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42414722
Set Theory and Logic (Dover Books on Mathematics) Revised ed. Edition
Item #:
42414722
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Mathematics students at the undergraduate level, and those who seek a rigorous but not unnecessarily technical introduction to mathematical concepts, will welcome the return to print of this most lucid work.
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What Stands Out
Comprehensive Coverage
This edition provides an extensive overview of set theory and logic, making it ideal for students and enthusiasts seeking a solid foundation in these mathematical disciplines.
Revised Content
Updated with contemporary examples and exercises, ensuring relevance and accessibility for modern learners while enhancing understanding of complex concepts.
Affordable Price
Dover's commitment to affordability makes this revised edition a valuable resource for students, providing high-quality content at a fraction of the cost compared to other textbooks.
Product Details
- Set Theory and Logic is the result of a course of lectures for advanced undergraduates, developed at Oberlin College for the purpose of introducing students to the conceptual foundations of mathematics. Mathematics, specifically the real number system, is approached as a unity whose operations can be logically ordered through axioms. One of the most complex and essential of modern mathematical innovations, the theory of sets (crucial to quantum mechanics and other sciences), is introduced in a most careful concept manner, aiming for the maximum in clarity and stimulation for further study in set logic. Contents include: Sets and Relations — Cantor's concept of a set, etc.Natural Number Sequence — Zorn's Lemma, etc.Extension of Natural Numbers to Real NumbersLogic — the Statement and Predicate Calculus, etc.Informal Axiomatic MathematicsBoolean AlgebraInformal Axiomatic Set TheorySeveral Algebraic Theories — Rings, Integral Domains, Fields, etc.First-Order Theories — Metamathematics, etc.Symbolic logic does not figure significantly until the final chapter. The main theme of the book is mathematics as a system seen through the elaboration of real numbers; set theory and logic are seen s efficient tools in constructing axioms necessary to the system. Mathematics students at the undergraduate level, and those who seek a rigorous but not unnecessarily technical introduction to mathematical concepts, will welcome the return to print of this most lucid work. Professor Stoll . . . has given us one of the best introductory texts we have seen. — Cosmos. In the reviewer's opinion, this is an excellent book, and in addition to its use as a textbook (it contains a wealth of exercises and examples) can be recommended to all who wish an introduction to mathematical logic less technical than standard treatises (to which it can also serve as preliminary reading). — Mathematical Reviews.
| Publisher | Dover Publications |
| Publication date | October 1, 1979 |
| Edition | Revised ed. |
| Language | English |
| Print length | 512 pages |
| ISBN-10 | 0486638294 |
| ISBN-13 | 978-0486638294 |
| Item Weight | 1.36 pounds (620 grams) |
| Dimensions | 5.6 x 1 x 8.2 inches (14.2 x 2.5 x 20.8 cm) |
| Part of series | Dover Books on Mathematics |
Who Should Buy?
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Mathematics Students
Undergraduate and graduate students studying mathematics and related fields will gain crucial foundational knowledge from this text.
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Logic Enthusiasts
Individuals interested in formal logic and its applications can deepen their understanding through clear explanations and examples.
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Educators
Teachers looking to enhance their curriculum with strong foundational concepts in set theory and logic will benefit significantly.
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Beginner Learners
Those with little to no background in mathematics may find the content too challenging and complex to understand.
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Casual Readers
Individuals seeking light reading or recreational material will likely find the rigorous approach and depth unsuitable.
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Professionals in Other Fields
Practitioners outside of mathematics or logic disciplines may not find relevant applications for the in-depth discussions presented.
Product Description
About This Item
Enhance your understanding of set theory and logic with this comprehensive and revised edition of "Set Theory and Logic" by Dover Books on Mathematics. This book is the perfect companion for students and professionals alike who want to dive deeper into the intriguing world of set theory and logic. Written by renowned experts in the field, this Dover publication covers a wide range of topics including basic set theory, logical operations, relations and functions, and formal proofs. It provides a solid foundation for further exploration and applications in mathematics and computer science. Whether you are a beginner looking to grasp the fundamental concepts or an advanced learner seeking to refine your skills, this book has something for everyone.
The clear and concise explanations, along with numerous examples, make complex ideas easy to understand. As a Dover book, you can trust the quality and authenticity of the content. Dover has a long-standing reputation for producing reliable and affordable mathematical texts, and this edition is no exception. It is an essential addition to any mathematics library. So, if you are passionate about math, logic, or simply want to expand your knowledge, "Set Theory and Logic" is a must-have book.
Order your copy today and unravel the mysteries of set theory and logic with Dover's comprehensive edition.
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Customer Questions & Answers
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Question:
What are the key topics covered in 'Set Theory and Logic' Dover Books?
Answer: The book delves into the foundational aspects of set theory, including the axioms of set theory, set operations, and relations. It further explores logical reasoning, quantifiers, and the structure of mathematical proofs. This foundational knowledge is essential for students embarking on advanced mathematics or related fields, making it a significant resource in understanding complex concepts. -
Question:
Who is the target audience for 'Set Theory and Logic'?
Answer: This book is intended for undergraduate students in mathematics and philosophy. It serves as a foundational text for anyone looking to deepen their understanding of mathematical structures. Whether you are preparing for higher academic pursuits or simply interested in enhancing your logical reasoning, this book offers an invaluable resource. -
Question:
How does 'Set Theory and Logic' support independent learning?
Answer: The book is structured in a clear and logical manner, allowing readers to progress at their own pace. Each chapter includes exercises that reinforce the concepts discussed, providing practical scenarios where set theory and logic apply. This makes it an ideal choice for self-study or supplementary reading in a mathematics course. -
Question:
Are there any prerequisites for understanding the content in this book?
Answer: A basic understanding of mathematical concepts such as functions, relations, and introductory logic is beneficial. Familiarity with high school algebra can further enhance comprehension. This groundwork ensures that readers can fully appreciate the abstract concepts of set theory and their practical applications in mathematics and logic. -
Question:
What makes this revised edition of 'Set Theory and Logic' significant?
Answer: The revised edition incorporates updates and clarifications based on feedback from educators and students. It aims to simplify complex topics and includes additional examples and exercises. This makes it a more robust tool for both teaching and learning, ensuring that readers grasp the essential concepts effectively. -
Question:
Can 'Set Theory and Logic' be used for advanced studies?
Answer: Yes, this book lays the groundwork for various advanced mathematical topics including topology, analysis, and algebra. Its emphasis on logical reasoning and proof techniques is crucial for higher-level mathematics. Therefore, it serves as a stepping stone for those wishing to pursue graduate studies or research in mathematics. -
Question:
What is the writing style of 'Set Theory and Logic'?
Answer: The writing style is clear, concise, and pedagogically sound, making complex topics accessible to readers. The authors use a conversational tone while maintaining academic rigor, facilitating a smoother learning experience. This style encourages readers to engage with the material and fosters a deeper understanding of concepts. -
Question:
Does the book include historical context for set theory and logic?
Answer: Yes, the book provides insights into the historical development of set theory, tracing its origins and evolution over time. Understanding the historical context enriches the learning experience by highlighting the significance of contributions from mathematicians throughout history. This perspective can inspire readers to appreciate the subject's depth and relevance. -
Question:
Are practical applications of set theory discussed in the book?
Answer: The book touches on practical applications of set theory and logic, illustrating how these concepts apply in fields such as computer science, statistics, and linguistics. Understanding these applications helps reinforce theoretical knowledge and demonstrates the relevance of set theory and logic in solving real-world problems. -
Question:
Where can I buy 'Set Theory and Logic' Dover Books on Mathematics Revised ed. Edition?
Answer: You can purchase 'Set Theory and Logic' Dover Books on Mathematics Revised ed. Edition through Ubuy in Liechtenstein. Ubuy offers a user-friendly platform and a variety of options, making it convenient for you to obtain this essential mathematics text.
Algebra Editorial Review
The "Set Theory and Logic" book by Robert Roth Stoll is widely praised for its comprehensive coverage of set theory and logic, with readers finding it very readable and accessible. The book also covers basic real analysis and the foundations of arithmetic, making it an ideal introduction to these advanced mathematical concepts. It has been lauded for providing a detailed and accessible introduction to set theory, enabling individuals with a solid background in pure mathematics to appreciate complex works by renowned mathematicians such as Cantor and Godel. Despite its advanced nature, some readers have noted that additional reading and effort may be required to fully understand the material, especially for those who are not trained mathematicians. However, the clarity of Stoll's writing and the presence of exercises are highlighted as beneficial features. Some readers recommended this book as an essential read for individuals with a couple of years of undergraduate pure mathematics background, while others appreciated the author's approach of starting with topics familiar from general mathematics before delving into formal logic. The book's comprehensive content includes chapters on sets, relations, functions, order, natural numbers, cardinal numbers, ordinal numbers, rational and real numbers, basic propositional and predicate calculus, axiomatization of set theory and algebra, and first-order languages and metamathematics. Additionally, the book has been commended for presenting a natural deduction logical calculus and for its lightweight introduction that prepares readers for more advanced logic and set theory books. While some have mentioned that the book is a bit dated, its low price is Considered to be a good bargain. Overall, "Set Theory and Logic" is described as a clear, simple, and comprehensive book that provides an excellent foundation for understanding advanced mathematical concepts. **
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Pros
- Comprehensive coverage of set theory and logic
- Readable and accessible
- Provides exercises for practice
- Good introduction for individuals with a background in pure mathematics
- Affordable price
Cons
- May require additional reading and effort for full understanding
Product Price History
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Features & Benefits
- Introduces students to the conceptual foundations of mathematics
- Approaches mathematics as a unity
- Introduces the theory of sets in a careful and clear manner
- Covers topics such as logic and algebraic theories
- Provides a rigorous yet not unnecessarily technical introduction to mathematical concepts
- Contains a wealth of exercises and examples