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Geometry


1. 

Analytical Modeling of Heterogeneous Cellular Networks

Analytical Modeling of Heterogeneous Cellular Networks

By: Sayandev Mukherjee

Publisher: Cambridge University Press

Publication Date: 31-DEC-2013

Insert Date: 25-FEB-2014

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This self-contained introduction shows how stochastic geometry techniques can be used for studying the behaviour of heterogeneous cellular networks (HCNs). The unified treatment of analytic results and approaches, collected for the first time in a single volume, includes the mathematical tools and techniques used to derive them. A single canonical problem formulation encompassing the analytic derivation of Signal to Interference plus Noise Ratio (SINR) distribution in the most widely-used deployment scenarios is presented, together with applications to systems based on the 3GPP-LTE...

2. 

The Riemann Hypothesis for Function Fields

The Riemann Hypothesis for Function Fields

By: Machiel van Frankenhuijsen

Publisher: Cambridge University Press

Publication Date: 31-DEC-2013

Insert Date: 25-FEB-2014

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This book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the Riemann Hypothesis for function fields, along with an explanation of the connections with Nevanlinna theory and non-commutative geometry. The connection with non-commutative geometry is given special attention, with a complete determination of the Weil terms in the explicit formula for the point...

3. 

Geometry, Second Edition

Geometry, Second Edition

By: David A. Brannan; Matthew F. Esplen; Jeremy J. Gray

Publisher: Cambridge University Press

Publication Date: 22-DEC-2011

Insert Date: 23-JAN-2014

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This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of...

4. 

Beautiful Geometry

Beautiful Geometry

By: Eli Maor; Eugen Jost

Publisher: Princeton University Press

Publication Date: 19-JAN-2014

Insert Date: 04-DEC-2013

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If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing...

5. 

Geometry

Geometry

By: David A. Brannan; Matthew F. Esplen; Jeremy J. Gray

Publisher: Cambridge University Press

Publication Date: 15-APR-1999

Insert Date: 05-NOV-2013

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This is an undergraduate textbook that reveals the intricacies of geometry. The approach used is that a geometry is a space together with a set of transformations of that space (as argued by Klein in his Erlangen programme). The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case the key results are explained carefully, and the relationships between the geometries are discussed. This richly illustrated and clearly written text includes full solutions to over 200 problems, and is suitable both for undergraduate courses on geometry and...

6. 

Geometry of Sporadic Groups

Geometry of Sporadic Groups

By: A.A. Ivanov

Publisher: Cambridge University Press

Publication Date: 17-JUN-1999

Insert Date: 05-OCT-2013

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This book is the first volume in a two-volume set, which will provide the complete proof of classification of two important classes of geometries, closely related to each other: Petersen and tilde geometries. There is an infinite family of tilde geometries associated with non-split extensions of symplectic groups over a field of two elements. Besides that there are twelve exceptional Petersen and tilde geometries. These exceptional geometries are related to sporadic simple groups, including the famous Monster group and this volume gives a construction for each of the Petersen and tilde...

7. 

Elementary Differential Geometry

Elementary Differential Geometry

By: Christian Bär

Publisher: Cambridge University Press

Publication Date: 06-MAY-2010

Insert Date: 08-SEP-2013

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The link between the physical world and its visualization is geometry. This easy-to-read, generously illustrated textbook presents an elementary introduction to differential geometry with emphasis on geometric results. Avoiding formalism as much as possible, the author harnesses basic mathematical skills in analysis and linear algebra to solve interesting geometric problems, which prepare students for more advanced study in mathematics and other scientific fields such as physics and computer science. The wide range of topics includes curve theory, a detailed study of surfaces, curvature,...

8. 

Hodge Theory and Complex Algebraic Geometry II

Hodge Theory and Complex Algebraic Geometry II

By: Claire Voisin; Leila Schneps

Publisher: Cambridge University Press

Publication Date: 03-JUL-2003

Insert Date: 05-SEP-2013

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The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard-Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. The main results of the second part are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly Nori's connectivity theorem, which generalizes the above. The last part of the book...

9. 

Computational Geometry in C, Second Edition

Computational Geometry in C, Second Edition

By: Joseph O'Rourke

Publisher: Cambridge University Press

Publication Date: 13-OCT-1998

Insert Date: 04-SEP-2013

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This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The...

10. 

Geometric Tomography, Second Edition

Geometric Tomography, Second Edition

By: Richard J. Gardner

Publisher: Cambridge University Press

Publication Date: 19-JUN-2006

Insert Date: 04-SEP-2013

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Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. The subject overlaps with convex geometry and employs many tools from that area, including some formulas from integral geometry. It also has connections to discrete tomography, geometric probing in robotics and to stereology. This comprehensive study provides a rigorous treatment of the subject. Although...

11. 

Matrices and Graphs in Geometry

Matrices and Graphs in Geometry

By: Miroslav Fiedler

Publisher: Cambridge University Press

Publication Date: 03-FEB-2011

Insert Date: 04-SEP-2013

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Simplex geometry is a topic generalizing geometry of the triangle and tetrahedron. The appropriate tool for its study is matrix theory, but applications usually involve solving huge systems of linear equations or eigenvalue problems, and geometry can help in visualizing the behaviour of the problem. In many cases, solving such systems may depend more on the distribution of non-zero coefficients than on their values, so graph theory is also useful. The author has discovered a method that in many (symmetric) cases helps to split huge systems into smaller parts. Many readers will welcome this...

12. 

Geometrical Methods of Mathematical Physics

Geometrical Methods of Mathematical Physics

By: Bernard F. Schutz

Publisher: Cambridge University Press

Publication Date: 06-NOV-1980

Insert Date: 04-SEP-2013

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In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced...

13. 

The Geometry of Walker Manifolds

The Geometry of Walker Manifolds

By: Peter Gilkey

Publisher: Morgan & Claypool Publishers

Publication Date: 08-JUL-2009

Insert Date: 02-SEP-2013

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This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are...

14. 

Ellipsoidal Harmonics

Ellipsoidal Harmonics

By: George Dassios

Publisher: Cambridge University Press

Publication Date: 12-JUL-2012

Insert Date: 02-SEP-2013

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The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal...

15. 

Contact Geometry and Nonlinear Differential Equations

Contact Geometry and Nonlinear Differential Equations

By: Alexei Kushner; Valentin Lychagin; Vladimir Rubtsov

Publisher: Cambridge University Press

Publication Date: 21-DEC-2006

Insert Date: 02-SEP-2013

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Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential...

16. 

Mumford-Tate Groups and Domains

Mumford-Tate Groups and Domains

By: Mark Green; Phillip A. Griffiths; Matt Kerr

Publisher: Princeton University Press

Publication Date: 22-APR-2012

Insert Date: 30-AUG-2013

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Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the...

17. 

Translating Euclid

Translating Euclid

By: Gerry Stahl

Publisher: Morgan & Claypool Publishers

Publication Date: 01-APR-2013

Insert Date: 29-AUG-2013

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Translating Euclid reports on an effort to transform geometry for students from a stylus-and-clay-tablet corpus of historical theorems to a stimulating computer-supported collaborative-learning inquiry experience. The origin of geometry was a turning point in the pre-history of informatics, literacy, and rational thought. Yet, this triumph of human intellect became ossified through historic layers of systematization, beginning with Euclid’s organization of the Elements of geometry. Often taught by memorization of procedures, theorems, and proofs, geometry in schooling rarely conveys its...

18. 

Isosurfaces:Geometry, Topology, and Algorithms

Isosurfaces:Geometry, Topology, and Algorithms

By: Rephael Wenger

Publisher: A K Peters/CRC Press

Publication Date: 24-JUN-2013

Insert Date: 28-AUG-2013

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This work represents the first book to focus on basic algorithms for isosurface construction. It also gives a rigorous mathematical perspective on some of the algorithms and results. In color throughout, the book covers the Marching Cubes algorithm and variants, dual contouring algorithms, multilinear interpolation, multiresolution isosurface extraction, isosurfaces in four dimensions, interval volumes, and contour trees. It also describes data structures for faster isosurface extraction as well as methods for selecting significant isovalues. ...

19. 

Applications of Affine and Weyl Geometry

Applications of Affine and Weyl Geometry

By: Eduardo García-Río; Peter Gilkey; Stana Nikcevic; Ramón Vázquez-Lorenzo

Publisher: Morgan & Claypool Publishers

Publication Date: 01-MAY-2013

Insert Date: 27-AUG-2013

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Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures,...

20. 

A Gyrovector Space Approach to Hyperbolic Geometry

A Gyrovector Space Approach to Hyperbolic Geometry

By: Abraham Ungar

Publisher: Morgan & Claypool Publishers

Publication Date: 08-MAR-2009

Insert Date: 24-AUG-2013

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The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar....