Classic Set Theory: For Guided Independent Study (Chapman & Hall Mathematics)

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Classic Set Theory: For Guided Independent Study (Chapman & Hall Mathematics) [Paperback]

D.C. Goldrei
4.8 out of 5 stars  See all reviews (10 customer reviews)

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Book Description

July 1, 1996 0412606100 978-0412606106 1
Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:

  • The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers
  • Defining natural numbers in terms of sets
  • The potential paradoxes in set theory
  • The Zermelo-Fraenkel axioms for set theory
  • The axiom of choice
  • The arithmetic of ordered sets
  • Cantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.

    The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.

    Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

  • Frequently Bought Together

    Classic Set Theory: For Guided Independent Study (Chapman & Hall Mathematics) + Set Theory and Logic (Dover Books on Mathematics) + Introduction to the Theory of Sets (Dover Books on Mathematics)
    Price for all three: $94.99

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    Product Details

    • Series: Chapman & Hall Mathematics
    • Paperback: 296 pages
    • Publisher: Chapman and Hall/CRC; 1 edition (July 1, 1996)
    • Language: English
    • ISBN-10: 0412606100
    • ISBN-13: 978-0412606106
    • Product Dimensions: 8.4 x 10 inches
    • Shipping Weight: 13.6 ounces (View shipping rates and policies)
    • Average Customer Review: 4.8 out of 5 stars  See all reviews (10 customer reviews)
    • Amazon Best Sellers Rank: #226,057 in Books (See Top 100 in Books)

    Customer Reviews

    Most Helpful Customer Reviews
    40 of 40 people found the following review helpful
    5.0 out of 5 stars The ideal textbook March 29, 2006
    I went to my university's library and tried to compare Goldrei's book with almost all other popular accounts on Set theory, prior to investing my time learning the basics of the subject. After having almost finished reading it, I believe that this a model of how textbooks in mathematics should be written. Let me be a little bit more specific:

    1)Suberb organization of the material. Ideas are built gradually without logical gaps or regressions. Definitions and theorems are clearly stated. "What follows from what" is always transparent. Even the choice of paragraphs is so well thought, that one can easilly assign a title in each of them for quick reference later on.

    2)Each subject is clearly introduced within its historical and logical context. Each theorem (and even exercise) is motivated for its importance and its merits in the global picture of Set theory.

    3)The logic and intuition behind the proofs is given (as well as the proof itself...) in a well organized and not unecessarily wordy manner.

    4) There are exercises within the main text (which, as usual, are well motivated for their importance) with solutions folowing right after. In this way, one may develop skills and understanding, without getting frustrated or spending too much time. There are also exercises in the end of each section which are interesting and not too difficult.

    5) There are comments aside of the main text, which range from ideas concerning a proof to historical remarks or recommendations to the reader. In this way, the main text remains clean of tangencies, but never dry.

    I could continue praising this book, but let me cut it short by saying just this: it is one of those proper (i.e.
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    34 of 35 people found the following review helpful
    5.0 out of 5 stars The ideal introductory book on set theory May 25, 2006
    Format:Paperback|Verified Purchase
    In recent months, I read (at least in part) about ten books on set theory, of different levels and styles. Goldrei's book is by far the best on my list. Goldrei has the talent of presenting a fairly difficult and abstract material in a friendly style, with abundant explanations, solved exercises, illustrations, and illuminating comments. I can highly recommend this book as a first reading on set theory, whether for self-study or as a supplementary text for a course on the subject. For the interested readers of this review, here is how I rank some of the other books I've read: Stoll is definitely a second, then Suppes (which goes deeper than both Goldrei and Stoll, but in my opinion is poorly organized and suffers from nonstandard and funny-looking notations), followed by Halmos, Machover, and a few more. And last and least, the incomprehensible "book" by Vaught.
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    9 of 9 people found the following review helpful
    5.0 out of 5 stars Especially useful for self-study. May 5, 2004
    This book is especially useful for self study, as it has more worked examples than usual, motivating hints in side bar, and explanitory comments in text. Perhaps the origin of this materical in Open University (I think roughly analogous to what USA schools call "Extension"?) course is reason. Found it helpful where Halmos was a bit concise for someone with fellow students or TA handy.
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    12 of 13 people found the following review helpful
    5.0 out of 5 stars very good book for self-study September 26, 2000
    By A Customer
    Recently, I had to learn set theory for my current work (automated reasoning and expert systems). This book proved to be an excellent supplement for learning set theory; which I then used to learn formal logic, resolution, etc.
    Very well written and with good examples and exercises.
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    8 of 8 people found the following review helpful
    5.0 out of 5 stars Extremely well written July 8, 2011
    Format:Paperback|Verified Purchase
    This book should be the first on your list if you plan to study set theory or foundations of mathematics in general. The writing style is informal but the material is well presented to the reader in a way that its rigor is not sacrificed. The author goes through many proofs outlining each and every step. Solutions to exercises are also included even though as the book progresses the author omits more and more solutions because he expects that the readers level should be increasing. I really liked this method. I have not read other books on set theory, but it is really hard to imagine a better one. Not much is expected as prerequisites. If you understand the mathematical concepts of convergence, sequences and functions then the book should be pretty much self-contained. If not I would recommend that you read something like "Sets, sequences & mappings" by Anderson and Hall. This is a really small book but its excellent in that it prepares you for more abstract courses.
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