Geometry from a Differentiable Viewpoint

Author: John McCleary

Publisher: Cambridge University Press

ISBN: 9780521424806

Category: Mathematics

Page: 308

View: 4768

This book offers a new treatment of the topic, one which is designed to make differential geometry an approachable subject for advanced undergraduates. Professor McCleary considers the historical development of non-Euclidean geometry, placing differential geometry in the context of geometry students will be familiar with from high school. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of a particular surface, the non-Euclidean or hyperbolic plane. The main theorems of non-Euclidean geometry are presented along with their historical development. The author then introduces the methods of differential geometry and develops them toward the goal of constructing models of the hyperbolic plane. While interesting diversions are offered, such as Huygen's pendulum clock and mathematical cartography, the book thoroughly treats the models of non-Euclidean geometry and the modern ideas of abstract surfaces and manifolds.

Classical Geometry

Euclidean, Transformational, Inversive, and Projective

Author: I. E. Leonard,J. E. Lewis,A. C. F. Liu,G. W. Tokarsky

Publisher: John Wiley & Sons

ISBN: 1118679148

Category: Mathematics

Page: 496

View: 1901

Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which provides the foundation for the rest of the material covered throughout; Part Two discusses Euclidean transformations of the plane, as well as groups and their use in studying transformations; and Part Three covers inversive and projective geometry as natural extensions of Euclidean geometry. In addition to featuring real-world applications throughout, Classical Geometry: Euclidean, Transformational, Inversive, and Projective includes: Multiple entertaining and elegant geometry problems at the end of each section for every level of study Fully worked examples with exercises to facilitate comprehension and retention Unique topical coverage, such as the theorems of Ceva and Menalaus and their applications An approach that prepares readers for the art of logical reasoning, modeling, and proofs The book is an excellent textbook for courses in introductory geometry, elementary geometry, modern geometry, and history of mathematics at the undergraduate level for mathematics majors, as well as for engineering and secondary education majors. The book is also ideal for anyone who would like to learn the various applications of elementary geometry.

Topics in Geometry

In Memory of Joseph D’Atri

Author: Simon Gindikin

Publisher: Springer Science & Business Media

ISBN: 1461224322

Category: Mathematics

Page: 370

View: 946

This collection of articles serves to commemorate the legacy of Joseph D'Atri, who passed away on April 29, 1993, a few days after his 55th birthday. Joe D' Atri is credited with several fundamental discoveries in ge ometry. In the beginning of his mathematical career, Joe was interested in the generalization of symmetrical spaces in the E. Cart an sense. Symmetric spaces, differentiated from other homogeneous manifolds by their geomet rical richness, allows the development of a deep analysis. Geometers have been constantly interested and challenged by the problem of extending the class of symmetric spaces so as to preserve their geometrical and analytical abundance. The name of D'Atri is tied to one of the most successful gen eralizations: Riemann manifolds in which (local) geodesic symmetries are volume-preserving (up to sign). In time, it turned out that the majority of interesting generalizations of symmetrical spaces are D'Atri spaces: natu ral reductive homogeneous spaces, Riemann manifolds whose geodesics are orbits of one-parameter subgroups, etc. The central place in D'Atri's research is occupied by homogeneous bounded domains in en, which are not symmetric. Such domains were discovered by Piatetskii-Shapiro in 1959, and given Joe's strong interest in the generalization of symmetric spaces, it was very natural for him to direct his research along this path.

Handbook of Differential Geometry

Author: Franki J.E. Dillen,Leopold C.A. Verstraelen

Publisher: Elsevier

ISBN: 9780080461205

Category: Mathematics

Page: 574

View: 5728

In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. 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. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics

Principles of Geometry

Author: H. F. Baker

Publisher: Cambridge University Press

ISBN: 1108017819

Category: Mathematics

Page: 262

View: 3332

A benchmark study of projective geometry and the birational theory of surfaces, first published between 1922 and 1925.

Selected Papers from the Journal of Differential Geometry 1967-2017

Author: Simon Donaldson

Publisher: N.A

ISBN: 9781571463340

Category:

Page: 630

View: 3135

This collection of thirteen papers takes the reader on a journey through many important mathematical developments over the past half century. Among the authors and topics are: J. Milnor on curvature and fundamental group; M. F. Atiyah on equivariant K-theory; Gheorghe Lusztig on Novikov's higher signature and families of elliptic operators; Edward Witten on super-symmetry and Morse theory; Kefeng Liu on modular invariance and rigidity theorems; and M. J. Hopkins and I. M. Singer on quadratic functions in geometry, topology, and M-theory. With a foreword by Shing-Tung Yau, and a preface by Simon Donaldson.

Selected Papers on Number Theory and Algebraic Geometry

Author: Valentin Vasilʹevich Lychagin

Publisher: American Mathematical Soc.

ISBN: 9780821804285

Category: Mathematics

Page: 294

View: 2378

Discusses quantization problems to emphasize the advantage of an algebraic geometry approach to nonlinear differential equations. This book features systematic use of geometry of jet spaces.

Perspectives on Projective Geometry

A Guided Tour Through Real and Complex Geometry

Author: Jürgen Richter-Gebert

Publisher: Springer Science & Business Media

ISBN: 9783642172861

Category: Mathematics

Page: 571

View: 5438

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

Statistical Optimization for Geometric Computation

Theory and Practice

Author: Kenichi Kanatani

Publisher: Courier Corporation

ISBN: 0486443086

Category: Mathematics

Page: 509

View: 1905

This text for graduate students discusses the mathematical foundations of statistical inference for building three-dimensional models from image and sensor data that contain noise--a task involving autonomous robots guided by video cameras and sensors. The text employs a theoretical accuracy for the optimization procedure, which maximizes the reliability of estimations based on noise data. The numerous mathematical prerequisites for developing the theories are explained systematically in separate chapters. These methods range from linear algebra, optimization, and geometry to a detailed statistical theory of geometric patterns, fitting estimates, and model selection. In addition, examples drawn from both synthetic and real data demonstrate the insufficiencies of conventional procedures and the improvements in accuracy that result from the use of optimal methods.

Selected Papers

On the Classification of Varieties and Moduli Spaces

Author: David Mumford

Publisher: Springer Science & Business Media

ISBN: 9780387210926

Category: Mathematics

Page: 795

View: 5620

Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics. Many of these papers are currently unavailable, and the commentaries by Gieseker, Lange, Viehweg and Kempf are being published here for the first time.

Theory and Applications of Image Analysis

Selected Papers from the 7th Scandinavian Conference on Image Analysis

Author: P Johansen,S Olsen

Publisher: World Scientific

ISBN: 9814505641

Category: Technology & Engineering

Page: 360

View: 4382

This book contains 31 papers carefully selected from among those presented at the 7th Scandinavian Conference on Image Analysis. The authors have extended their papers to give a more in-depth discussion of the theory, or of the experimental validation of the method they have proposed. The topics covered are current and wide-ranging and include both 2D- and 3D-vision, and low to high level vision. Contents:Theory:Human Image Understanding (I Biederman)Local Image Structure (J J Koenderink)An Algebraic/Analytic Method for Reconstruction from Image Correspondences (G Sparr)Computational Aspects:Efficient Matching of Dynamically Changing Graphs (H Bunke et al.)Using a Genetic Algorithm to Solve Constraint Satisfaction Problems Generated by An Image Interpreter (S Truvé)Estimation of Velocity and Acceleration in Time Sequences (L Haglund et al.)Applications:Towards Continuously Operating Integrated Vision Systems for Robotics Applications (J L Crowley)Real Time 3D-Road Modeling for Autonomous Vehicle Guidance (U Franke)Studies on Classification of LANDSAT Image Data Using a Neural Network Approach (S Kamata et al.)Texture Discrimination of Normal and Malignant Mouse Liver Cell Nuclei (F Albregtsen et al.)and other papers Readership: Computer scientists and engineers. keywords:Image Analysis;Human Image Perception;T-junction;Feature;Extraction;Image Reconstruction;Autonomous Vehicle Guidance;3D Pose;Shape Analysis;Texture Analysis;Segmentation

Riemannian Geometry

A Modern Introduction

Author: Isaac Chavel

Publisher: Cambridge University Press

ISBN: 1139452576

Category: Mathematics

Page: N.A

View: 6386

This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.

Selected Papers on Probability and Statistics

Author: N.A

Publisher: American Mathematical Soc.

ISBN: 0821848216

Category: Mathematics

Page: 231

View: 8687

This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.

Selected Papers on Differential Equations and Analysis

Author: N.A

Publisher: American Mathematical Soc.

ISBN: 9780821839270

Category: Mathematics

Page: 145

View: 1965

This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics, including differential equations with free boundary, singular integral operators, operator algebras, and relations between the Brownian motion on a manifold with function theory. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.

Foundations of Differential Geometry, 2 Volume Set

Author: Shoshichi Kobayashi,Katsumi Nomizu

Publisher: Wiley

ISBN: 9780470555583

Category: Mathematics

Page: 832

View: 8837

This set features: Foundations of Differential Geometry, Volume 1 (978-0-471-15733-5) and Foundations of Differential Geometry, Volume 2 (978-0-471-15732-8), both by Shoshichi Kobayashi and Katsumi Nomizu This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. Volume 2 continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.

Selected Papers on Analysis, Probability, and Statistics

Author: Katsumi Nomizu

Publisher: American Mathematical Soc.

ISBN: 9780821875124

Category: Mathematics

Page: 151

View: 9122

This book presents papers that originally appeared in the Japanese journal ""Sugaku"". The papers fall into the general area of mathematical analysis as it pertains to probability and statistics, dynamical systems, differential equations and analytic function theory. Among the topics discussed are: stochastic differential equations, spectra of the Laplacian and Schrodinger operators, nonlinear partial differential equations which generate dissipative dynamical systems, fractal analysis on self-similar sets and their global structure of analytic functions.

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1507