curves and singularities a geometrical introduction to singularity theory

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Curves And Singularities

Author : James William Bruce
ISBN : 0521429994
Genre : Mathematics
File Size : 36. 55 MB
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The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors take a novel approach by casting the theory into a new light, that of singularity theory. The second edition of this successful textbook has been thoroughly revised throughout and includes a multitude of new exercises and examples. A new final chapter has been added that covers recently developed techniques in the classification of functions of several variables, a subject central to many applications of singularity theory. Also in this second edition are new sections on the Morse lemma and the classification of plane curve singularities. The only prerequisites for students to follow this textbook are a familiarity with linear algebra and advanced calculus. Thus it will be invaluable for anyone who would like an introduction to the modern theories of catastrophes and singularities.

Singular Points Of Plane Curves

Author : C. T. C. Wall
ISBN : 0521547741
Genre : Mathematics
File Size : 75. 21 MB
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Even the simplest singularities of planar curves, e.g. where the curve crosses itself, or where it forms a cusp, are best understood in terms of complex numbers. The full treatment uses techniques from algebra, algebraic geometry, complex analysis and topology and makes an attractive chapter of mathematics, which can be used as an introduction to any of these topics, or to singularity theory in higher dimensions. This book is designed as an introduction for graduate students and draws on the author's experience of teaching MSc courses; moreover, by synthesising different perspectives, he gives a novel view of the subject, and a number of new results.

Introduction To Singularities And Deformations

Author : Gert-Martin Greuel
ISBN : 9783540284192
Genre : Mathematics
File Size : 27. 79 MB
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Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.

Singularities Of Smooth Functions And Maps

Author : J. Martinet
ISBN : 0521233984
Genre : Mathematics
File Size : 32. 14 MB
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Singularities In Geometry And Topology

Author : Jean-Paul Brasselet
ISBN : 9789812700223
Genre : Mathematics
File Size : 56. 45 MB
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Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.

Algebraic Geometry And Singularities

Author : Antonio Campillo Lopez
ISBN : 9783034890205
Genre : Mathematics
File Size : 82. 15 MB
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Singularity Theory

Author : Charles Terence Clegg Wall
ISBN : 0521658888
Genre : Computers
File Size : 85. 12 MB
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An up-to-date survey of research in singularity theory.

Nonlinear Computational Geometry

Author : Ioannis Z Emiris
ISBN : 9781441909992
Genre : Mathematics
File Size : 48. 15 MB
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An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.

Singularities

Author : Vladimir I. Arnold
ISBN : 9783034887700
Genre : Mathematics
File Size : 52. 59 MB
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In July 1996, a conference was organized by the editors of this volume at the Mathematische Forschungsinstitut Oberwolfach to honour Egbert Brieskorn on the occasion of his 60th birthday. Most of the mathematicians invited to the conference have been influenced in one way or another by Brieskorn's work in singularity theory. It was the first time that so many people from the Russian school could be present at a conference in singularity theory outside Russia. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrating the breadth of Brieskorn's own interests. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrates the breadth of Brieskorn's own interests.

Singularities

Author : Jean-Paul Brasselet
ISBN : 0521466318
Genre : Mathematics
File Size : 59. 93 MB
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This book contains papers given at the International Singularity Conference held in 1991 at Lille.

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