A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs, A First Course in Mathematical Logic and Set Theory by Michael L. O’Leary offers a comprehensive exploration of foundational concepts essential for advanced mathematics. The book begins with propositional logic, introducing two-column proofs and truth table applications, before delving into first-order logic, which serves as the backbone for constructing mathematical arguments. Set theory is introduced next, providing the framework necessary to define relations, functions, numbers, and ordinals, along with an in-depth look at mathematical induction and cardinality.
The latter part of the book focuses on basic model theory and its applications in abstract algebra. Throughout the text, section exercises are designed to demonstrate the interplay between different topics and reinforce key ideas. Numerous examples illustrate theoretical concepts, including the use of Euclid’s lemma, the Fibonacci sequence, and unique factorization. Ideal for students seeking a rigorous foundation in mathematical logic and set theory, this book equips readers with the skills needed for advanced study in mathematics.
Published by Wiley on September 8, 2015, with an ISBN-13 of 978-0470905883 and a print length of 464 pages, A First Course in Mathematical Logic and Set Theory is both a valuable resource for students and a comprehensive guide for educators. With its clear explanations and practical applications, the book serves as an excellent starting point for anyone interested in delving into the intricacies of mathematical logic and set theory.
Key Features:
- Introduction to propositional and first-order logic
- In-depth exploration of set theory
- Practical applications through exercises and examples
- Emphasis on writing proofs and constructing arguments
- Coverage of mathematical induction, ordinals, cardinals, and model theory