Thalia.de

The Real Numbers

An Introduction to Set Theory and Analysis

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.
Rezension
From the book reviews:
"This book is an interesting introduction to set theory and real analysis embedded in properties of the real numbers. ... The 300-plus problems are frequently challenging and will interest both upper-level undergraduate students and readers with a strong mathematical background. ... A list of approximately 100 references at the end of the book will help students to further explore the topic. ... Summing Up: Recommended. Lower-division undergraduates." (D. P. Turner, Choice, Vol. 51 (11), August, 2014)
"This is an informal look at the nature of the real numbers ... . There are extensive historical notes about the evolution of real analysis and our understanding of real numbers. ... Stillwell has deliberately set out to provide a different sort of construction where you understand what the foundation is supporting and why it is important. I think this is very successful, and his book ... is much more informative and enjoyable." (Allen Stenger, MAA Reviews, February, 2014)
"This book will be fully appreciated by either professional mathematicians or those students, who already have passed a course in analysis or set theory. ... The book contains a quantity of motivation examples, worked examples and exercises, what makes it suitable also for self-study." (Vladimír Janis, zbMATH, 2014)
"The book offers a rigorous foundation of the real number system. It is intended for senior undergraduates who have already studied calculus, but a wide range of readers will find something interesting, new, or instructive in it. ... This is an extremely reader-friendly book. It is full of interesting examples, very clear explanations, historical background, applications. Each new idea comes after proper motivation." (László Imre Szabó, Acta Scientiarum Mathematicarum (Szeged), Vol. 80 (1-2), 2014)
Portrait

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.

… weiterlesen
In den Warenkorb
Filialabholung

Versandkostenfrei

Bezahlung bei Abholung

Beschreibung

Produktdetails


Einband gebundene Ausgabe
Seitenzahl 244
Erscheinungsdatum 28.10.2013
Sprache Englisch
ISBN 978-3-319-01576-7
Verlag Springer
Maße (L/B/H) 235/155/20 mm
Gewicht 555
Abbildungen 62 schwarzweisse Abbildungen
Auflage 2013
Buch (gebundene Ausgabe, Englisch)
37,98
inkl. gesetzl. MwSt.
Versandfertig in 3 - 5 Tagen
Versandkostenfrei
In den Warenkorb
Filialabholung

Versandkostenfrei

Bezahlung bei Abholung

Andere Kunden interessierten sich auch für

  • 45243079
    Fantastic Beasts and Where to Find Them. The Original Screenplay
    von Joanne K. Rowling
    (8)
    Buch (gebundene Ausgabe)
    15,99 bisher 21,49
  • 44725232
    Harry Potter and the Cursed Child - Parts I & II (Special Rehearsal Edition)
    von John Tiffany
    (55)
    Buch (gebundene Ausgabe)
    19,99
  • 39151356
    Harry Potter: The Complete Collection
    von Joanne K. Rowling
    (6)
    Buch (Taschenbuch)
    48,95 bisher 71,99
  • 43564382
    Milk and Honey
    von Rupi Kaur
    Buch (Taschenbuch)
    12,99
  • 42413879
    All the Light We Cannot See
    von Anthony Doerr
    (2)
    Buch (Taschenbuch)
    7,87 bisher 10,49
  • 34910866
    The Life List
    von Lori Nelson Spielman
    (5)
    Buch (Taschenbuch)
    6,99 bisher 9,70
  • 45965122
    The Chemist
    von Stephenie Meyer
    Buch (Taschenbuch)
    13,49 bisher 27,99
  • 38930428
    We Were Liars
    von E. Lockhart
    (10)
    Buch (Taschenbuch)
    7,99 bisher 10,49
  • 17914934
    One Line a Day
    von Books LLC Staff Chronicle
    (2)
    Buch
    9,99
  • 42769827
    The Girl on the Train
    von Paula Hawkins
    (14)
    Buch (Taschenbuch)
    6,99
  • 31405171
    Game of Thrones 5-Copy Boxed Set
    von George R. R. Martin
    (6)
    Buch (Taschenbuch)
    25,90 bisher 37,49
  • 43809866
    It Ends with Us
    von Colleen Hoover
    (2)
    Buch (Taschenbuch)
    8,99 bisher 11,50
  • 39151343
    Harry Potter 1 and the Philosopher's Stone
    von Joanne K. Rowling
    (14)
    Buch (Taschenbuch)
    6,99
  • 42416940
    George R. R. Martin's a Game of Thrones Leather Cloth Boxed Set (Song of Ice and Fire Series)
    von George R. R. Martin
    Buch (Leder)
    49,50 bisher 70,76
  • 41516671
    Scratch the World
    Buch (Poster)
    22,99
  • 46095035
    Born A Crime
    von Trevor Noah
    (2)
    Buch (Taschenbuch)
    14,99
  • 39151342
    Harry Potter 2 and the Chamber of Secrets
    von Joanne K. Rowling
    Buch (Taschenbuch)
    6,99
  • 46395110
    Tools of Titans
    von Timothy Ferriss
    Buch (Taschenbuch)
    13,99
  • 45996981
    The Bikini Body 28-Day Healthy Eating & Lifestyle Guide
    von Kayla Itsines
    Buch (Taschenbuch)
    17,99 bisher 23,49
  • 44656071
    Holding Up the Universe
    von Jennifer Niven
    (5)
    Buch (Taschenbuch)
    8,99 bisher 10,49

Kundenbewertungen


Es wurden noch keine Bewertungen geschrieben.

Wird oft zusammen gekauft

The Real Numbers

The Real Numbers

von John Stillwell

Buch (gebundene Ausgabe, Englisch)
37,98
+
=
Elements of Number Theory

Elements of Number Theory

von John Stillwell

Buch (gebundene Ausgabe)
44,99
+
=

für

82,97

inkl. gesetzl. MwSt.

Alle kaufen