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Elements of Abstract Analysis 🔍
Mícheál Ó Searcóid (auth.) Springer London : Imprint: Springer, Springer Undergraduate Mathematics Series, Springer Undergraduate Mathematics Series, 1, 2002
英语 [en] · PDF · 10.1MB · 2002 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/zlib · Save
描述
In nature's infinite book ofsecrecy A little I can read. Antony and Cleopatra, l. ii. This is a book about a few elementary concepts of analysis and the mathe matical structures which enfold them. It is more concerned with the interplay amongst these concepts than with their many applications. The book is self-contained; in the first chapter, after acknowledging the fundamental role ofmathematical logic, wepresent seven axioms of Set Theory; everything else is developed from these axioms. It would therefore be true, if misleading, to say that the reader requires no prior knowledge of mathematics. In reality, the reader we have in mind has that level of sophistication achieved in about three years of undergraduate study of mathematics and is already well acquainted with most of the structures discussed-rings, linear spaces, metric spaces, and soon-and with many ofthe principal analytical concepts convergence, connectedness, continuity,compactness and completeness. Indeed, it is only after gaining familiarity with these concepts and their applications that it is possible to appreciate their place within a broad framework of set based mathematics and to consolidate an understanding of them in such a framework. To aid in these pursuits, wepresent our reader with things familiar and things new side by side in most parts of the book-and we sometimes adopt an unusual perspective. That this is not an analysis textbook is clear from its many omissions.
Erscheinungsdatum: 09.11.2001
备用文件名
lgrsnf/A:/compressed/10.1007%2F978-1-4471-0179-6.pdf
备用文件名
nexusstc/Elements of Abstract Analysis/20a1e03cccbb17fcb8acb7872f30aba0.pdf
备用文件名
scihub/10.1007/978-1-4471-0179-6.pdf
备用文件名
zlib/Mathematics/Mícheál Ó Searcóid/Elements of Abstract Analysis_2129732.pdf
备选作者
Mícheál Ó Searcóid; SpringerLink (Online service)
备选作者
Mícheál O'Searcoid
备选作者
Micheal O'Searcoid
备用出版商
Springer London, Limited
备用出版商
Springer Nature
备用版本
Springer undergraduate mathematics series, London, New York, England, 2002
备用版本
Springer undergraduate mathematics series, 1st ed. 2002, London, 2002
备用版本
Springer Nature (Textbooks & Major Reference Works), London, 2012
备用版本
Springer undergraduate mathematics series, London, c 2001
备用版本
United Kingdom and Ireland, United Kingdom
备用版本
1 edition, December 6, 2001
备用版本
2002, PS, 2001
备用版本
6, 20121206
元数据中的注释
0
元数据中的注释
lg975810
元数据中的注释
{"container_title":"Springer Undergraduate Mathematics Series","edition":"1","isbns":["1447101790","185233424X","9781447101796","9781852334246"],"issns":["1615-2085"],"last_page":312,"publisher":"Springer London","series":"Springer Undergraduate Mathematics Series"}
元数据中的注释
Includes bibliographical references (p. 285) and index
备用描述
In nature's infinite book ofsecrecy A little I can read. Antony and Cleopatra, l. ii. This is a book about a few elementary concepts of analysis and the mathe matical structures which enfold them. It is more concerned with the interplay amongst these concepts than with their many applications. The book is self-contained; in the first chapter, after acknowledging the fundamental role ofmathematical logic, wepresent seven axioms of Set Theory; everything else is developed from these axioms. It would therefore be true, if misleading, to say that the reader requires no prior knowledge of mathematics. In reality, the reader we have in mind has that level of sophistication achieved in about three years of undergraduate study of mathematics and is already well acquainted with most of the structures discussed-rings, linear spaces, metric spaces, and soon-and with many ofthe principal analytical concepts convergence, connectedness, continuity, compactness and completeness. Indeed, it is only after gaining familiarity with these concepts and their applications that it is possible to appreciate their place within a broad framework of set based mathematics and to consolidate an understanding of them in such a framework. To aid in these pursuits, wepresent our reader with things familiar and things new side by side in most parts of the book-and we sometimes adopt an unusual perspective. That this is not an analysis textbook is clear from its many omissions."
备用描述
<p><P>While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis.<br>The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed - for example, rings, linear spaces, and metric spaces - and with many of the principal analytical concepts - convergence, connectedness, continuity, compactness and completeness. 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.<br>Carefully crafted, clearly written and precise, and with numerous exercises and examples, Elements of Abstract Analysis is a rigorous, self-contained introduction to functional analysis that will also serve as a text on abstract mathematics.</p>
备用描述
While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis. The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed - for example, rings, linear spaces, and metric spaces - and with many of the principal analytical concepts - convergence, connectedness, continuity, compactness and completeness. 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. Carefully crafted, clearly written and precise, and with numerous exercises and examples, Elements of Abstract Analysis is a rigorous, self-contained introduction to functional analysis that will also serve as a text on abstract mathematics.
备用描述
Front Matter....Pages i-xii
Sets....Pages 1-40
Counting....Pages 41-56
Algebraic Structure....Pages 57-90
Analytic Structure....Pages 91-114
Linear Structure....Pages 115-132
Geometric Structure....Pages 133-158
Topological Structure....Pages 159-176
Continuity and Openness....Pages 177-206
Connectedness....Pages 207-214
Convergence....Pages 215-230
Compactness....Pages 231-244
Completeness....Pages 245-268
Back Matter....Pages 269-300
备用描述
Set Theory might attempt to formalize the intuitive idea that a set is a class of objects which are its members.
开源日期
2013-08-01
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