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Set Theory and Logic (Dover Books on Mathematics),Used
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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.FirstOrder 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.
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- Q: What is the main focus of 'Set Theory and Logic' by Robert R. Stoll? A: The book primarily focuses on introducing advanced undergraduates to the conceptual foundations of mathematics, emphasizing set theory and logic as essential tools for understanding mathematical systems.
- Q: Who is the intended audience for this book? A: The book is aimed at undergraduate mathematics students and anyone seeking a clear, rigorous introduction to mathematical concepts without overly technical language.
- Q: What topics are covered in 'Set Theory and Logic'? A: Key topics include sets and relations, natural number sequences, the extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebra, and several algebraic theories.
- Q: Is this book suitable for beginners in mathematics? A: While it is suitable for undergraduates, it is not intended for complete beginners. It provides a rigorous introduction, making it beneficial for those with some prior knowledge of mathematics.
- Q: What is the format of the book? A: The book is available in paperback format and consists of 512 pages.
- Q: When was 'Set Theory and Logic' published? A: The book was published on October 1, 1979.
- Q: Does the book include exercises or examples? A: Yes, the book contains a wealth of exercises and examples to aid in understanding the material presented.
- Q: What makes this book distinct from other mathematics textbooks? A: The book is noted for its clarity and conceptual approach, focusing on the unity of mathematics and presenting complex ideas in an accessible manner.
- Q: Is there a specific edition of this book? A: Yes, this is the revised edition of 'Set Theory and Logic'.
- Q: Who is the author of the book? A: The book is authored by Robert R. Stoll.