Elements of Abstract Analysis: Springer Undergraduate Mathematics Series
Autor Mícheál O'Searcoiden Limba Engleză Paperback – 9 noi 2001
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Specificații
ISBN-13: 9781852334246
ISBN-10: 185233424X
Pagini: 316
Ilustrații: XII, 300 p. 3 illus.
Dimensiuni: 178 x 235 x 17 mm
Greutate: 0.5 kg
Ediția:2002
Editura: SPRINGER LONDON
Colecția Springer
Seria Springer Undergraduate Mathematics Series
Locul publicării:London, United Kingdom
ISBN-10: 185233424X
Pagini: 316
Ilustrații: XII, 300 p. 3 illus.
Dimensiuni: 178 x 235 x 17 mm
Greutate: 0.5 kg
Ediția:2002
Editura: SPRINGER LONDON
Colecția Springer
Seria Springer Undergraduate Mathematics Series
Locul publicării:London, United Kingdom
Public țintă
Lower undergraduateCuprins
1. Sets.- 1.1 Set Theory.- 1.2 Relations and Functions.- 1.3 Ordered Sets.- 1.4 Ordinals.- 1.5 The Axiom of Choice.- 2. Counting.- 2.1 Counting Numbers.- 2.2 Cardinality.- 2.3 Enumeration.- 2.4 Cardinality of Unions and Products.- 3. Algebraic Structure.- 3.1 Elementary Algebraic Structures.- 3.2 Vector Spaces.- 3.3 Algebras.- 3.4 Preservation of Algebraic Structure.- 4. Analytic Structure.- 4.1 Ordered Algebraic Structure.- 4.2 Number Systems.- 4.3 Real and Complex Functions.- 4.4 Inequalities.- 5. Linear Structure.- 5.1 Linear Spaces and Algebras.- 5.2 Linear Shapes.- 5.3 Linear Functionals.- 6. Geometric Structure.- 6.1 Semimetrics and Metrics.- 6.2 Seminorms and Norms.- 6.3 Sesquilinear Forms and Inner Products.- 7. Topological Structure.- 7.1 Topologies.- 7.2 Neighbourhoods.- 7.3 Cardinality and Topology.- 7.4 Separation.- 8. Continuity and Openness.- 8.1 Preservation of Topological Structure.- 8.2 Topologies Denned by Functions.- 8.3 Derived Topological Spaces.- 8.4 Topologies on Linear Spaces.- 9. Connectedness.- 9.1 Connected Spaces.- 9.2 Pathwise Connectedness.- 10. Convergence.- 10.1 Filters.- 10.2 Limits.- 11. Compactness.- 11.1 Compact Topological Spaces.- 11.2 Compact Hausdorff Spaces.- 11.3 Local Compactness.- 12. Completeness.- 12.1 Complete Metric Spaces.- 12.2 Banach Spaces.- 12.3 Hilbert Spaces.- 12.4 Banach Algebras.- Solutions.
Recenzii
From the reviews of the first edition:
BULLETIN OF MATHEMATICS BOOKS
"…an interesting mix of algebra, topology and functional analysis, with chapter titles like Algebraic Structure, Linear Structure, Geometric Structure and Topological Structure."
"Michael O’Searcoid’s book ‘Element of Abstract Analysis’ is a book that deals with the fundamental principles of mathematics in a broad framework of set-theoretic approach. The book is written with a deep insight. … The contents are conceptually useful to students. … The book is a nice readable treat for every student of mathematics and is highly recommended for one semester course at M.Sc. level." (Madhu Tiwari, Journal of the Indian Academy of Mathematics, Vol. 25 (1), 2003)
"This book covers the elements of abstract analysis, treated mostly within the context of topological spaces. … This is a carefully written book, starting from set-theoretic axioms, and containing about 180 problems and exercises with hints and solutions. It is an ideal source of information for independent student study. There is a comprehensive index." (European Mathematical Society Newsletter, September, 2002)
"The book presents some concepts of analysis and the mathematical structures which enfold them. … the reviewer recommends the book to everyone interested in analysis, especially those scholars interested in studying more advanced areas like Functional Analysis, or Operator Theory." (Catalin Badea, Zentralblatt MATH, Vol. 999 (24), 2002)
"The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed … . It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. This book is a rigorous, self-contained introduction to functional analysis that will also serve as a text onabstract mathematics." (L’Enseignement Mathematique, Vol. 48 (1-2), 2002)
"This is a book about a few elementary concepts of analysis and the mathematical structures which enfold them. … The book is written specifically for final-year and undergraduate students who should already be familiar with most of the mathematical structures discussed … and with many of the principal analytical concepts … . It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics." (Zentralblatt für Didaktik der Mathematik, February, 2002)
BULLETIN OF MATHEMATICS BOOKS
"…an interesting mix of algebra, topology and functional analysis, with chapter titles like Algebraic Structure, Linear Structure, Geometric Structure and Topological Structure."
"Michael O’Searcoid’s book ‘Element of Abstract Analysis’ is a book that deals with the fundamental principles of mathematics in a broad framework of set-theoretic approach. The book is written with a deep insight. … The contents are conceptually useful to students. … The book is a nice readable treat for every student of mathematics and is highly recommended for one semester course at M.Sc. level." (Madhu Tiwari, Journal of the Indian Academy of Mathematics, Vol. 25 (1), 2003)
"This book covers the elements of abstract analysis, treated mostly within the context of topological spaces. … This is a carefully written book, starting from set-theoretic axioms, and containing about 180 problems and exercises with hints and solutions. It is an ideal source of information for independent student study. There is a comprehensive index." (European Mathematical Society Newsletter, September, 2002)
"The book presents some concepts of analysis and the mathematical structures which enfold them. … the reviewer recommends the book to everyone interested in analysis, especially those scholars interested in studying more advanced areas like Functional Analysis, or Operator Theory." (Catalin Badea, Zentralblatt MATH, Vol. 999 (24), 2002)
"The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed … . It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics. This book is a rigorous, self-contained introduction to functional analysis that will also serve as a text onabstract mathematics." (L’Enseignement Mathematique, Vol. 48 (1-2), 2002)
"This is a book about a few elementary concepts of analysis and the mathematical structures which enfold them. … The book is written specifically for final-year and undergraduate students who should already be familiar with most of the mathematical structures discussed … and with many of the principal analytical concepts … . It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics." (Zentralblatt für Didaktik der Mathematik, February, 2002)
Caracteristici
Provides a thorough treatment of the elements of modern analysis including a systematic treatment of the set theory which analysts need to know Aimed specifically at final year undergraduates, it reviews and consolidates the mathematics learned in previous years Also serves as a book on abstract mathematics