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An introduction to naive set theory and its applications/ Shashi Mohan Srivastava

By: Material type: TextTextSeries: University Texts in the Mathematical SciencesPublication details: Singapore: Springer, 2024Description: xii, 136 pages; 24 cmISBN:
  • 9789819746422
Subject(s): DDC classification:
  • 23rd 511.322 Sr774
Contents:
Introduction -- Functions and Relations -- More on Cardinals and Ordinals -- Applications in Other Branches of Mathematics -- Banach-Tarski Paradox -- Preliminary Concepts and Terminologies from Logic -- Zermelo–Fraenkel Set Theory
Summary: Primarily designed for graduate students of mathematics, this textbook delves into Nave set theory, offering valuable insights for senior undergraduate students and researchers specializing in set theory. Commencing with a comprehensive exploration of functions and relations, the book extends its coverage to various applications of Nave set theory across multiple mathematical branches, including real analysis, linear and abstract algebra, general topology, and introductory aspects of complex analysis and measure theory. The text meticulously introduces cardinal and ordinal numbers, along with transfinite induction, following the natural progression discovered by Cantor during his examination of trigonometric series. While this book provides a solid foundation, students intrigued by set theory for its intrinsic value should recognize that the subject extends far beyond the scope of this text.
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Holdings
Item type Current library Call number Status Notes Date due Barcode Item holds
Books ISI Library, Kolkata 511.322 Sr774 (Browse shelf(Opens below)) Available Gifted by Prof. Shashi Mohan Srivastava C27751
Total holds: 0

Includes bibliography and index

Introduction -- Functions and Relations -- More on Cardinals and Ordinals -- Applications in Other Branches of Mathematics -- Banach-Tarski Paradox -- Preliminary Concepts and Terminologies from Logic -- Zermelo–Fraenkel Set Theory

Primarily designed for graduate students of mathematics, this textbook delves into Nave set theory, offering valuable insights for senior undergraduate students and researchers specializing in set theory. Commencing with a comprehensive exploration of functions and relations, the book extends its coverage to various applications of Nave set theory across multiple mathematical branches, including real analysis, linear and abstract algebra, general topology, and introductory aspects of complex analysis and measure theory. The text meticulously introduces cardinal and ordinal numbers, along with transfinite induction, following the natural progression discovered by Cantor during his examination of trigonometric series. While this book provides a solid foundation, students intrigued by set theory for its intrinsic value should recognize that the subject extends far beyond the scope of this text.

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