The Resource Elementary pointset topology : a transition to advanced mathematics, André L. Yandl, Seattle University; Adam Bowers, University of California San Diego
Elementary pointset topology : a transition to advanced mathematics, André L. Yandl, Seattle University; Adam Bowers, University of California San Diego
Resource Information
The item Elementary pointset topology : a transition to advanced mathematics, André L. Yandl, Seattle University; Adam Bowers, University of California San Diego represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Public Libraries of Suffolk County, New York.This item is available to borrow from 1 library branch.
Resource Information
The item Elementary pointset topology : a transition to advanced mathematics, André L. Yandl, Seattle University; Adam Bowers, University of California San Diego represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Public Libraries of Suffolk County, New York.
This item is available to borrow from 1 library branch.
 Summary
 In addition to serving as an introduction to the basics of pointset topology, this text bridges the gap between the elementary calculus sequence and higherlevel mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations
 Language
 eng
 Extent
 254 pages
 Contents

 1 Mathematical Proofs and Sets  1.1 Introduction to Elementary Logic  1.2 More Elementary Logic  1.3 Quantifiers  1.4 Methods of Mathematical Proof  1.5 Introduction to Elementary Set Theory  1.6 Cardinality  1.7 Cardinal Arithmetic  2 Topological Spaces  2.1 Introduction  2.2 Topologies  2.3 Bases  2.4 Subspaces  2.5 Interior, Closure, and Boundary  2.6 Hausdorff spaces  2.7 Metric Spaces  2.8 Euclidean Spaces  3 Continuous Functions
 3.1 Review of the Function Concept  3.2 More on Image and Inverse Image  3.3 Continuous Functions  3.4 More on Continuous Functions  3.5 More on Homeomorphism  4 Product Spaces  4.1 Products of Sets  4.2 Product Spaces  4.3 More on Product Spaces  5 Connectedness  5.1 Introduction to Connectedness  5.2 Products of Connected Spaces  5.3 Connected Subsets of the Real Line  6 Compactness  6.1 Introduction to Compactness  6.2 Compactness in the Space of Real Numbers  6.3 The Product of Compact Spaces  6.4 Compactness in Metric Spaces
 6.5 More on Compactness in Metric Spaces  6.6 The Cantor Set  7 Fixed Point Theorems and Applications  7.1 Sperner's Lemma  7.2 Brouwer's Fixed Point Theorem  7.3 The Fundamental Theorem of Algebra  7.4 Function Spaces  7.5 Contractions
 Isbn
 9780486803494
 Label
 Elementary pointset topology : a transition to advanced mathematics
 Title
 Elementary pointset topology
 Title remainder
 a transition to advanced mathematics
 Statement of responsibility
 André L. Yandl, Seattle University; Adam Bowers, University of California San Diego
 Language
 eng
 Summary
 In addition to serving as an introduction to the basics of pointset topology, this text bridges the gap between the elementary calculus sequence and higherlevel mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations
 Cataloging source
 np
 http://library.link/vocab/creatorName
 Yandl, André L
 Dewey number
 514/.322
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA603
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Bowers, Adam
 Series statement

 Aurora Dover modern math originals
 Dover Books on mathematics
 http://library.link/vocab/subjectName

 Point set theory
 Propositional calculus
 Topology
 Calculus
 Label
 Elementary pointset topology : a transition to advanced mathematics, André L. Yandl, Seattle University; Adam Bowers, University of California San Diego
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 1 Mathematical Proofs and Sets  1.1 Introduction to Elementary Logic  1.2 More Elementary Logic  1.3 Quantifiers  1.4 Methods of Mathematical Proof  1.5 Introduction to Elementary Set Theory  1.6 Cardinality  1.7 Cardinal Arithmetic  2 Topological Spaces  2.1 Introduction  2.2 Topologies  2.3 Bases  2.4 Subspaces  2.5 Interior, Closure, and Boundary  2.6 Hausdorff spaces  2.7 Metric Spaces  2.8 Euclidean Spaces  3 Continuous Functions
 3.1 Review of the Function Concept  3.2 More on Image and Inverse Image  3.3 Continuous Functions  3.4 More on Continuous Functions  3.5 More on Homeomorphism  4 Product Spaces  4.1 Products of Sets  4.2 Product Spaces  4.3 More on Product Spaces  5 Connectedness  5.1 Introduction to Connectedness  5.2 Products of Connected Spaces  5.3 Connected Subsets of the Real Line  6 Compactness  6.1 Introduction to Compactness  6.2 Compactness in the Space of Real Numbers  6.3 The Product of Compact Spaces  6.4 Compactness in Metric Spaces
 6.5 More on Compactness in Metric Spaces  6.6 The Cantor Set  7 Fixed Point Theorems and Applications  7.1 Sperner's Lemma  7.2 Brouwer's Fixed Point Theorem  7.3 The Fundamental Theorem of Algebra  7.4 Function Spaces  7.5 Contractions
 Dimensions
 23 cm.
 Extent
 254 pages
 Isbn
 9780486803494
 Lccn
 2015050597
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 Label
 Elementary pointset topology : a transition to advanced mathematics, André L. Yandl, Seattle University; Adam Bowers, University of California San Diego
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 1 Mathematical Proofs and Sets  1.1 Introduction to Elementary Logic  1.2 More Elementary Logic  1.3 Quantifiers  1.4 Methods of Mathematical Proof  1.5 Introduction to Elementary Set Theory  1.6 Cardinality  1.7 Cardinal Arithmetic  2 Topological Spaces  2.1 Introduction  2.2 Topologies  2.3 Bases  2.4 Subspaces  2.5 Interior, Closure, and Boundary  2.6 Hausdorff spaces  2.7 Metric Spaces  2.8 Euclidean Spaces  3 Continuous Functions
 3.1 Review of the Function Concept  3.2 More on Image and Inverse Image  3.3 Continuous Functions  3.4 More on Continuous Functions  3.5 More on Homeomorphism  4 Product Spaces  4.1 Products of Sets  4.2 Product Spaces  4.3 More on Product Spaces  5 Connectedness  5.1 Introduction to Connectedness  5.2 Products of Connected Spaces  5.3 Connected Subsets of the Real Line  6 Compactness  6.1 Introduction to Compactness  6.2 Compactness in the Space of Real Numbers  6.3 The Product of Compact Spaces  6.4 Compactness in Metric Spaces
 6.5 More on Compactness in Metric Spaces  6.6 The Cantor Set  7 Fixed Point Theorems and Applications  7.1 Sperner's Lemma  7.2 Brouwer's Fixed Point Theorem  7.3 The Fundamental Theorem of Algebra  7.4 Function Spaces  7.5 Contractions
 Dimensions
 23 cm.
 Extent
 254 pages
 Isbn
 9780486803494
 Lccn
 2015050597
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
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