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82922353
Set Theory and the Continuum Hypothesis (Dover Books on Mathematics)
Item #:
82922353
COP 78734
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An invaluable reference book for mathematicians and mathematical theorists, this text is suitable for graduate and postgraduate students and is rich with hints and ideas that will lead readers to further work in mathematical logic.
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What Stands Out
Comprehensive Coverage
Offers an in-depth exploration of set theory and the continuum hypothesis, making complex concepts accessible for learners and enthusiasts alike, promoting a thorough understanding of fundamental mathematical principles.
Illustrated Edition
Enhanced with illustrations that clarify intricate ideas, this edition transforms abstract theories into visual representations, engaging readers and facilitating a deeper appreciation for mathematical structures and relationships.
Dover Quality
Published by Dover, known for high-quality academic resources, ensuring durability and clarity, making it an essential addition to any mathematics library for students, educators, and researchers seeking authoritative texts.
Product Details
- This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The independence of the continuum hypothesis is the focus of this study by Paul J. Cohen. It presents not only an accessible technical explanation of the author's landmark proof but also a fine introduction to mathematical logic. An emeritus professor of mathematics at Stanford University, Dr. Cohen won two of the most prestigious awards in mathematics: in 1964, he was awarded the American Mathematical Society's Bôcher Prize for analysis; and in 1966, he received the Fields Medal for Logic. In this volume, the distinguished mathematician offers an exposition of set theory and the continuum hypothesis that employs intuitive explanations as well as detailed proofs. The self-contained treatment includes background material in logic and axiomatic set theory as well as an account of Kurt Gödel's proof of the consistency of the continuum hypothesis. An invaluable reference book for mathematicians and mathematical theorists, this text is suitable for graduate and postgraduate students and is rich with hints and ideas that will lead readers to further work in mathematical logic.
| Publisher | Dover Publications |
| Publication date | December 9, 2008 |
| Edition | Illustrated |
| Language | English |
| Print length | 190 pages |
| ISBN-10 | 0486469212 |
| ISBN-13 | 978-0486469218 |
| Item Weight | 10.4 ounces (294.84 grams) |
| Dimensions | 6.1 x 0.4 x 9.1 inches (15.5 x 1 x 23.1 cm) |
| Part of series | Dover Books on Mathematics |
Who Should Buy?
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Mathematics Students
Ideal for college-level students studying set theory and modern mathematical concepts to enhance their understanding.
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Researchers
Suitable for mathematicians or researchers who are delving into set theory and the continuum hypothesis for advanced study.
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Self-Learners
Great for individuals interested in independent study of advanced mathematics concepts through a well-illustrated resource.
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Casual Readers
Not suitable for those without a strong mathematical background or interest in complex mathematical theories.
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Set Theory Editorial Review
**** "Set Theory and the Continuum Hypothesis" by Paul Cohen is a landmark work in the field of mathematics, often compared to significant scientific texts like Darwin's "On the Origin of Species." Cohen does not merely engage with complex ideas; he distills intricate concepts into a format that is both challenging and rewarding for educated readers with a genuine interest in mathematics. This illustrated edition, a reproduction of the book's first edition, features a minimalist typewritten design that may strike some as rustic, yet it complements the clarity of Cohen's Prose, making the subject matter accessible. Readers familiar with formal logic and mathematical notation will find the first segments informative, as Cohen succinctly introduces foundational elements of formal set theory—specifically Zermelo-Fraenkel set theory, which forms a bedrock for modern mathematics. After establishing this groundwork, Cohen navigates toward the heart of the book: the Continuum Hypothesis. His groundbreaking proof asserts that this longstanding problem in mathematics does not have a definitive solution, highlighting the limitations of formal systems to encapsulate all mathematical truths. Though this book is graduate-level, it manages to cater to a broader audience. Those who have enjoyed works by mathematicians and writers such as Ian Stewart, Douglas Hofstadter, or the late Martin Gardner will find Cohen's writing resonates with their experiences. The text's thorough exploration of cardinal numbers, infinite sets, and related concepts illustrates Cohen's intended communication that not only informs but invites curiosity into the infinite realms of mathematics. Overall, Cohen's "Set Theory and the Continuum Hypothesis" is a remarkable amalgamation of depth and readability that empowers readers to appreciate the profound complexities of mathematics. **
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Pros
- Clear, accessible writing style for educated readers.
- Thorough introduction to formal logic and set theory.
- Insightful exploration of the Continuum Hypothesis and its implications.
- Engages readers with a genuine interest in mathematics.
- Suitable for both graduate students and interested laypersons.
Cons
- Challenging for those without a foundational understanding of mathematics.
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COP 78734
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Features & Benefits
- Written by the man who discovered the solution to the continuum hypothesis
- Accessible technical explanation of the landmark proof
- Introduction to mathematical logic
- Includes background material in logic and axiomatic set theory
- Suitable for graduate and postgraduate students
- Rich with hints and ideas for further work in mathematical logic
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