“…Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. …”
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“…The appendices provide a refresher in such areas as linear algebra, set theory, random variables, and more. Probability and Random Processes also includes applications in digital communications, informati…”
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“…The salient features of this book include: Strong coverage of key topics involving recurrence relation, combinatorics, Boolean algebra, graph theory and fuzzy set theory. Algorithms and examples integrated throughout the book to bring clarity to the fundamental concepts. …”
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“…Soft computing (SC) consists of several computing paradigms, including neural networks, fuzzy set theory, approximate reasoning, and derivative-free optimization methods such as genetic algorithms. …”
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“…It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. …”
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“…The Lebesgue measure of linear sets is discussed, along with measurable functions and the definite Lebesgue integral.Comprised of 13 chapters, this volume begins with an overview of basic concepts such as set theory, the denumerability and non-denumerability of sets, and open sets and closed sets…”
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“…The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory.Comprised of eight chapters, this book begins with an introduction to first-order logic. …”
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“…Logic Statements, Negation, and Compound Statements Truth Tables and Logical Equivalences Conditional and Biconditional Statements Logical Arguments Open Statements and Quantifiers Chapter Review Deductive Mathematical Systems and Proofs Deductive Mathematical Systems Mathematical Proofs Chapter Review Set Theory Sets and Subsets Set Operations Additional Set Operations Generalized Set Union and Intersection Chapter ReviewRelations Relations The Order Relations , Reflexive, Symmetric, Transitive, and Equivalence Relations Equivalence Relations, Equivalence Classes, and Partitions Chapter Revie…”
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“…Topics include logic, set theory, relations and functions, vectors and matrices, graph theory, counting and binomial theorem, probability, Boolean algebra, and linear programming and …”
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“…Topology includes an overview of elementary set theory, relations and functions, ordinals and cardinals, topological spaces, continuous functions, metric spaces and normed spaces, co…”
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“…Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean…”
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“…It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.The sixth edition incorporates recent work on Gödel's second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. …”
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“…Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. …”
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“…<br><br>Comprised of 10 chapters, this book begins with exercises related to set theory and concepts such as the union and intersection of sets. …”
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“…Topical problems and exercises are discussed on set theory, numbers, functions, limits and continuity, derivative, integral calculus, Rolle’s theorem, mean value theorem, optimization problems, sequences and series. …”
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“…We start by describing the nature of imperfect data, and giving an overview of the various models that have been proposed. Fuzzy sets theory is shown to be an extension of classical set theory, and as such has a proeminent role or modelling imperfect data. …”
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“…Sheaves also appear in logic as carriers for models of set theory. This text presents topos theory as it has developed from the study of sheaves. …”
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“…After a brief survey of Hamiltonian theory and of relevant notions of set theory and manifolds, these lecture notes present some general properties of orbits, paying special attention to integrable systems. …”
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“…The novelty of the proposed approach is that, unlike other rough set theory techniques, it uses the domain knowledge of the data set. …”
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