Introduction to Topology

Pure and Applied


Author: Colin Conrad Adams,Robert David Franzosa

Publisher: Prentice Hall


Category: Mathematics

Page: 489

View: 4428

For juniors and seniors of various majors, taking a first course in topology. This book introduces topology as an important and fascinating mathematics discipline. Students learn first the basics of point-set topology, which is enhanced by the real-world application of these concepts to science, economics, and engineering as well as other areas of mathematics. The second half of the book focuses on topics like knots, robotics, and graphs. The text is written in an accessible way for a range of undergraduates to understand the usefulness and importance of the application of topology to other fields.

Introduction to Topology , Pure and Applied


Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1467278858

Category: Education

Page: 65

View: 2160

Facts101 is your complete guide to Introduction to Topology , Pure and Applied. In this book, you will learn topics such as Interior, Closure, and Boundary, Creating New Topological Spaces, Continuous Functions and Homeomorphisms, and Metric Snares plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Advances in Applied and Computational Topology

American Mathematical Society Short Course on Computational Topology, January 4-5, 2011, New Orleans, Louisiana


Author: American Mathematical Society. Short Course on Computational Topology

Publisher: American Mathematical Soc.

ISBN: 0821853279

Category: Mathematics

Page: 232

View: 8103

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.

Cubical Homotopy Theory


Author: Brian A. Munson,Ismar Volić

Publisher: Cambridge University Press

ISBN: 1107030250

Category: Mathematics

Page: 625

View: 3959

A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.

Handbuch der Mathematik


Author: L. Kuipers,R. Timman

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110836688

Category: Mathematics

Page: 849

View: 6718

Topological Vector Spaces, Distributions and Kernels

Pure and Applied Mathematics


Author: François Treves

Publisher: Elsevier

ISBN: 1483223620

Category: Mathematics

Page: 582

View: 8035

Topological Vector Spaces, Distributions and Kernels discusses partial differential equations involving spaces of functions and space distributions. The book reviews the definitions of a vector space, of a topological space, and of the completion of a topological vector space. The text gives examples of Frechet spaces, Normable spaces, Banach spaces, or Hilbert spaces. The theory of Hilbert space is similar to finite dimensional Euclidean spaces in which they are complete and carry an inner product that can determine their properties. The text also explains the Hahn-Banach theorem, as well as the applications of the Banach-Steinhaus theorem and the Hilbert spaces. The book discusses topologies compatible with a duality, the theorem of Mackey, and reflexivity. The text describes nuclear spaces, the Kernels theorem and the nuclear operators in Hilbert spaces. Kernels and topological tensor products theory can be applied to linear partial differential equations where kernels, in this connection, as inverses (or as approximations of inverses), of differential operators. The book is suitable for vector mathematicians, for students in advanced mathematics and physics.

Introduction to Topology and Geometry


Author: Saul Stahl,Catherine Stenson

Publisher: John Wiley & Sons

ISBN: 1118546148

Category: Mathematics

Page: 536

View: 9083

An easily accessible introduction to over threecenturies of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalizedtreatments bound to the old thinking. This clearly written,well-illustrated book supplies sufficient background to beself-contained.” —CHOICE This fully revised new edition offers the most comprehensivecoverage of modern geometry currently available at an introductorylevel. The book strikes a welcome balance between academic rigorand accessibility, providing a complete and cohesive picture of thescience with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction toTopology and Geometry, Second Edition discusses introductorytopology, algebraic topology, knot theory, the geometry ofsurfaces, Riemann geometries, fundamental groups, and differentialgeometry, which opens the doors to a wealth of applications. Withits logical, yet flexible, organization, the SecondEdition: • Explores historical notes interspersed throughout theexposition to provide readers with a feel for how the mathematicaldisciplines and theorems came into being • Provides exercises ranging from routine to challenging,allowing readers at varying levels of study to master the conceptsand methods • Bridges seemingly disparate topics by creating thoughtfuland logical connections • Contains coverage on the elements of polytope theory, whichacquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is anexcellent introductory text for topology and geometry courses atthe upper-undergraduate level. In addition, the book serves as anideal reference for professionals interested in gaining a deeperunderstanding of the topic.

Visualization and Processing of Tensor Fields


Author: Joachim Weickert,Hans Hagen

Publisher: Springer Science & Business Media

ISBN: 3540312722

Category: Mathematics

Page: 481

View: 9510

Matrix-valued data sets – so-called second order tensor fields – have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.

Topological Embeddings


Author: N.A

Publisher: Academic Press

ISBN: 9780080873671

Category: Mathematics

Page: 315

View: 916

Topological Embeddings

Geometry and Topology of Submanifolds, VI

Pure and Applied Differential Geometry and the Theory of Submanifolds


Author: Franki Dillen,Ignace Van de Woestyne,Leopold Verstraelen

Publisher: World Scientific

ISBN: 9814550655


Page: 324

View: 1498

The topics covered are pure differential geometry, especially submanifolds and affine differential geometry, and applications of geometry to human vision, robotics, and gastro-entrology. Contents:A Riemannian Invariant for Submanifolds in Space Forms and Its Applications (B Y Chen)Some Variational Problems in Submanifold Theory (F Dillen)Isoparametric Systems on Symmetric Spaces (S Mullen)Focal Sets in Affine Geometry (R Niebergall  P J Ryan)Buckling Eigenvalues and Variational Problems for Surfaces in the Three Sphere (B Palmer)On Completeness of Compact Lorentzian Manifolds (A Romero & M Sánchez)On Para Sasakian Manifolds (R Rosca)A Unified Equiaffine Theory for Surfaces in R4, Part 1: The Definite Surfaces (C P Wang)Cartan's Method of Moving Frames Applied to the Study of Surfaces in Affine 4-Space (J L Weiner)A Survey on the Theory of Harmonic (Pseudo)-Riemannian Spaces (T J Willmore)Human Representation of Closed Contours (K Waeytens et al)Affine Shape Equivalence (J Wagemans et al)and other papers Readership: Mathematicians and engineers. keywords:

Aspects of topology


Author: Charles O. Christenson,William L. Voxman

Publisher: Marcel Dekker Inc


Category: Mathematics

Page: 517

View: 2976

Nuclear groups and Lie groups


Author: E. Martin-Peinador,Juana Núñez García

Publisher: N.A

ISBN: 9783885382249

Category: Lie groups

Page: 249

View: 5867