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Differential Geometry


A Panoramic View of Riemannian Geometry

A Panoramic View of Riemannian Geometry Lowest new price: $73.91
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Author: Marcel Berger
Brand: Brand: Springer

This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field.

From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS

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Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition (Textbooks in Mathematics)

Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition (Textbooks in Mathematics) Lowest new price: $89.80
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Author: Elsa Abbena

Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions.

The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted.

Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.

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Selected Works (Springer Collected Works in Mathematics) (English, Spanish and French Edition)

Selected Works (Springer Collected Works in Mathematics) (English, Spanish and French Edition) Lowest new price: $59.72
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Author: Luis Antonio Santaló
Brand: Santalo Luis Antonio

Luis Antonio Santaló (Spain 1911 – Argentina 2001) contributed to several branches of Geometry, his laying of the mathematical foundations of Stereology and its applications perhaps being his most outstanding achievement. A considerable power of abstraction, a brilliant geometric intuition and an outstanding gift as a disseminator of science were among his virtues. The present volume contains a selection of his best papers.

Part I consists of a short biography and some photographs together with a complete list of his publications, classified into research papers, books, and articles on education and the popularization of mathematics, as well as a comprehensive analysis of his contribution to science.

Part II, the main part of the book, includes selected papers, arranged into five sections according to the nature of their contents: Differential Geometry, Integral Geometry, Convex Geometry, Affine Geometry, and Statistics and Stereology. Each section is preceded by a commentary by a renowned specialist: Teufel, Langevin, Schneider, Leichtweiss, and Cruz-Orive, respectively.

Finally, Part III emphasizes the influence of his work. It contains commentaries by several specialists regarding modern results based on, or closely related to, those of Santaló, some book reviews written by Santaló, as well as some reviews of his books. As a curious addendum, a ranking of his articles, given by Santaló himself, is included.


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  • Selected Works Springer Collected Works in Mathematics English Spanish and French Edition


The Ricci Flow: Techniques and Applications: Geometric Aspects (Mathematical Surveys and Monographs) (Pt. 1)

The Ricci Flow: Techniques and Applications: Geometric Aspects (Mathematical Surveys and Monographs) (Pt. 1) Lowest new price: $112.00
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Author: Bennett Chow

This book gives a presentation of topics in Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject. The authors have aimed at presenting technical material in a clear and detailed manner. In this volume, geometric aspects of the theory have been emphasized. The book presents the theory of Ricci solitons, Kähler-Ricci flow, compactness theorems, Perelman's entropy monotonicity and no local collapsing, Perelman's reduced distance function and applications to ancient solutions, and a primer of 3-manifold topology. Various technical aspects of Ricci flow have been explained in a clear and detailed manner. The authors have tried to make some advanced material accessible to graduate students and nonexperts. The book gives a rigorous introduction to Perelman's work and explains technical aspects of Ricci flow useful for singularity analysis. Throughout, there are appropriate references so that the reader may further pursue the statements and proofs of the various results.


Michael Atiyah Collected Works: 7 Volume Set

Michael Atiyah Collected Works: 7 Volume Set Lowest new price: $910.73
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Author: Michael Atiyah

Professor Atiyah is one of the greatest living mathematicians and is renowned in the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still actively involved in the mathematics community. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into seven volumes, with the first five volumes divided thematically and the sixth and seventh arranged by date.

This seven volume set of the collected works of Professor Sir Michael Atiyah, includes:
Collected Works: Volume 1: Early Papers; General Papers
Collected Works: Volume 2: K-Theory
Collected Works: Volume 3: Index Theory: 1
Collected Works: Volume 4: Index Theory: 2
Collected Works: Volume 5: Gauge Theories
Collected Works: Volume 6: Publications between 1987 and 2002
New for 2014:
Collected Works: Volume 7: 2002-2013, including Sir Michael's work on skyrmions; K-theory and cohomology; geometric models of matter; curvature, cones and characteristic numbers; and reflections on the work of Riemann, Einstein and Bott.


Visual Motion of Curves and Surfaces

Visual Motion of Curves and Surfaces Lowest new price: $72.60
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Author: Roberto Cipolla
Brand: Cambridge University Press

The world is full of objects, many of which are visible to us as surfaces. Examples are people, cars, machines, computers and bananas. Exceptions are such things as clouds and trees, which have a more detailed, fuzzy structure. Computer vision aims to detect and reconstruct features of surfaces from the images produced by cameras, in some ways mimicking the way in which humans reconstruct features of the world around them by using their eyes. This book describes how the 3D shape of surfaces can be recovered from image sequences of outlines. Cipolla and Giblin provide all the necessary background in differential geometry (assuming knowledge of elementary algebra and calculus) and in the analysis of visual motion, and emphasizes intuitive visual understanding of the geometric techniques with computer-generated illustrations. They also give a thorough introduction to the mathematical techniques and the details of the implementations, and apply the methods to data from real images.

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Curved Spaces: From Classical Geometries to Elementary Differential Geometry

Curved Spaces: From Classical Geometries to Elementary Differential Geometry Lowest new price: $168.76
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Author: P. M. H. Wilson
Brand: Brand: Cambridge University Press

This self-contained 2007 textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra.

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A Comprehensive Introduction to Differential Geometry, Vol. 5, 3rd Edition

A Comprehensive Introduction to Differential Geometry, Vol. 5, 3rd Edition Lowest new price: $50.00
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Author: Michael Spivak
Brand: Brand: Publish or Perish

Spivak's 5 volume set is a classic and overall the best and most thorough treatment of differential geometry

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Lectures on Differential Geometry (2010 re-issue)

Lectures on Differential Geometry (2010 re-issue) Lowest new price: $35.00
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Author: Richard Schoen

This volume presents lectures given by Richard Schoen and Shing-Tung Yau at the Institute for Advanced Studies at Princeton University in 1984 and 1985. The lectures describe the major advances in differential geometry, which progressed rapidly in the twentieth century.

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L2-Invariants: Theory and Applications to Geometry and K-Theory (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) (v. 44)

L2-Invariants: Theory and Applications to Geometry and K-Theory (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) (v. 44) Lowest new price: $50.88
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Author: Wolfgang Lück
Brand: Brand: Springer

In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

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