : 9780080532837

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Handbook of Differential Geometry, Volume 1 by F.J.E. Dillen,L.C.A. Verstraelen Pdf

In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

Differential Geometry of Varieties with Degenerate Gauss Maps

Maks A. Akivis,Vladislav V. Goldberg
Differential Geometry of Varieties with Degenerate Gauss Maps Book PDF

Author : Maks A. Akivis,Vladislav V. Goldberg
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 55,6 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387215112

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Differential Geometry of Varieties with Degenerate Gauss Maps by Maks A. Akivis,Vladislav V. Goldberg Pdf

This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.

Topology, Geometry, Integrable Systems, and Mathematical Physics

V. M. Buchstaber,B. A. Dubrovin, I. M. Krichever
Topology Geometry Integrable Systems and Mathematical Physics Book PDF

Author : V. M. Buchstaber,B. A. Dubrovin, I. M. Krichever
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 55,7 Mb
Release : 2014-11-18
Category : Mathematics
ISBN : 9781470418717

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Topology, Geometry, Integrable Systems, and Mathematical Physics by V. M. Buchstaber,B. A. Dubrovin, I. M. Krichever Pdf

Articles in this collection are devoted to modern problems of topology, geometry, mathematical physics, and integrable systems, and they are based on talks given at the famous Novikov's seminar at the Steklov Institute of Mathematics in Moscow in 2012-2014. The articles cover many aspects of seemingly unrelated areas of modern mathematics and mathematical physics; they reflect the main scientific interests of the organizer of the seminar, Sergey Petrovich Novikov. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.

Differential Geometry and Relativity Theory

RichardL. Faber
Differential Geometry and Relativity Theory Book PDF

Author : RichardL. Faber
Publisher : Routledge
Page : 150 pages
File Size : 51,6 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351455145

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Differential Geometry and Relativity Theory by RichardL. Faber Pdf

Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force. Uniting differential geometry and both special and generalrelativity in a single source, this easy-to-understand text opens the general theory of relativityto mathematics majors having a backgr.ound only in multivariable calculus and linearalgebra.The book offers a broad overview of the physical foundations and mathematical details ofrelativity, and presents concrete physical interpretations of numerous abstract concepts inRiemannian geometry. The work is profusely illustrated with diagrams aiding in the understandingof proofs and explanations. Appendices feature important material on vectoranalysis and hyperbolic functions.Differential Geometry and Relativity Theory: An Introduction serves as the ideal textfor high-level undergraduate couues in mathematics and physics, and includes a solutionsmanual augmenting classroom study. It is an invaluable reference for mathematicians interestedin differential and IUemannian geometry, or the special and general theories ofrelativity