Synopsis
While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself.
By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been contentto "assume" the real numbers. Its prerequisites are calculus and basic mathematics.
Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de l?auteur
John Stillwell is a professor of mathematics at the University of San Francisco. He is also an accomplished author, having published several books with Springer, including Mathematics and Its History; The Four Pillars of Geometry; Elements of Algebra; Numbers and Geometry; and many more.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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The Real Numbers
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Springer International Publishing Aug 2016, 2016
ISBN 10 : 3319347268
ISBN 13 : 9783319347264
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory-uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself.By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis-the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to 'assume' the real numbers. Its prerequisites are calculus and basic mathematics.Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor-Schröder-Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions. 260 pp. Englisch. N° de réf. du vendeur 9783319347264
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The Real Numbers
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ISBN 10 : 3319347268
ISBN 13 : 9783319347264
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Fills a gap in the standard curriculum by linking analysis to set theoryContains background, history, examples, and explanatory remarksIncludes (almost) two courses for the price of one by providing a unified treatment of analysis and set t. N° de réf. du vendeur 385703750
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The Real Numbers: An Introduction to Set Theory and Analysis
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The Real Numbers
ISBN 10 : 3319347268
ISBN 13 : 9783319347264
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Taschenbuch. Etat : Neu. Neuware -While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory¿uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself.By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis¿the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been contentto 'assume' the real numbers. Its prerequisites are calculus and basic mathematics.Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor¿Schröder¿Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 260 pp. Englisch. N° de réf. du vendeur 9783319347264
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The Real Numbers : An Introduction to Set Theory and Analysis
Edité par
Springer International Publishing, 2016
ISBN 10 : 3319347268
ISBN 13 : 9783319347264
Neuf
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory-uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself.By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis-the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been contentto 'assume' the real numbers. Its prerequisites are calculus and basic mathematics.Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor-Schröder-Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions. N° de réf. du vendeur 9783319347264
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The Real Numbers: An Introduction to Set Theory and Analysis (Undergraduate Texts in Mathematics)
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The Real Numbers | An Introduction to Set Theory and Analysis
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Taschenbuch. Etat : Neu. The Real Numbers | An Introduction to Set Theory and Analysis | John Stillwell | Taschenbuch | xvi | Englisch | 2016 | Springer | EAN 9783319347264 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. N° de réf. du vendeur 103434331
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The Real Numbers: An Introduction to Set Theory and Analysis (Undergraduate Texts in Mathematics)
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Springer, 2016
ISBN 10 : 3319347268
ISBN 13 : 9783319347264
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