A First Course in Mathematical Logic and Set Theory (Hardcover)

Michael L. O'Leary

ISBN 10: 0470905883 / ISBN 13: 9780470905883

Verlag: John Wiley & Sons Inc, New York, 2015

Beschreibung

Hardcover. A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and conceptsNumerous examples that illustrate theorems and employ basic concepts such as Euclids lemma, the Fibonacci sequence, and unique factorizationCoverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of LoewenheimSkolem, Burali-Forti, Hartogs, CantorSchroederBernstein, and Koenig An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis. Rather than teach mathematics and the structure of proofssimultaneously, this book first introduces logic as the foundationof proofs and then demonstrates how logic applies to mathematicaltopics. This method ensures that readers gain a firmunderstanding of how logic interacts with mathematics and empowersthem to solve more complex problems. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Bestandsnummer des Verkäufers 9780470905883

Bibliografische Details

• Titel: A First Course in Mathematical Logic and Set Theory (Hardcover)
• Verlag: John Wiley & Sons Inc, New York
• Erscheinungsjahr: 2015
• Sprache: Englisch
• ISBN-10: 0470905883
• ISBN-13: 9780470905883
• Einband: Hardcover
• Auflage: 1. Auflage
• Zustand: new

Über diesen Titel

Inhaltsangabe

A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs

Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems.

The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes:

• Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts
• Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization
• Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König

An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.

 

Über die Autorin bzw. den Autor

Michael L. O'Leary, PhD, is Professor of Mathematics at the College of DuPage in Glen Ellyn, Illinois. He received his doctoral degree in mathematics from the University of California, Irvine in 1994 and is the author of Revolutions of Geometry, also published by Wiley.