Subjects:  1. Applied    2. Mathematics    3. Probabilities    4. Probability & Statistics - General    5. Random sets    6. Science/Mathematics    7. Set Theory    8. Textbooks    9. Mathematics / Set Theory    10. Probability & statistics   

Reviews (3)

Straightforward and clear
This is aimed at undergrads, the same as Enderton's _Elements of Set Theory_. I didn't read the whole thing, but it seemed more clear and cohesive than that text. This is the only book I've found that looks like a direct alternative for Enderton. I would say, though, that it doesn't have quite as much detail and it doesn't have the handwavy introductions that Enderton has in some parts.

Close to Perfect
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 best text I had as a graduate student
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. ... Read more

Subjects:  1. Applied    2. Mathematics    3. Science/Mathematics    4. Set Theory    5. Mathematics / Set Theory   

Subjects:  1. Mathematics    2. Science/Mathematics    3. Set Theory    4. Mathematical logic    5. Mathematics / Set Theory    6. Mathematics | Logic   

Reviews (2)

Not much alternative to this
There is a bit of unintended humor in the preface: "This book is essentially self-contained. The only thing it requires is familiarity...with the basics of general topology, measure theory, and functional analysis, as well as the elements of set theory..."
Excellent reference
A truly outstanding reference for the purely classical aspects of descriptive set theory, it falls under Kelley's label, "What every young set theorist needs to know." It is not an easy book for the beginner as it is very concise and gives little motivation, but for the advanced student it is essential.
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Subjects:  1. Logic    2. Mathematics    3. Science/Mathematics    4. Set Theory    5. Fuzzy set theory    6. Mathematical logic    7. Mathematics / Logic    8. Mathematics / Set Theory   

Reviews (3)

Too short on explanation
This text is intended for seniors or beginning grads. The first three of seven chapters form a very quick survey of naive set theory. Since it aims at a more advanced audience, it is not as explanatory as Enderton and the exercises assume more maturity. Chapters 4 - 7 survey some advanced topics that aren't part of the usual introductory set theory course. These chapters have no exercises.
Superb!
Keith Devlin is one of those rare research mathematicians who is able to make recent advances in mathematics understandable and interesting to those whose mathematical education is obsolete or incomplete. I'm in the former category, having done my graduate work in pure math 50 years ago; although I've tried to keep up, constraints of time and other obligations have made it difficult.
At times not so easygoing, but indeed a joy to read ...
Anyone seeking a deeper understanding of the foundations of the mathematics will benefit from reading this excellent book.Read more

Subjects:  1. General    2. Logic    3. Mathematics    4. Science    5. Science/Mathematics    6. Set Theory    7. Mathematics / Logic    8. Mathematics / Set Theory    9. Science-General   

Subjects:  1. Applied    2. Computer science    3. Logic    4. Logic, Symbolic and mathematic    5. Logic, Symbolic and mathematical    6. Mathematical And Symbolic Logic    7. Mathematics    8. Number Theory    9. Science/Mathematics    10. Set Theory    11. Mathematical logic    12. Mathematics / Logic   

Subjects:  1. Euclidean Geometry    2. Geometry - General    3. Mathematics    4. Measure Theory    5. Probability & Statistics - General    6. Science/Mathematics    7. Set Theory    8. Topology - Fractals    9. Functional analysis    10. Geometric measure theory    11. Mathematics / Differential Equations   

Subjects:  1. Constructibility (Set theory)    2. Large cardinals (Mathematics)    3. Logic    4. Mathematics    5. Medical    6. Set Theory    7. Mathematical logic   

Subjects:  1. Business / Economics / Finance    2. Business/Economics    3. Mathematical Analysis    4. Mathematics    5. Performance standards    6. Project Management    7. Quality control    8. Science/Mathematics    9. Set Theory    10. Work measurement   

Reviews (3)

probably the best undergraduate level topology book
It starts the discussion with the familiar metric spaces and the real line and then I wish all math books were like this...
I'm a graduate student in mathematics and this is one of the few math books I can highly recommend. Topological concepts are made intuitive, so when you get to the formal definitions, they are no surprise, you evenexpect them. Sometimes it is explained why a 'seemingly obvious solution'doesn't work after all. This really helps you to see WHY things are donethe way they are. After reading this book you'll have a good basicunderstanding of what topology is all about. With this background it shouldbe no problem to tackle more advanced texts on topology. Best book ever on topology!
This book is an extremely valuable asset to anyone with enthusiasm for mathematics.Using at first only fundemental calculus, the book carefully draws the reader into the scope of the field.The book contains detailed explanation of all terms used in the axioms and theorms presented.It leaves an unambiguous picture of the developed ideas in the reader's mind.I strongly recommend it, (it even has a neat cover!) ... Read more

Subjects:  1. Geometry - General    2. Mathematics    3. Science/Mathematics    4. Set Theory    5. Topological spaces    6. Topology    7. Geometry    8. Mathematics / Geometry / General    9. Mathematics / Set Theory   

Reviews (3)

good- but not true to title
While this book is well-written and appears to provide a sufficient introduction to the concepts of set theory, it approaches but falls short of its titular subject- discussing the impact of set theory on philosophy.
Fascinating Introduction to the Generalized Continuum Hypothesis
The Philosophy of Set Theory - An Historical Introduction to Cantor's Paradise by Mary Tiles is a fascinating mix of mathematics, mathematical logic, and philosophy that should appeal to (and challenge) both mathematics and philosophy majors at the undergraduate and graduate level.
Finitistic Philosophy, with Some Comments on Cantor
When Newton and his successors defined the calculus in the 17th and 18th centuries, they were quite cavalier about infinities.For example, they treated sums of infinitely many numbers essentially the same way they treated sums of finitely many numbers.And when talking about derivatives, they were content to talk of changes over infinitely shrinking intervals without quite saying what they meant by that.As mathematics developed increasingly abstract methods, more divorced from the simple observations of physics, many problems cropped up, mostly having to do with the careless use of infinities.In order to deal with these problems, mathematicians devised precise definitions which made no explicit use of infinities.
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Subjects:  1. Mathematics    2. Philosophy    3. Science/Mathematics    4. Set Theory    5. Mathematics / Set Theory   

Reviews (4)

It is one clear exposition of very much subjects
To me, this book has the following questions:
Excellent and readable book
I'm not particularly strong in math, and I've never taken a course in topology, but this has been a great book to read thru to learn the tools and topics.The writing is crisp and clear, and the author pushes one thru the material slowly and gradually.

I paid Full Price and don't regret it!
Although this is so much better than the other Dover book by R. Vaidyanathaswamy, I can't say that it is the best topology text that I have read or the best reference, but it covers topics from Banach spaces to functional topology in a pretty readable manner and it is fairly inexpensive! ... Read more

Subjects:  1. Geometry - General    2. Mathematics    3. Science/Mathematics    4. Set Theory    5. Topological spaces    6. Topology    7. Vector Analysis    8. Geometry    9. Mathematics / General   

Reviews (1)

The Banach-Tarski Paradox
If you're really interested in the Banach-Tarski Paradox this book is what you have to read. The straightness of thoughts of Stan Wagon and his beautiful ideas not only about the paradox but also set theorie in generalwere so impressing, that thi s book became one of my favourites. ... Read more

Subjects:  1. Banach-Tarski paradox    2. Decomposition (Mathematics)    3. Differential Equations    4. Mathematics    5. Measure Theory    6. Probability & Statistics - General    7. Science/Mathematics    8. Set Theory    9. Calculus & mathematical analysis    10. Mathematics / Differential Equations   

Reviews (1)

logic and mathematics
This book is good for concise information, but is very pricey for its contents.My advice is find a better book. ... Read more

Subjects:  1. Logic    2. Mathematics    3. Probability & Statistics - General    4. Science/Mathematics    5. Mathematical foundations    6. Mathematics / Set Theory   

Subjects:  1. Algebra - Linear    2. Esperimental design    3. Mathematics    4. Probability & Statistics - General    5. Science/Mathematics    6. Set Theory    7. Mathematics / Statistics    8. Mathematics for scientists & engineers    9. Optimization   

Subjects:  1. Logic    2. Mathematics    3. Science/Mathematics    4. Set Theory    5. Mathematics / Logic    6. Mathematics / Set Theory   

Reviews (8)

This book is adequate but needs improvement
I have an older edition of this book. It is well-written and has a good selection of homework problems, but it lacks clarity and does not emphasize practice. Most proof books are good for learning the basics of proofs but aren't sufficient to do proofs in a specific area of math. My website focuses on how to practice doing proofs, fsc729.ifreepages.com.
Do not buy this book!
I had one of my math courses at Macalester College use this book in addition to the main textbook. It is one of the most boring readings in math ever. If you want a beginning book that would teach you how to do problem-oriented math, you had better consider George Polya's How to Solve It or consult a math teacher near you;-) In order to further underscore my poit, I will just say that it was not only I but the whole class that disgruntled against the book and we hated it so much that the professor does not use it anymore.

Big Improvement in Second Edition
Contrary to the review by the person from Louisiana I feel the second edition is better than the first. The typesetting is greatly improved, and there are a few new tools for your toolbag in the second edition.Read more

Subjects:  1. Logic    2. Logic, Symbolic and mathematic    3. Logic, Symbolic and mathematical    4. Mathematical And Symbolic Logic    5. Mathematics    6. Philosophy Of Mathematics    7. Proof theory    8. Science/Mathematics    9. Set Theory    10. Mathematical logic    11. Mathematics / Logic   

Subjects:  1. Fuzzy sets    2. Mathematics    3. Mathematics (Specific Aspects)    4. Methodology    5. Research    6. Science/Mathematics    7. Set Theory    8. Social Sciences (General)    9. Social sciences    10. Sociology    11. Fuzzy set theory    12. Research methods: general    13. Social Science / Research    14. Social research & statistics   

Subjects:  1. Children: Grades 1-2    2. Comics & Graphic Novels - General    3. Juvenile Fiction    4. Juvenile literature    5. Mathematics    6. Set Theory   

Subjects:  1. Children's Books/Ages 4-8 Nonfiction    2. Children: Kindergarten    3. Juvenile Mathematics    4. Juvenile Nonfiction    5. Juvenile literature    6. Mathematics - General    7. Set Theory    8. Juvenile Nonfiction / Mathematics / General