Learn IT - Books tags topological

Topological Data Structures for Surfaces: An Introduction to Geographical Information Science

John Wiley & Sons, 2004

In Geography and GIS, surfaces can be analysed and visualised through various data structures, and topological data structures describe surfaces in the form of a relationship between certain surface-specific features. Drawn from many disciplines with a strong applied aspect, this is a research-led, interdisciplinary approach to the creation,...

Elementary Concepts of Topology

Dover Publications, 1961

Concise work presents topological concepts in clear, elementary fashion without sacrificing their profundity or exactness. Author proceeds from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups.

FEW BRANCHES of geometry have...

Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)

Cambridge University Press, 2005

Written by a computer scientist for computer scientists, this book teaches topology from a computational point of view, and shows how to solve real problems that have topological aspects involving computers. Such problems arise in many areas, such as computer graphics, robotics, structural biology, and chemistry. The author starts from the basics...

Algebraic Models in Geometry (Oxford Graduate Texts in Mathematics)

Oxford University Press, 2008

Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also...

Topological Methods in Data Analysis and Visualization II: Theory, Algorithms, and Applications (Mathematics and Visualization)

Springer, 2012

When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures—as...

The Topology of Chaos: Alice in Stretch and Squeezeland (German Edition)

John Wiley & Sons, 2012

The subject of this book is chaos as seen through the filter of topology. The origin of this book lies in the analysis of data generated by a dynamical system operating in a chaotic regime. Throughout this book we develop topological tools for analyzing chaotic data and then show how they are applied to experimental data sets. ...

Quantum Topology (Series on knots & everything)

World Scientific Publishing, 1993

Discusses topics in the field of quantum topology, including: knot theory, exotic spheres and global gravitational anomolies; construction of 4D topological quantum field theories; computing the arf invariants of links; and the Casson invariants for two-fold branched covers of links.

This book...

Group Theoretical Methods in Image Processing (Lecture Notes in Computer Science)

Springer, 1990

These Lecture Notes are based on a series of lectures I gave at the Linkoping University Department of Electrical Engineering in 1988. In these lectures 1 tried to give an overview of the theory of representation of compact groups and some applications in the fields of image science and pattern recognition.

The participants...

Locally Convex Spaces (Graduate Texts in Mathematics)

Springer, 2013

For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of...

Graphs on Surfaces: Dualities, Polynomials, and Knots (SpringerBriefs in Mathematics)

Springer, 2013

This monograph aims to provide an accessible and fairly comprehensive treatment of recent developments on generalised dualities for graphs on surfaces and their applications. Duality arises in many areas, particularly topological and algebraic graph theory, topology, and physics. The importance of duality derives not only from its inherent...

Formal Geometry and Bordism Operations (Cambridge Studies in Advanced Mathematics)

Cambridge University Press, 2019

This text organizes a range of results in chromatic homotopy theory, running a single thread through theorems in bordism and a detailed understanding of the moduli of formal groups. It emphasizes the naturally occurring algebro-geometric models that presage the topological results, taking the reader through a pedagogical development of the...

Introduction to Chemical Graph Theory (Discrete Mathematics and Its Applications)

CRC Press, 2018

Introduction to Chemical Graph Theory is a concise introduction to the main topics and techniques in chemical graph theory, specifically the theory of topological indices. These include distance-based, degree-based, and counting-based indices. The book covers some of the most commonly used mathematical...

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