Author: Wilson A Sutherland
Publisher: Oxford University Press
Release Date: 2009-06-18
This fully updated new edition of Wilson Sutherland's classic text, Introduction to Metric and Topological Spaces, establishes the language of metric and topological spaces with continuity as the motivating concept, before developing its discussion to cover compactness, connectedness, and completeness.
This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.
Author: Chattrakul Sombattheera
Publisher: Springer Science & Business Media
Release Date: 2011-11-24
This volume constitutes the refereed proceedings of the 5th Multi-disciplinary International Workshop On Artificial Intelligence, MIWAI 2011, held in Hyderabad, India, in December 2011. The 38 revised full papers presented were carefully reviewed and selected from 71 submissions. The papers cover the multifarious nature of the Artificial Intelligence research domain, ranging from theoretical to real world applications and address topics such as agent-based simulation, agent-oriented software engineering, agents and Web services, agent-based electronic commerce, auctions and markets, AI in video games, computer vision, constraint satisfaction, data mining, decision theory, distributed AI, e-commerce and AI, game theory, internet/www intelligence, industrial applications of AI, intelligent tutoring, knowledge representation and reasoning, machine learning, multi-agent planning and learning, multi-agent systems and their applications, multi-agent systems and evolving intelligence, natural language processing, neural networks, planning and scheduling, robotics, uncertainty in AI, and Web services.
Author: Robert Lowen
Publisher: Oxford University Press
Release Date: 1997
In topology the three basic concepts of metrics, topologies and uniformities have been treated so far as separate entities by means of different methods and terminology. This is the first book to treat all three concepts as a special case of the concept of approach spaces. The book explains the richness of approach structures in great detail; it provides a comprehensive explanation of the categorical set-up, develops the basic theory and provides many examples,displaying links with various areas of mathematics such as approximation theory, probability theory, analysis and hyperspace theory.
Author: I. M. James
Publisher: Cambridge University Press
Release Date: 1990-05-03
This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, much of which is published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces. Readers interested in general topology will find much to interest them here.
Author: Donald G. Babbitt
Publisher: American Mathematical Soc.
Release Date: 2000-05-05
This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.
Author: Graham R. Allan
Publisher: Oxford University Press
Release Date: 2011
Genre: Banach algebras
A graduate level text in functional analysis, with an emphasis on Banach algebras. Based on lectures given for Part III of the Cambridge Mathematical Tripos, the text will assume a familiarity with elementary real and complex analysis, and some acquaintance with metric spaces, analytic topology and normed spaces (but not theorems depending on Baire category, or any version of the Hahn-Banach theorem).
Author: Joaquim M. Domingos
Publisher: World Scientific
Release Date: 2006
This is a brief introduction to some geometrical topics including topological spaces, the metric tensor, Euclidean space, manifolds, tensors, r- forms, the orientation of a manifold and the Hodge star operator. It provides the reader who is approaching the subject for the first time with a deeper understanding of the geometrical properties of vectors and covectors. The material prepares the reader for discussions on basic concepts such as the differential of a function as a covector, metric dual, inner product, wedge product and cross product. J M Domingos received his D Phil from the University of Oxford and has now retired from the post of Professor of Physics at the University of Coimbra, Portugal. Sample Chapter(s). Chapter 1: Topological Spaces (181 KB). Contents: Topological Spaces; Metric Tensor; Differentiable Manifolds: Basic Definitions, Tangent Vectors and Spaces, Parallelization; Metric Dual; Tensors; r- Forms; Orientation of a Manifold; Hodge Star Operator; Wedge Product and Cross Product. Readership: Advanced undergraduate students in physics and mathematics.
Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.