Some Modern Mathematics for Physicists and Other Outsiders

Some Modern Mathematics for Physicists and Other Outsiders

An Introduction to Algebra, Topology, and Functional Analysis

1st Edition - January 1, 1975

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  • Author: Paul Roman
  • eBook ISBN: 9781483187372

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Description

Some Modern Mathematics for Physicists and Other Outsiders: An Introduction to Algebra, Topology, and Functional Analysis, Volume 1 focuses on the operations, principles, methodologies, and approaches employed in algebra, topology, and functional analysis. The publication first offers information on sets, maps, and algebraic composition laws and systems. Discussions focus on morphisms of algebraic systems, sequences and families, cardinal numbers, ordered sets and maps, equivalence relations and maps, composite functions and inverses, operations with sets, and relations in sets. The text then ponders on special algebraic systems, topological spaces, and topological spaces with special properties. Topics include complete metric spaces, compact spaces, separable and connected spaces, homeomorphism and isometry, convergence, continuity, general structure of topological spaces, rings and fields, linear spaces, linear algebras, and nonassociative algebras. The book elaborates on the theory of integration and measure spaces, including measurable spaces, general properties of the integral, and measureable functions. The publication is a valuable reference for theoretical physicists, research engineers, and scientists who are concerned with structural problems.

Table of Contents


  • Contents of Volume

    Preface

    Organization of the Book

    Acknowledgments

    Introduction

    Part One: The Raw Materials of Mathematics

    Chapter 1 Sets

    1.1 Operations with Sets

    1.2 Relations in Sets

    Chapter 2 Maps

    2.1 Composite Functions and Inverses

    2.2 Equivalence Relations and Maps

    2.3 Ordered Sets and Maps

    2.4 Cardinal Numbers

    2.5 Sequences and Families

    Part Two: The Basic Structures of Mathematics

    IIA : Algebraic Structures

    Chapter 3 Algebraic Composition Laws and Systems

    3.1 Morphisms of Algebraic Systems

    Chapter 4 Survey of Special Algebraic Systems

    4.1 Groups

    4.2 Rings and Fields

    4.3 Linear Spaces

    4.4 Linear Algebras

    4.5 Nonassociative Algebras

    IIB : Topological Structures

    Chapter 5 Topological Spaces

    5.1 Examples; Metric Spaces

    5.2 General Structure of Topological Spaces

    5.3 Neighborhoods; Special Points; Closed Sets

    5.4 Convergence

    5.5 Continuity

    5.6 Homeomorphism and Isometry

    Chapter 6 Topological Spaces with Special Properties

    6.1 Connected Spaces

    6.2 Separable Spaces

    6.3 Compact Spaces

    6.4 Complete Metric Spaces

    IIC: Measure Structures

    Chapter 7 Measure Spaces

    7.1 Measurable Spaces

    7.2 Measure and Measure Spaces

    Chapter 8 Theory of Integration

    8.1 Measurable Functions

    8.2 Definition of the Integral

    8.3 General Properties of the Integral

    8.4 Comments on Lebesgue and Lebesgue-Stieltjes Integrals

    8.5 The Radon-Nikodym Theorem

    Appendices

    Appendix I Some Inequalities

    Appendix III Annotated Reading List

    Appendix IV Frequently Used Symbols

    Index

Product details

  • No. of pages: 426
  • Language: English
  • Copyright: © Pergamon 1975
  • Published: January 1, 1975
  • Imprint: Pergamon
  • eBook ISBN: 9781483187372

About the Author

Paul Roman

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