An Invitation To Computational Homotopy
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An Invitation To Computational Homotopy
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Author : Graham Ellis
language : en
Publisher: Oxford University Press
Release Date : 2019-08-14
An Invitation To Computational Homotopy written by Graham Ellis and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-14 with Mathematics categories.
An Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming. It expertly illustrates how the basics of the subject can be implemented on a computer through its focus on fully-worked examples designed to develop problem solving techniques. The transition from basic theory to practical computation raises a range of non-trivial algorithmic issues which will appeal to readers already familiar with basic theory and who are interested in developing computational aspects. The book covers a subset of standard introductory material on fundamental groups, covering spaces, homology, cohomology and classifying spaces as well as some less standard material on crossed modules. These topics are covered in a way that hints at potential applications of topology in areas of computer science and engineering outside the usual territory of pure mathematics, and also in a way that demonstrates how computers can be used to perform explicit calculations within the domain of pure algebraic topology itself. The initial chapters include in-depth examples from data mining, biology and digital image analysis, while the later chapters cover a range of computational examples on the cohomology of classifying spaces that are likely beyond the reach of a purely paper-and-pen approach to the subject. An Invitation to Computational Homotopy serves as a self-contained and informal introduction to these topics and their implementation in the sphere of computer science. Written in a dynamic and engaging style, it skilfully showcases a range of useful machine computations, and will serve as an invaluable aid to graduate students working with algebraic topology.
An Invitation To Computational Homotopy
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Author : Graham Ellis
language : en
Publisher:
Release Date : 2019
An Invitation To Computational Homotopy written by Graham Ellis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Homotopy theory categories.
'An Invitation to Computational Homotopy' is an introduction to elementary algebraic topology for those with an interest in computers and computer programming. It expertly illustrates how the basics of the subject can be implemented on a computer through its focus on fully-worked examples designed to develop problem solving techniques.
Computational Chemistry
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Author : Jerzy Leszczynski
language : en
Publisher: World Scientific
Release Date : 2000
Computational Chemistry written by Jerzy Leszczynski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.
This volume comprises six chapters which explore the development and applications of the methods of computational chemistry. The first chapter is on new developments in coupled-cluster (CC) theory. The homotopy method is used to obtain complete sets of solutions of nonlinear CC equations. The correspondence between multiple solutions to the CCSD, CCSDT, and full CI equations is established, and the applications of the new approach in modeling molecular systems are discussed. The second chapter reviews the computational theory for the time-dependent calculations of a solution to the Schrodinger equation for two electrons and focuses on the development of propagators to the solution. The next chapter features a discussion on a new self-consistent field for molecular interactions (SCF-MI) scheme for modifying Roothaan equations in order to avoid basis set superposition errors (BSSE). This method is especially suitable for computations of intermolecular interactions. Details of the theory, alongwith examples of applications to nucleic acid base pair complexes, are given. This chapter is well complemented by the following chapter, which reports the current status of computational studies of aromatic stacking and hydrogen bonding interactions among nucleic acid bases. The next chapter reveals the possibility of calculating the kinetics of chemical reactions in biological systems from the first principles. The last chapter reviews the results of rigorous ab initio studies of the series of derivatives of methane, silane, and germane. The presented molecular and vibrational parameters complement experimental data for these systems. In addition, the theoretical approach allows the predictionof the effects of halogeno-substitutions on their structures and properties.
Combinatorial Algebraic Topology
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Author : Dimitry Kozlov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-24
Combinatorial Algebraic Topology written by Dimitry Kozlov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-24 with Mathematics categories.
This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.
A Course In Computational Algebraic Number Theory
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Author : Henri Cohen
language : en
Publisher: Copernicus
Release Date : 1993
A Course In Computational Algebraic Number Theory written by Henri Cohen and has been published by Copernicus this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Describes 148 algorithms that are fundamental for number-theoretic computations including computations related to algebraic number theory, elliptic curves, primality testing, and factoring. A complete theoretical introduction is given for each subject, reducing prerequisites to a minimum. The detailed description of each algorithm allows immediate.
Polynomial Optimization Moments And Applications
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Author : Michal Kočvara
language : en
Publisher: Springer Nature
Release Date : 2023-12-27
Polynomial Optimization Moments And Applications written by Michal Kočvara and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-27 with Mathematics categories.
Polynomial optimization is a fascinating field of study that has revolutionized the way we approach nonlinear problems described by polynomial constraints. The applications of this field range from production planning processes to transportation, energy consumption, and resource control. This introductory book explores the latest research developments in polynomial optimization, presenting the results of cutting-edge interdisciplinary work conducted by the European network POEMA. For the past four years, experts from various fields, including algebraists, geometers, computer scientists, and industrial actors, have collaborated in this network to create new methods that go beyond traditional paradigms of mathematical optimization. By exploiting new advances in algebra and convex geometry, these innovative approaches have resulted in significant scientific and technological advancements. This book aims to make these exciting developments accessible to a wider audienceby gathering high-quality chapters on these hot topics. Aimed at both aspiring and established researchers, as well as industry professionals, this book will be an invaluable resource for anyone interested in polynomial optimization and its potential for real-world applications.
Topology
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Author : Richard Earl
language : en
Publisher: Oxford University Press, USA
Release Date : 2020-01-11
Topology written by Richard Earl and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-11 with MATHEMATICS categories.
How is a subway map different from other maps? What makes a knot knotted? What makes the M�bius strip one-sided? These are questions of topology, the mathematical study of properties preserved by twisting or stretching objects. In the 20th century topology became as broad and fundamental as algebra and geometry, with important implications for science, especially physics. In this Very Short Introduction Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Everyday Cryptography
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Author : Keith M. Martin
language : en
Publisher: OUP Oxford
Release Date : 2012-02-29
Everyday Cryptography written by Keith M. Martin and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-29 with Mathematics categories.
Cryptography is a vital technology that underpins the security of information in computer networks. This book presents a comprehensive introduction to the role that cryptography plays in providing information security for technologies such as the Internet, mobile phones, payment cards, and wireless local area networks. Focusing on the fundamental principles that ground modern cryptography as they arise in modern applications, it avoids both an over-reliance on transient current technologies and over-whelming theoretical research. Everyday Cryptography is a self-contained and widely accessible introductory text. Almost no prior knowledge of mathematics is required since the book deliberately avoids the details of the mathematical techniques underpinning cryptographic mechanisms, though a short appendix is included for those looking for a deeper appreciation of some of the concepts involved. By the end of this book, the reader will not only be able to understand the practical issues concerned with the deployment of cryptographic mechanisms, including the management of cryptographic keys, but will also be able to interpret future developments in this fascinating and increasingly important area of technology.
An Invitation To Applied Category Theory
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Author : Brendan Fong
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-18
An Invitation To Applied Category Theory written by Brendan Fong and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with Computers categories.
Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.
Lectures On Geometry
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Author : Nicholas Michael John Woodhouse
language : en
Publisher: Oxford University Press
Release Date : 2017
Lectures On Geometry written by Nicholas Michael John Woodhouse and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
This book contains a series of chapters by leading researchers and practitioners on community engagement approaches in the field of counterterrorism and counterinsurgency. It presents existing and emerging community engagement models in various parts of the world which could serve as effective models for governments keen to work with community leaders to manage and reduce the terrorist threat. The book emphasizes the strength of communities as central to government approaches in countering violent extremism.