A Short Course In Computational Geometry And Topology

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A Short Course in Computational Geometry and Topology

Herbert Edelsbrunner
A Short Course in Computational Geometry and Topology Book PDF

Author : Herbert Edelsbrunner
Publisher : Springer Science & Business
Page : 110 pages
File Size : 52,5 Mb
Release : 2014-04-28
Category : Computers
ISBN : 9783319059570

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A Short Course in Computational Geometry and Topology by Herbert Edelsbrunner Pdf

This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.

Advances in Applied and Computational Topology

American Mathematical Society. Short Course on Computational Topology
Advances in Applied and Computational Topology Book PDF

Author : American Mathematical Society. Short Course on Computational Topology
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 45,7 Mb
Release : 2012-07-05
Category : Mathematics
ISBN : 9780821853276

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Advances in Applied and Computational Topology by American Mathematical Society. Short Course on Computational Topology Pdf

What is the shape of data? How do we describe flows? Can we count by integrating? How do we plan with uncertainty? What is the most compact representation? These questions, while unrelated, become similar when recast into a computational setting. Our input is a set of finite, discrete, noisy samples that describes an abstract space. Our goal is to compute qualitative features of the unknown space. It turns out that topology is sufficiently tolerant to provide us with robust tools. This volume is based on lectures delivered at the 2011 AMS Short Course on Computational Topology, held January 4-5, 2011 in New Orleans, Louisiana. The aim of the volume is to provide a broad introduction to recent techniques from applied and computational topology. Afra Zomorodian focuses on topological data analysis via efficient construction of combinatorial structures and recent theories of persistence. Marian Mrozek analyzes asymptotic behavior of dynamical systems via efficient computation of cubical homology. Justin Curry, Robert Ghrist, and Michael Robinson present Euler Calculus, an integral calculus based on the Euler characteristic, and apply it to sensor and network data aggregation. Michael Erdmann explores the relationship of topology, planning, and probability with the strategy complex. Jeff Erickson surveys algorithms and hardness results for topological optimization problems.

Computational Topology

Herbert Edelsbrunner,John L. Harer
Computational Topology Book PDF

Author : Herbert Edelsbrunner,John L. Harer
Publisher : American Mathematical Society
Page : 241 pages
File Size : 54,9 Mb
Release : 2022-01-31
Category : Mathematics
ISBN : 9781470467692

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Computational Topology by Herbert Edelsbrunner,John L. Harer Pdf

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.

A First Course in Computational Algebraic Geometry

Wolfram Decker
A First Course in Computational Algebraic Geometry Book PDF

Author : Wolfram Decker
Publisher : Unknown
Page : 128 pages
File Size : 44,9 Mb
Release : 2013
Category : Curves, Algebraic
ISBN : 1107309247

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A First Course in Computational Algebraic Geometry by Wolfram Decker Pdf

A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

Geometric and Topological Inference

Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec
Geometric and Topological Inference Book PDF

Author : Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec
Publisher : Cambridge University Press
Page : 247 pages
File Size : 42,7 Mb
Release : 2018-09-27
Category : Computers
ISBN : 9781108419390

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Geometric and Topological Inference by Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec Pdf

A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

Computational Topology for Data Analysis

Tamal Krishna Dey,Yusu Wang
Computational Topology for Data Analysis Book PDF

Author : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 53,8 Mb
Release : 2022-03-10
Category : Computers
ISBN : 9781009098168

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Computational Topology for Data Analysis by Tamal Krishna Dey,Yusu Wang Pdf

This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.

Geometry and Topology for Mesh Generation

Herbert Edelsbrunner
Geometry and Topology for Mesh Generation Book PDF

Author : Herbert Edelsbrunner
Publisher : Cambridge University Press
Page : 206 pages
File Size : 41,7 Mb
Release : 2001-05-28
Category : Mathematics
ISBN : 0521793092

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Geometry and Topology for Mesh Generation by Herbert Edelsbrunner Pdf

This graduate text combines geometry, topology, algorithms, and engineering and emphasizes topics that are both elementary and useful.

Discrete and Computational Geometry

Satyan L. Devadoss,Joseph O'Rourke
Discrete and Computational Geometry Book PDF

Author : Satyan L. Devadoss,Joseph O'Rourke
Publisher : Princeton University Press
Page : 270 pages
File Size : 48,9 Mb
Release : 2011-04-11
Category : Mathematics
ISBN : 9781400838981

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Discrete and Computational Geometry by Satyan L. Devadoss,Joseph O'Rourke Pdf

An essential introduction to discrete and computational geometry Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only).

Topological Persistence in Geometry and Analysis

Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang
Topological Persistence in Geometry and Analysis Book PDF

Author : Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 51,5 Mb
Release : 2020-05-11
Category : Education
ISBN : 9781470454951

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Topological Persistence in Geometry and Analysis by Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang Pdf

The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.

A Concise Course in Algebraic Topology

J. P. May
A Concise Course in Algebraic Topology Book PDF

Author : J. P. May
Publisher : University of Chicago Press
Page : 262 pages
File Size : 52,9 Mb
Release : 1999-09
Category : Mathematics
ISBN : 0226511839

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A Concise Course in Algebraic Topology by J. P. May Pdf

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

An Excursion Through Discrete Differential Geometry

American Mathematical Society. Short Course, Discrete Differential Geometry
An Excursion Through Discrete Differential Geometry Book PDF

Author : American Mathematical Society. Short Course, Discrete Differential Geometry
Publisher : American Mathematical Soc.
Page : 140 pages
File Size : 44,8 Mb
Release : 2020-09-02
Category : Education
ISBN : 9781470446628

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An Excursion Through Discrete Differential Geometry by American Mathematical Society. Short Course, Discrete Differential Geometry Pdf

Discrete Differential Geometry (DDG) is an emerging discipline at the boundary between mathematics and computer science. It aims to translate concepts from classical differential geometry into a language that is purely finite and discrete, and can hence be used by algorithms to reason about geometric data. In contrast to standard numerical approximation, the central philosophy of DDG is to faithfully and exactly preserve key invariants of geometric objects at the discrete level. This process of translation from smooth to discrete helps to both illuminate the fundamental meaning behind geometric ideas and provide useful algorithmic guarantees. This volume is based on lectures delivered at the 2018 AMS Short Course ``Discrete Differential Geometry,'' held January 8-9, 2018, in San Diego, California. The papers in this volume illustrate the principles of DDG via several recent topics: discrete nets, discrete differential operators, discrete mappings, discrete conformal geometry, and discrete optimal transport.

Computational Proximity

James F. Peters
Computational Proximity Book PDF

Author : James F. Peters
Publisher : Springer
Page : 433 pages
File Size : 52,6 Mb
Release : 2016-04-20
Category : Technology & Engineering
ISBN : 9783319302621

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Computational Proximity by James F. Peters Pdf

This book introduces computational proximity (CP) as an algorithmic approach to finding nonempty sets of points that are either close to each other or far apart. Typically in computational proximity, the book starts with some form of proximity space (topological space equipped with a proximity relation) that has an inherent geometry. In CP, two types of near sets are considered, namely, spatially near sets and descriptivelynear sets. It is shown that connectedness, boundedness, mesh nerves, convexity, shapes and shape theory are principal topics in the study of nearness and separation of physical aswell as abstract sets. CP has a hefty visual content. Applications of CP in computer vision, multimedia, brain activity, biology, social networks, and cosmology are included. The book has been derived from the lectures of the author in a graduate course on the topology of digital images taught over the past several years. Many of the students have provided important insights and valuable suggestions. The topics in this monograph introduce many forms of proximities with a computational flavour (especially, what has become known as the strong contact relation), many nuances of topological spaces, and point-free geometry.

A Short Course in Differential Geometry and Topology

A. T. Fomenko,Aleksandr Sergeevich Mishchenko
A Short Course in Differential Geometry and Topology Book PDF

Author : A. T. Fomenko,Aleksandr Sergeevich Mishchenko
Publisher : Unknown
Page : 292 pages
File Size : 54,7 Mb
Release : 2009
Category : Mathematics
ISBN : UOM:39015080871190

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A Short Course in Differential Geometry and Topology by A. T. Fomenko,Aleksandr Sergeevich Mishchenko Pdf

This volume is intended for graduate and research students in mathematics and physics. It covers general topology, nonlinear co-ordinate systems, theory of smooth manifolds, theory of curves and surfaces, transformation groupstensor analysis and Riemannian geometry theory of intogration and homologies, fundamental groups and variational principles in Riemannian geometry. The text is presented in a form that is easily accessible to students and is supplemented by a large number of examples, problems, drawings and appendices.

A Short Course in Differential Topology

Bjørn Ian Dundas
A Short Course in Differential Topology Book PDF

Author : Bjørn Ian Dundas
Publisher : Cambridge University Press
Page : 265 pages
File Size : 42,7 Mb
Release : 2018-06-28
Category : Mathematics
ISBN : 9781108425797

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A Short Course in Differential Topology by Bjørn Ian Dundas Pdf

This book offers a concise and modern introduction to differential topology, the study of smooth manifolds and their properties, at the advanced undergraduate/beginning graduate level. The treatment throughout is hands-on, including many concrete examples and exercises woven into the text with hints provided to guide the student.

Differential Geometry and Topology, Discrete and Computational Geometry

Mohamed Boucetta,J.-M. Morvan
Differential Geometry and Topology Discrete and Computational Geometry Book PDF

Author : Mohamed Boucetta,J.-M. Morvan
Publisher : Ios PressInc
Page : 373 pages
File Size : 47,9 Mb
Release : 2005
Category : Mathematics
ISBN : 158603507X

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Differential Geometry and Topology, Discrete and Computational Geometry by Mohamed Boucetta,J.-M. Morvan Pdf

The aim of this volume is to give an introduction and overview to differential topology, differential geometry and computational geometry with an emphasis on some interconnections between these three domains of mathematics. The chapters give the background required to begin research in these fields or at their interfaces. They introduce new research domains and both old and new conjectures in these different subjects show some interaction between other sciences close to mathematics. Topics discussed are; the basis of differential topology and combinatorial topology, the link between differential geometry and topology, Riemanian geometry (Levi-Civita connextion, curvature tensor, geodesic, completeness and curvature tensor), characteristic classes (to associate every fibre bundle with isomorphic fiber bundles), the link between differential geometry and the geometry of non smooth objects, computational geometry and concrete applications such as structural geology and graphism.