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Learn how to develop your reasoning skills and how to writewell-reasoned proofs Learning to Reason shows you how to use the basic elements ofmathematical language to develop highly sophisticated, logicalreasoning skills. You'll get clear, concise, easy-to-followinstructions on the process of writing proofs, including thenecessary reasoning techniques and syntax for constructingwell-written arguments. Through in-depth coverage of logic, sets,and relations, Learning to Reason offers a meaningful, integratedview of modern mathematics, cuts through confusing terms and ideas,and provides a much-needed bridge to advanced work in mathematicsas well as computer science. Original, inspiring, and designed formaximum comprehension, this remarkable book: * Clearly explains how to write compound sentences in equivalentforms and use them in valid arguments * Presents simple techniques on how to structure your thinking andwriting to form well-reasoned proofs * Reinforces these techniques through a survey of sets--thebuilding blocks of mathematics * Examines the fundamental types of relations, which is "where theaction is" in mathematics * Provides relevant examples and class-tested exercises designed tomaximize the learning experience * Includes a mind-building game/exercise space atwww.wiley.com/products/subject/mathematics/
This book provides an approachable introduction to mathematical concepts explaining their importance and how they fit into the study of computing. It is written for students who are taking a first unit in 'Computing Mathematics' as part of a Computing Degree or HND. Relating theory to practice helps demonstrate difficult concepts to students. The author therefore concludes most topics with a short discussion of some areas of application to aid comprehension. Self-test questions are included in each chapter to allow the reader to review a topic and check their understanding before progressing. This book provides an approachable introduction to mathematical concepts explaining their importance and how they fit into the study of computing. It is written for students who are taking a first unit in 'Computing Mathematics' as part of a Computing Degree or HND. Relating theory to practice helps demonstrate difficult concepts to students. The author therefore concludes most topics with a short discussion of some areas of application to aid comprehension. Self-test questions are included in each chapter to allow the reader to review a topic and check their understanding before progressing.
This volume contains revised refereed versions of the best papers presented during the CSL '94 conference, held in Kazimierz, Poland in September 1994; CSL '94 is the eighth event in the series of workshops held for the third time as the Annual Conference of the European Association for Computer Science Logic. The 38 papers presented were selected from a total of 151 submissions. All important aspects of the methods of mathematical logic in computer science are addressed: lambda calculus, proof theory, finite model theory, logic programming, semantics, category theory, and other logical systems. Together, these papers give a representative snapshot of the area of logical foundations of computer science.
This first textbook on multi-relational data mining and inductive logic programming provides a complete overview of the field. It is self-contained and easily accessible for graduate students and practitioners of data mining and machine learning.
The book discusses the fate of universality and a universal set in several set theories. The book aims at a philosophical study of ontological and conceptual questions around set theory. Set theories are ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the collection of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the universal set. We have to ask: Are there different aspects to universality in set theory, which stand in conflict to each other? May inconsistency be the price to pay to circumvent ineffability? And most importantly: How far can axiomatic ontology take us out of the problems around universality?