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Produktbeschreibungen
Pressestimmen
"The book remains an excellent text for a senior undergraduate or first-year graduate level course. There is sufficient material for instructors of widely differing views to assemble one-semester courses. . ..the chapter on the axiom of choice is particularly strong." ---Mathematical Reviews ." . .a fine text. . ..The proofs are both elegant and readable." ---American Mathematical Monthly ." . .offers many benefits including. . .interesting applications of abstract set theory to real analysis. . .enriching standard classroom material." ---L'Enseignement mathematique ." . .an excellent and much needed book. . .Especially valuable are a number of remarks sprinkled throughout the text which afford a glimpse of further developments." ---The Mathematical Intelligencer "The authors show that set theory is powerful enough to serve as an underlying framework for mathematics by using it to develop the beginnings of the theory of natural, rational, and real numbers." ---Quarterly Review of Applied Mathematics ." . .In the third edition, Chapter 11 has been expanded, and four new chapters have been added." ---Mathematical Reviews
Book Description
Third Edition covers "the basics"r one-semester course; provides five additional self-contained chapters to supplement the basic course or serve as a second-semester syllabus; consolidates the material on real numbers in a single updated chapter affording flexibility in course design; supplies end-of-section problems; and more.
In diesem Buch
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Einleitungssatz
The central concept of this book, that of a set, is, at least on the surface, extremely simple. Lesen Sie die erste Seite
Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis | Rückseite
The central concept of this book, that of a set, is, at least on the surface, extremely simple. Lesen Sie die erste Seite
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Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis | Rückseite
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4 Rezensionen
29 von 29 Kunden fanden die folgende Rezension hilfreich
Close to Perfect
13. April 2004
Format:Gebundene Ausgabe
This is pretty much the perfect introduction to set theory for someone having some familiarity with rigorous mathematics. The treatment is axiomatic but doesn't employ the usual logical formalism, everything is written in plain english. The book emphasizes the foundational character of set theory and shows how all the usual objects of mathematics can be developed using only sets. It also demonstrates the application of set theoretic methods to "ordinary" mathematics by giving complete proofs of some powerful theorems like the Hahn-Banach theorem in functional analysis.
The pace is leisurely with a close look at the details. The axiom of choice is used only when necessary and it's uses are highlighted. The exercises contain real meat but are broken up in handable pieces. They also give alternative approaches to topics treated in the main text. Solutions are not contained.
The last section is devoted to an outlook at more advanced set theory. The ideas of the constructible universe and of forcing are outlined, as far as that is possible on that level. There is also a discussion on candidates for additional axioms.
The reader will gain both insight into what set theory is and how powerful it is. There is no better book for the same audience.
23 von 23 Kunden fanden die folgende Rezension hilfreich
The best text I had as a graduate student
29. September 2001
Format:Gebundene Ausgabe
One of the first classes I took as a graduate student in mathematics was in the foundations of mathematics. The topic was set theory and this was the text we used. There have been many times in my mathematical career that I have been grateful for the knowledge learned in the class and this is one of two course textbooks that I still regularly consult as a reference. It is an excellent introduction to the fundamentals of set theory and ordinal arithmetic and I heartily recommend this book to anyone teaching or learning the fundamentals of sets.
16 von 16 Kunden fanden die folgende Rezension hilfreich
Excellent contribution!
13. Februar 2007
Format:Gebundene Ausgabe
This is one of the best book on Set Theory in the market. The authors' exposition is highly appealing as well as clear and friendly. This is a modern Non-Naive Set Theory as against that of Halmos' famous book--Naive Set Theory. By the way, you probably don't know there is a companion book by Sigler 0387901930 Exercises in Set Theory which was an very petinent companion to both of the two famous books on Set Theory. can't miss it
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