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Understanding Topology : A Practical Introduction

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Title: Understanding Topology : A Practical Introduction
Description: Topology—the branch of mathematics that studies the properties of spaces that remain unaffected by stretching and other distortions—can present significant challenges for undergraduate students of mathematics and the sciences. Understanding Topology aims to change that.The perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from mapping DNA to determining the shape of the universe, will engage students in a way traditional topology textbooks do not.This groundbreaking new text:• presents Euclidean, abstract, and basic algebraic topology• explains metric topology, vector spaces and dynamics, point-set topology, surfaces, knot theory, graphs and map coloring, the fundamental group, and homology• includes worked example problems, solutions, and optional advanced sections for independent projectsFollowing a path that will work with any standard syllabus, the book is arranged to help students reach that'Aha!'moment, encouraging readers to use their intuition through local-to-global analysis and emphasizing topological invariants to lay the groundwork for algebraic topology.
Authors: Shaun V. Ault
Resource Type: eBook.
Subjects: Topology
Categories: MATHEMATICS / Topology, MATHEMATICS / Algebra / Abstract, MATHEMATICS / Geometry / General, MATHEMATICS / Mathematical Analysis
Database: eBook Collection (EBSCOhost)
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 1619067
RelevancyScore: 1084
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
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  Data: Topology—the branch of mathematics that studies the properties of spaces that remain unaffected by stretching and other distortions—can present significant challenges for undergraduate students of mathematics and the sciences. Understanding Topology aims to change that.The perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from mapping DNA to determining the shape of the universe, will engage students in a way traditional topology textbooks do not.This groundbreaking new text:• presents Euclidean, abstract, and basic algebraic topology• explains metric topology, vector spaces and dynamics, point-set topology, surfaces, knot theory, graphs and map coloring, the fundamental group, and homology• includes worked example problems, solutions, and optional advanced sections for independent projectsFollowing a path that will work with any standard syllabus, the book is arranged to help students reach that'Aha!'moment, encouraging readers to use their intuition through local-to-global analysis and emphasizing topological invariants to lay the groundwork for algebraic topology.
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      – Code: 514
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Topology
        Type: general
    Titles:
      – TitleFull: Understanding Topology : A Practical Introduction
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            NameFull: Shaun V. Ault
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            – D: 01
              M: 01
              Type: published
              Y: 2018
            – D: 18
              M: 03
              Type: profile
              Y: 2026
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              Value: 9781421424071
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              Value: 9781421424088
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