A Topology of Mind

A Topology of Mind
Author: Robert K. Logan
Publisher: Springer Nature
Total Pages: 255
Release: 2022-05-06
Genre: Mathematics
ISBN: 3030964361

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

Elementary Topology

Elementary Topology
Author: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Publisher: American Mathematical Soc.
Total Pages: 432
Release:
Genre: Mathematics
ISBN: 9780821886250

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.

Introduction to Topology

Introduction to Topology
Author: Theodore W. Gamelin
Publisher: Courier Corporation
Total Pages: 258
Release: 2013-04-22
Genre: Mathematics
ISBN: 0486320189

This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

A First Course in Topology

A First Course in Topology
Author: Robert A Conover
Publisher: Courier Corporation
Total Pages: 276
Release: 2014-05-21
Genre: Mathematics
ISBN: 0486780015

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

Tough Topology Problems & Other Puzzles

Tough Topology Problems & Other Puzzles
Author: Ivan Moscovich
Publisher: Sterling Publishing Company, Inc.
Total Pages: 134
Release: 2006
Genre: Games & Activities
ISBN: 9781402727320

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.

Principles of Topology

Principles of Topology
Author: Fred H. Croom
Publisher: Courier Dover Publications
Total Pages: 340
Release: 2016-02-17
Genre: Mathematics
ISBN: 0486801543

Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.

Topology and Robotics

Topology and Robotics
Author: Michael Farber
Publisher: American Mathematical Soc.
Total Pages: 202
Release: 2007
Genre: Mathematics
ISBN: 0821842463

Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science. Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.

Fundamentals of Brain Network Analysis

Fundamentals of Brain Network Analysis
Author: Alex Fornito
Publisher: Academic Press
Total Pages: 496
Release: 2016-03-04
Genre: Medical
ISBN: 0124081185

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
Total Pages: 260
Release: 2013-04-09
Genre: Mathematics
ISBN: 1475717938

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.

Interdisciplinary Perspectives on Math Cognition

Interdisciplinary Perspectives on Math Cognition
Author: Marcel Danesi
Publisher: Springer Nature
Total Pages: 343
Release: 2019-09-14
Genre: Mathematics
ISBN: 3030225372

This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.