Author: Jonathan A. Barmak Publisher: Springer Science & Business Media ISBN: 3642220029 Category : Mathematics Languages : en Pages : 184
Book Description
This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
Author: Colin Conrad Adams Publisher: Pearson ISBN: Category : Mathematics Languages : en Pages : 520
Book Description
Learn the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics. Introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Is written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields. Introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics. Covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness. A useful reference for readers wanting an intuitive introduction to topology.
Author: R. N. Mohapatra Publisher: Springer Nature ISBN: 9813346469 Category : Mathematics Languages : en Pages : 661
Book Description
This book is a collection of selected papers presented at the International Conference on Mathematical Analysis and Computing (ICMAC 2019) held at Sri Sivasubramaniya Nadar College of Engineering, Chennai, India, from 23–24 December 2019. Having found its applications in game theory, economics, and operations research, mathematical analysis plays an important role in analyzing models of physical systems and provides a sound logical base for problems stated in a qualitative manner. This book aims at disseminating recent advances in areas of mathematical analysis, soft computing, approximation and optimization through original research articles and expository survey papers. This book will be of value to research scholars, professors, and industrialists working in these areas.
Author: Wilson A Sutherland Publisher: Oxford University Press ISBN: 0191568309 Category : Mathematics Languages : en Pages : 219
Book Description
One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.
Author: William J. Pervin Publisher: Academic Press ISBN: 1483225151 Category : Mathematics Languages : en Pages : 222
Book Description
Foundations of General Topology presents the value of careful presentations of proofs and shows the power of abstraction. This book provides a careful treatment of general topology. Organized into 11 chapters, this book begins with an overview of the important notions about cardinal and ordinal numbers. This text then presents the fundamentals of general topology in logical order processing from the most general case of a topological space to the restrictive case of a complete metric space. Other chapters consider a general method for completing a metric space that is applicable to the rationals and present the sufficient conditions for metrizability. This book discusses as well the study of spaces of real-valued continuous functions. The final chapter deals with uniform continuity of functions, which involves finding a distance that satisfies certain requirements for all points of the space simultaneously. This book is a valuable resource for students and research workers.
Author: Alan J. Lockett Publisher: Springer Nature ISBN: 3662620073 Category : Computers Languages : en Pages : 561
Book Description
This book examines the mismatch between discrete programs, which lie at the center of modern applied mathematics, and the continuous space phenomena they simulate. The author considers whether we can imagine continuous spaces of programs, and asks what the structure of such spaces would be and how they would be constituted. He proposes a functional analysis of program spaces focused through the lens of iterative optimization. The author begins with the observation that optimization methods such as Genetic Algorithms, Evolution Strategies, and Particle Swarm Optimization can be analyzed as Estimation of Distributions Algorithms (EDAs) in that they can be formulated as conditional probability distributions. The probabilities themselves are mathematical objects that can be compared and operated on, and thus many methods in Evolutionary Computation can be placed in a shared vector space and analyzed using techniques of functional analysis. The core ideas of this book expand from that concept, eventually incorporating all iterative stochastic search methods, including gradient-based methods. Inspired by work on Randomized Search Heuristics, the author covers all iterative optimization methods and not just evolutionary methods. The No Free Lunch Theorem is viewed as a useful introduction to the broader field of analysis that comes from developing a shared mathematical space for optimization algorithms. The author brings in intuitions from several branches of mathematics such as topology, probability theory, and stochastic processes and provides substantial background material to make the work as self-contained as possible. The book will be valuable for researchers in the areas of global optimization, machine learning, evolutionary theory, and control theory.
Author: J. P. May Publisher: University of Chicago Press ISBN: 9780226511832 Category : Mathematics Languages : en Pages : 262
Book Description
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.
Author: K. Kunen Publisher: Elsevier ISBN: 148329515X Category : Mathematics Languages : en Pages : 1282
Book Description
This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.
Author: Jonathan A. Barmak
Author: Colin Conrad Adams
Author: W. B. Vasantha Kandasamy, Florentin Smarandache
Author: R. N. Mohapatra
Author: Wilson A Sutherland
Author: William J. Pervin
Author: Alan J. Lockett
Author: J. P. May
Author: K. Kunen
Author: Vladimir A. Kovalevsky