A Topology of Mind
A Topology of Mind

Author: Robert K. Logan

Publisher: Springer Nature

Published: 2022-05-06

Total Pages: 255

ISBN-13: 3030964361

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This volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication. It examines mathematics in mind from the perspective of the spiral, cyclic and hyperlinked structures of the human mind in terms of its language, its thoughts and its various modes of communication in science, philosophy, literature and the arts including a chapter devoted to the spiral structure of the thought of Marshall McLuhan. In it, the authors examine the topological structures of hypertext, hyperlinking, and hypermedia made possible by the Internet and the hyperlinked structures that existed before its emergence. It also explores the cognitive origins of mathematical thinking of the human mind and its relation to the emergence of spoken language, and studies the emergence of mathematical notation and its impact on education. Topics addressed include: • The historical context of any topic that involves how mathematical thinking emerged, focusing on archaeological and philological evidence. • Connection between math cognition and symbolism, annotation and other semiotic processes. • Interrelationships between mathematical discovery and cultural processes, including technological systems that guide the thrust of cognitive and social evolution. • Whether mathematics is an innate faculty or forged in cultural-historical context • What, if any, structures are shared between mathematics and language

Tough Topology Problems & Other Puzzles
Tough Topology Problems & Other Puzzles

Author: Ivan Moscovich

Publisher: Sterling Publishing Company, Inc.

Published: 2006

Total Pages: 134

ISBN-13: 9781402727320

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Colorful geometrical pentagors, composed of pentagons and triangles and dissected into pieces: Can you put the shapes together again to form a whole? A classic paradox about the nature of motion from a famous Greek mathematician: Can you see what’s wrong with it? Put on your thinking cap and prepare to give your math and logic abilities a workout, because these super-looking puzzles demand real brainpower. Solve a graphic problem that involves the calculation of a square root. Examine six linear processions of egg-carrying ants, and figure out which lines are “surprising” and which ones aren’t. Go step by step through a multihued grid and try to find 32 different configurations within. These puzzles are challenging, entertaining, and satisfying to unravel.

Elementary Topology
Elementary Topology

Author: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov

Publisher: American Mathematical Soc.

Published:

Total Pages: 432

ISBN-13: 9780821886250

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This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.

Team Topologies
Team Topologies

Author: Matthew Skelton

Publisher: IT Revolution

Published: 2019-09-17

Total Pages: 210

ISBN-13: 1942788827

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Effective software teams are essential for any organization to deliver value continuously and sustainably. But how do you build the best team organization for your specific goals, culture, and needs? Team Topologies is a practical, step-by-step, adaptive model for organizational design and team interaction based on four fundamental team types and three team interaction patterns. It is a model that treats teams as the fundamental means of delivery, where team structures and communication pathways are able to evolve with technological and organizational maturity. In Team Topologies, IT consultants Matthew Skelton and Manuel Pais share secrets of successful team patterns and interactions to help readers choose and evolve the right team patterns for their organization, making sure to keep the software healthy and optimize value streams. Team Topologies is a major step forward in organizational design for software, presenting a well-defined way for teams to interact and interrelate that helps make the resulting software architecture clearer and more sustainable, turning inter-team problems into valuable signals for the self-steering organization.

A First Course in Topology
A First Course in Topology

Author: Robert A Conover

Publisher: Courier Corporation

Published: 2014-05-21

Total Pages: 276

ISBN-13: 0486780015

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Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com

Topologies of the Flesh
Topologies of the Flesh

Author: Steven M. Rosen

Publisher: Ohio University Press

Published: 2006

Total Pages: 361

ISBN-13: 0821416766

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This is an unprecedented marriage of topology (a branch of mathematics dealing with the properties of geometric figures that stay the same when the figures are distorted) and phenomenology. Through his unique application of qualitative mathematics, Rosen offers a detailed exploration of previously uncharted dimensions of human experience and the natural world.

Algebraic Topology
Algebraic Topology

Author: Allen Hatcher

Publisher: Cambridge University Press

Published: 2002

Total Pages: 572

ISBN-13: 9780521795401

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An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.

Fundamentals of Brain Network Analysis
Fundamentals of Brain Network Analysis

Author: Alex Fornito

Publisher: Academic Press

Published: 2016-03-04

Total Pages: 496

ISBN-13: 0124081185

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Fundamentals of Brain Network Analysis is a comprehensive and accessible introduction to methods for unraveling the extraordinary complexity of neuronal connectivity. From the perspective of graph theory and network science, this book introduces, motivates and explains techniques for modeling brain networks as graphs of nodes connected by edges, and covers a diverse array of measures for quantifying their topological and spatial organization. It builds intuition for key concepts and methods by illustrating how they can be practically applied in diverse areas of neuroscience, ranging from the analysis of synaptic networks in the nematode worm to the characterization of large-scale human brain networks constructed with magnetic resonance imaging. This text is ideally suited to neuroscientists wanting to develop expertise in the rapidly developing field of neural connectomics, and to physical and computational scientists wanting to understand how these quantitative methods can be used to understand brain organization. - Winner of the 2017 PROSE Award in Biomedicine & Neuroscience and the 2017 British Medical Association (BMA) Award in Neurology - Extensively illustrated throughout by graphical representations of key mathematical concepts and their practical applications to analyses of nervous systems - Comprehensively covers graph theoretical analyses of structural and functional brain networks, from microscopic to macroscopic scales, using examples based on a wide variety of experimental methods in neuroscience - Designed to inform and empower scientists at all levels of experience, and from any specialist background, wanting to use modern methods of network science to understand the organization of the brain

Basic Topology
Basic Topology

Author: M.A. Armstrong

Publisher: Springer Science & Business Media

Published: 2013-04-09

Total Pages: 260

ISBN-13: 1475717938

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In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties help students gain a thorough understanding of the subject.

Differential Topology
Differential Topology

Author: Morris W. Hirsch

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 230

ISBN-13: 146849449X

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"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS