You are here: Home / Shop / Product Detail Page |

## A Course in Metric Geometry (Hardback)"This book is not a research monograph or a reference book (although research interests of the authors influenced it a lot)—this is a textbook. Its structure is similar to that of a graduate course." — From the Preface (page xi) ## $35.79 |

### Need More Info?

Please contact us if you've got questions about this product.## Condition

**VERY GOOD:** This book is in very good condition, showing only a few signs of use and wear. The book opens as if it were new, but the spine’s cover has faded slightly. It was printed on acid-free paper.

## Description

This textbook is Volume 33 in the American Mathematical Society’s **Graduate Studies in Mathematics** series.

Continued from the Preface: “**Course description.** The objective of this book is twofold. First of all, we wanted to give a detailed exposition of basic notions and techniques in the theory of length spaces, a theory which experienced a very fast development in the past few decades and penetrated into many other mathematical disciplines (such as Group Theory, Dynamical Systems, and Partial Differential Equations). However, we have a wider goal of giving an elementary introduction into a broad variety of the most geometrical topics in geometry—the ones related to the notion of distance. This is the reason why we included metric introductions to Riemannian and hyperbolic geometries. This book tends to work with ‘easy-to-touch’ mathematical objects by means of ‘easy-to-visualize’ methods. There is a remarkable book [Gro3], which gives a vast panorama of ‘geometrical mathematics from a metric viewpoint’. Unfortunately, Gromov’s books seems hardly accessible to graduate students and non-experts in geometry. One of the objectives of this book is to bridge the gap between students and researchers interested in metric geometry, and modern mathematical literature.

“**Prerequisite.** It is minimal. We set a challenging goal of making the core part of the book accessible to first-year graduate students. Our expectations of the reader’s background gradually grow as we move further in the book. We tried to introduce and illustrate most of new concepts and methods by using their simplest case and avoiding technicalities that take attention away from the gist of the material.”

**Chapters**

- Metric Spaces
- Length Spaces
- Constructions
- Spaces of Bounded Curvature
- Smooth Length Structures
- Curvature of Riemannian Metrics
- Space of Metric Spaces
- Large-scale Geometry
- Spaces of Curvature Bounded Above
- Spaces of Curvature Bounded Below

The book concludes with Bibliography and Index.

## Details

- SKU:
- 1767
- Subject:
- Geometry
- Author:
- Burago, Dmitri and Yuri Burago and Sergei Ivanov
- Publisher:
- American Mathematical Society
- Publish Date:
- 2001 (First Printing)
- Format:
- Hardback
- Weight (pounds):
- 2.11
- Dimensions (W”xL”xH”):
- 7.3″x10.3″x1″
- ISBN-13:
- 9780821821299
- ISBN-10:
- 0821821296
- Grade Level:
- Graduate
- Series:
- Graduate Studies in Mathematics

## Related Products

### Products related to "A Course in Metric Geometry (Hardback)"

- Views:

#### History of Algebraic Geometry: An Outline of the History and Development of Algebraic Geometry (Hardback)

$136.99

"Algebraic geometry is undoubtedly the area of mathematics where the deviation is greatest between the intuitive ideas forming its starting point and the abstract and complex concepts at the foundation of modern research. The purpose of this work is to help the willing reader abridge the gap." — From the Foreword (page VII)

#### Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality (Hardback)

$71.59

"Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century—a feat he celebrated by carving the founding equations into a stone bridge—mathematicians and engineers have been fascinated by these mathematical objects." — From the back cover

#### Mathematics and Its Applications: Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics (Hardback)

$68.32

"This is a book of ideas. Most of them arise out of my fascination with the division algebras and their tantalizing potential for a deep connection to physics....Inevitably many of these mathematical ideas will be shown to be intimately linked to the design of our physical world." — Geoffrey M. Dixon, Author

#### Undergraduate Texts in Mathematics: Projective Geometry (Softcover)

$68.29

"The prerequisites for reading this book are fairly limited: a good command of linear algebra, some knowledge of quadratic forms and field extensions, and a few notions about the irreducibility of polynomials and factorization in rings of polynomials." — Pierre Samuel, Author, in the Introduction

#### Quantum Hall Effects: Field Theoretical Approach and Related Topics, Second Edition (Hardback)

$67.99

"Presenting an instructive and comprehensive overview of the QHE, this book is also suitable as an introduction to quantum field theory with vivid applications." — From the back cover

#### Introduction to Geometric Computing (Softcover)

$62.40

"If geometric computing is neither computer graphics nor computational geometry, then what is it? Briefly, it is the mathematics and the engineering that underlie both." — From the Preface

#### The Morgan Kaufmann Series in Interactive 3D Technology: Visualizing Quaternions (Hardback)

$61.75

"The game industry is a powerful and driving force in the evolution of computer technology. As the capabilities of personal computers, peripheral hardware, and game consoles have grown, so has the demand for high quality information about the algorithms, tools, and descriptions needed to take advantage of this new technology. This book is part of the series that covers the state of the art in real-time 3D.

#### Geometry, Topology and Physics, Second Edition (Softcover)

$59.95

"GEOMETRY, TOPOLOGY AND PHYSICS introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields." — From the back cover

#### World Scientific Lecture Notes in Physics - Vol. 79: Geometry and Phase Transitions in Colloids and Polymers (Hardback)

$59.85

"In this work, we will mainly be concerned with the static aspects of two particular condensed-matter systems: colloidal crystals and loop polymers." — William Kung, Author

#### Problem-Solving Through Problems (Softcover)

$59.49

"This is a practical anthology of some of the best elementary problems in different branches of mathematics. They are selected for their aesthetic appeal as well as their instructional value, and are organized to highlight the most common problem-solving techniques encountered in undergraduate mathematics." — From the back cover

#### Three-Dimensional Geometry and Topology, Volume 1 (Hardback)

$55.75

"This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology." — From the back cover

#### Methods of Information Geometry (Softcover)

$54.95

"The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability distributions, and the general theory of dual affine connections. the second half of the text provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, convex analysis, neural networks, and affine differential geometry. The book can serve as a suitable text for a topics course for advanced undergraduates and graduate students." — From the back cover

#### Introduction to Circle Packing: The Theory of Discrete Analytic Functions (Hardback)

$54.15

"The topic of 'circle packing' was born of the computer age but takes its inspiration and themes from core areas of classical mathematics." — From inside the dust jacket

#### Classical Mechanics: Theory and Mathematical Modeling (Hardcover)

$49.95

"Classical mechanics is a chief example of the scientific method organizing a 'complex' collection of information into theoretically rigorous, unifying principles; in this sense, mechanics represents one of the highest forms of mathematical modeling. This textbook covers standard topics of a mechanics course, namely, the mechanics of rigid bodies, Lagrangian and Hamiltonian formalism, stability and small oscillations, an introduction to celestial mechanics, and Hamilton-Jacobi theory, but at the same time features unique examples—such as the spinning top including friction and gyroscopic compass—seldom appearing in this context. In addition, variational principles like Lagrangian and Hamiltonian dynamics are treated in great detail." — From the back cover

#### Dolciani Mathematical Expositions No. 42: Charming Proofs: A Journey Into Elegant Mathematics (Hardback)

$47.95

"

*Charming Proofs*presents a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct." — From the back cover#### Interdisciplinary Applied Mathematics: Systems and Control: Nonholonomic Mechanics and Control (Hardback)

$47.29

"This book is intended for graduate and advanced undergraduate students in mathematics, physics and engineering who wish to learn this subject and for researchers in the area who want to enhance their techniques." — From the back cover

#### Polyhedra (Softcover)

$45.99

"Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics and group theory." — From the back cover

#### SMF/AMS Texts and Monographs, Volume 15: Hamiltonian Systems and Their Integrability (Softcover)

$43.65

"This book would be suitable for a graduate course in Hamiltonian systems." — From the back cover

#### Conceptual Mathematics: A First Introduction to Categories, Second Edition (Softcover)

$39.89

"In the last sixty years, the use of the notion of category has led to a remarkable unification and simplification of mathematics.

*Conceptual Mathematics*introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists." — From the back cover#### Student Mathematical Library, Volume 46: Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them (Softcover)

$39.59

"The assumed background is the standard calculus sequence, some linear algebra, and rudiments of ODE and real analysis. All notions are introduced and discussed, and virtually all results proved, based on this background." — From the back cover