A.D. Alexandrov

Selected Works Part II: Intrinsic Geometry of Convex Surfaces

Author: S.S. Kutateladze

Publisher: CRC Press

ISBN: 113442907X

Category: Mathematics

Page: 440

View: 651

A.D. Alexandrov is considered by many to be the father of intrinsic geometry, second only to Gauss in surface theory. That appraisal stems primarily from this masterpiece--now available in its entirely for the first time since its 1948 publication in Russian. Alexandrov's treatise begins with an outline of the basic concepts, definitions, and results relevant to intrinsic geometry. It reviews the general theory, then presents the requisite general theorems on rectifiable curves and curves of minimum length. Proof of some of the general properties of the intrinsic metric of convex surfaces follows. The study then splits into two almost independent lines: further exploration of the intrinsic geometry of convex surfaces and proof of the existence of a surface with a given metric. The final chapter reviews the generalization of the whole theory to convex surfaces in the Lobachevskii space and in the spherical space, concluding with an outline of the theory of nonconvex surfaces. Alexandrov's work was both original and extremely influential. This book gave rise to studying surfaces "in the large," rejecting the limitations of smoothness, and reviving the style of Euclid. Progress in geometry in recent decades correlates with the resurrection of the synthetic methods of geometry and brings the ideas of Alexandrov once again into focus. This text is a classic that remains unsurpassed in its clarity and scope.
Posted in Mathematics

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 8857

Posted in Mathematics

A. D. Alexandrov Selected Works

Selected Scientific Papers

Author: Yu. G. Reshetnyak,S.S. Kutateladze

Publisher: CRC Press

ISBN: 9782881249846

Category: Mathematics

Page: 332

View: 7120

Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the discipline's most difficult and enduring challenges. He was the first to apply many of the tools and methods of the theory of real functions and functional analysis that are now current in geometry. The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski's theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.
Posted in Mathematics

A. D. Alexandrov Selected Works Part I

Selected Scientific Papers

Author: Yu. G. Reshetnyak,S.S. Kutateladze

Publisher: CRC Press

ISBN: 148228717X

Category: Mathematics

Page: 332

View: 7309

Alexandr Danilovich Alexandrov has been called a giant of 20th-century mathematics. This volume contains some of the most important papers by this renowned geometer and hence, some of his most influential ideas. Alexandrov addressed a wide range of modern mathematical problems, and he did so with intelligence and elegance, solving some of the discipline's most difficult and enduring challenges. He was the first to apply many of the tools and methods of the theory of real functions and functional analysis that are now current in geometry. The topics here include convex polyhedrons and closed surfaces, an elementary proof and extension of Minkowski's theorem, Riemannian geometry and a method for Dirichlet problems. This monograph, published in English for the first time, gives unparalleled access to a brilliant mind, and advanced students and researchers in applied mathematics and geometry will find it indispensable.
Posted in Mathematics

Computational Topology

An Introduction

Author: Herbert Edelsbrunner,John Harer

Publisher: American Mathematical Soc.

ISBN: 0821849255

Category: Mathematics

Page: 241

View: 6660

Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
Posted in Mathematics

Differential Geometry of Curves and Surfaces

A Concise Guide

Author: Victor Andreevich Toponogov

Publisher: Springer Science & Business Media

ISBN: 0817644024

Category: Mathematics

Page: 206

View: 6277

Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels
Posted in Mathematics

Convexity and Its Applications

Author: GRUBER,WILLS

Publisher: Birkhäuser

ISBN: 3034858582

Category: Science

Page: 421

View: 8296

This collection of surveys consists in part of extensions of papers presented at the conferences on convexity at the Technische Universitat Wien (July 1981) and at the Universitat Siegen (July 1982) and in part of articles written at the invitation of the editors. This volume together with the earlier volume «Contributions to Geometry» edited by Tolke and Wills and published by Birkhauser in 1979 should give a fairly good account of many of the more important facets of convexity and its applications. Besides being an up to date reference work this volume can be used as an advanced treatise on convexity and related fields. We sincerely hope that it will inspire future research. Fenchel, in his paper, gives an historical account of convexity showing many important but not so well known facets. The articles of Papini and Phelps relate convexity to problems of functional analysis on nearest points, nonexpansive maps and the extremal structure of convex sets. A bridge to mathematical physics in the sense of Polya and Szego is provided by the survey of Bandle on isoperimetric inequalities, and Bachem's paper illustrates the importance of convexity for optimization. The contribution of Coxeter deals with a classical topic in geometry, the lines on the cubic surface whereas Leichtweiss shows the close connections between convexity and differential geometry. The exhaustive survey of Chalk on point lattices is related to algebraic number theory. A topic important for applications in biology, geology etc.
Posted in Science

An Open Door to Number Theory

Author: Duff Campbell

Publisher: American Mathematical Soc.

ISBN: 1470443481

Category: Number theory

Page: 283

View: 4897

A well-written, inviting textbook designed for a one-semester, junior-level course in elementary number theory. The intended audience will have had exposure to proof writing, but not necessarily to abstract algebra. That audience will be well prepared by this text for a second-semester course focusing on algebraic number theory. The approach throughout is geometric and intuitive; there are over 400 carefully designed exercises, which include a balance of calculations, conjectures, and proofs. There are also nine substantial student projects on topics not usually covered in a first-semester course, including Bernoulli numbers and polynomials, geometric approaches to number theory, the -adic numbers, quadratic extensions of the integers, and arithmetic generating functions.
Posted in Number theory

Connectivity, Complexity, and Catastrophe in Large-scale Systems

Author: J. L. Casti

Publisher: John Wiley & Sons

ISBN: N.A

Category: Catastrophes (Mathematics)

Page: 203

View: 6346

Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.
Posted in Catastrophes (Mathematics)

The Porous Medium Equation

Mathematical Theory

Author: Juan Luis Vazquez

Publisher: Oxford University Press

ISBN: 0198569033

Category: Mathematics

Page: 624

View: 8621

Aimed at research students and academics in mathematics and engineering, as well as engineering specialists, this book provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation.
Posted in Mathematics

Convex Bodies: The Brunn–Minkowski Theory

Author: Rolf Schneider

Publisher: Cambridge University Press

ISBN: 1107601010

Category: Mathematics

Page: 760

View: 2086

A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Posted in Mathematics

Italian Mathematics Between the Two World Wars

Author: Angelo Guerraggio,Pietro Nastasi

Publisher: Springer Science & Business Media

ISBN: 3764375124

Category: Mathematics

Page: 299

View: 7440

This book describes Italian mathematics in the period between the two World Wars. It analyzes the development by focusing on both the interior and the external influences. Italian mathematics in that period was shaped by a colorful array of strong personalities who concentrated their efforts on a select number of fields and won international recognition and respect in an incredibly short time. Consequently, Italy was considered a third mathematical power after France and Germany.
Posted in Mathematics

Graphics Recognition. Algorithms and Applications

4th International Workshop, GREC 2001, Kingston, Ontario, Canada, September 7-8, 2001. Selected Papers

Author: Dorothea Blostein,Young-Bin Kwon

Publisher: Springer

ISBN: 3540458689

Category: Computers

Page: 370

View: 4767

This book presents refereed and revised papers presented at GREC 2001, the 4th IAPR International Workshop on Graphics Recognition, which took place in Kingston, Ontario, Canada in September 2001. Graphics recognition is a branch of document image analysis that focuses on the recognition of two-dimensional notations such as engineering drawings, maps, mathematical notation, music notation, tables, and chemical structure diagrams. Due to the growing demand for both o?-line and on-line document recognition systems, the ?eld of graphics recognition has an excitingand promisingfuture. The GREC workshops provide an opportunity for researchers at all levels of experience to share insights into graphics recognition methods. The workshops enjoy strongparticipation from researchers in both industry and academia. They are sponsored by IAPR TC-10, the Technical Committee on Graphics Recog- tion within the International Association for Pattern Recognition. Edited v- umes from the previous three workshops in this series are available as Lecture Notes in Computer Science, Vols. 1072, 1389, and 1941. After the GREC 2001 workshop, authors were invited to submit enhanced versions of their papers for review. Every paper was evaluated by three reviewers. We are grateful to both authors and reviewers for their careful work during this review process. Many of the papers that appear in this volume were thoroughly revised and improved, in response to reviewers’ suggestions.
Posted in Computers

1089 and All that : a Journey Into Mathematics

Author: D. J. Acheson

Publisher: Oxford University Press, USA

ISBN: 9780198516231

Category: Mathematics

Page: 178

View: 8819

This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famous cartoonists. This unusual book is one of the most readable explanations of mathematics available.
Posted in Mathematics

The Poincare Conjecture

In Search of the Shape of the Universe

Author: Donal O'Shea

Publisher: Bloomsbury Publishing USA

ISBN: 9780802718945

Category: Mathematics

Page: 304

View: 9344

Henri Poincaré was one of the greatest mathematicians of the late nineteenth and early twentieth century. He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincaré conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point. Poincaré's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award. In telling the vibrant story of The Poincaré Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.
Posted in Mathematics

Classical and Stochastic Laplacian Growth

Author: Bjorn Gustafsson,Razvan Teodorescu,Alexander Vasiliev

Publisher: Springer

ISBN: 3319082876

Category: Science

Page: 317

View: 8987

This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Löwner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive bibliography covering over twelve decades of results and an introduction rich in historical and biographical details complement the eight main chapters of this monograph. Given its systematic and consistent notation and background results, this book provides a self-contained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics.
Posted in Science

A Survey of Minimal Surfaces

Author: Robert Osserman

Publisher: Courier Corporation

ISBN: 0486167690

Category: Mathematics

Page: 224

View: 1412

Newly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein’s theorem, much more, including such recent developments as new work on Plateau’s problem and on isoperimetric inequalities. Clear, comprehensive examination provides profound insights into crucial area of pure mathematics. 1986 edition. Index.
Posted in Mathematics

Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition

Author: Elsa Abbena,Simon Salamon,Alfred Gray

Publisher: CRC Press

ISBN: 1351992201

Category: Mathematics

Page: 1016

View: 9414

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.
Posted in Mathematics

Information Retrieval Meets Information Visualization

PROMISE Winter School 2012, Zinal, Switzerland, January 23-27, 2012, Revised Tutorial Lectures

Author: Maristella Agosti,Nicola Ferro,Pamela Forner,Henning Müller,Giuseppe Santucci

Publisher: Springer

ISBN: 3642364152

Category: Computers

Page: 177

View: 678

The research domains information retrieval and information visualization have always been independent from each other. However, they have the potential to be mutually beneficial. With this in mind, a writer school was organized in Zinal, Switzerland, in January 2012, within the context of the EU-funded research project PROMISE (Participative Research Laboratory for Multimedia and Multilingual Information Systems Evaluation). PROMISE aims at advancing the experimental evaluation of complex multimedia and multilingual information systems in order to support individuals, commercial entities, and communities who design, develop, employ, and improve such complex systems. The overall goal of PROMISE is to deliver a unified environment collecting data, knowledge, tools, and methodologies, and to help the user community involved in experimental evaluation. This book constitutes the outcome of the PROMISE Winter School 2012 and contains 11 invited lectures from the research domains information retrieval and information visualization. A large variety of subjects are covered, including hot topics such as crowdsourcing and social media.
Posted in Computers

Deep Beauty

Understanding the Quantum World through Mathematical Innovation

Author: Hans Halvorson

Publisher: Cambridge University Press

ISBN: 113949922X

Category: Mathematics

Page: N.A

View: 7565

No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts at the cutting edge of future physics. These creative developments in mathematics may catalyze the advances that enable us to understand our current physical theories, especially quantum theory. The authors bring diverse perspectives, unified only by the attempt to introduce fresh concepts that will open up new vistas in our understanding of future physics.
Posted in Mathematics