By (author) George Tourlakis
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Mathematical Logic by George Tourlakis
Book DescriptionA comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Godel). Logic cannot certify all "conditional" truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Godel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.
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Book DetailsISBN: 9780470280744
(239mm x 164mm x 20mm)
Publisher: John Wiley and Sons Ltd
Publish Date: 12-Sep-2008
Country of Publication: United States
Books By Author George Tourlakis
Theory of Computation, Hardback (April 2012)
With a focus on Unbound Register Machines (URMs), this book introduces new ideas and topics using real computer-related examples to help readers gain the skills and intuition that are key to successful programming.
Lectures in Logic and Set Theory: Volume 1, Mathematical Logic, Paperback (September 2010)
This two-volume set bridges the gap between introductory texts and the research literature.
Lectures in Logic and Set Theory: Volume 2, Set Theory, Paperback (September 2010)» View all books by George Tourlakis
This two-volume work bridges the gap between introductory texts and the research literature.
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Author Biography - George Tourlakis
GEORGE TOURLAKIS, PhD , is University Professor of Computer Science and Engineering at York University, Canada. Dr. Tourlakis has authored or coauthored numerous articles in his areas of research interest, which include calculational logic, modal logic, computability, complexity theory, and arithmetical forcing.
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