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This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. A wide range of material is presented, from classical results such as Dilworth's, Szpilrajn's and Hashimoto's Theorems to more recent results such as the Li--Milner Structure Theorem. Major topics covered include: chains and antichains, lowest upper and greatest lower bounds, retractions, lattices, the dimension of ordered sets, interval orders, lexicographic sums, products, enumeration, algorithmic approaches and the role of algebraic topology. Since there are few prerequisites, the text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory class. After working through a comparatively lean core, the reader can choose from a diverse range of topics such as structure theory, enumeration or algorithmic aspects. Also presented are some key topics less customary to discrete mathematics/graph theory, including a concise introduction to homology for graphs, and the presentation of forward checking as a more efficient alternative to the standard backtracking algorithm. The coverage throughout provides a solid foundation upon which research can be started by a mathematically mature reader. Rich in exercises, illustrations, and open problems, Ordered Sets: An Introduction is an excellent text for undergraduate and graduate students and a good resource for the interested researcher. Readers will discover order theory's role in discrete mathematics as a supplier of ideas as well as an attractive source of applications.

Ordered sets --- Ensembles ordonnés --- Ensembles ordonnés --- Ensembles ordonnés. --- Mathematical logic. --- Algebra. --- Ordered algebraic structures. --- Combinatorics. --- Algebraic topology. --- Mathematical Logic and Foundations. --- Order, Lattices, Ordered Algebraic Structures. --- Algebraic Topology. --- Topology --- Combinatorics --- Algebra --- Mathematical analysis --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Mathematics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas involved. It can be used for introductory students and is broad and deep enough to bring the reader near the boundaries of current research. Students and researchers in the field will find the book invaluable both as a study material and as a desktop reference.

Set theory --- Set theory. --- Théorie des ensembles --- Mathematical logic. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Syllogism --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical

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Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. To provide a balanced treatment of logic, tableaux are related to deductive proof systems. The logical systems presented are: - Propositional calculus (including binary decision diagrams); - Predicate calculus; - Resolution; - Hoare logic; - Z; - Temporal logic. Answers to exercises (for instructors only) as well as Prolog source code for algorithms may be found via the Springer London web site: http://www.springer.com/978-1-85233-319-5   Mordechai Ben-Ari is an associate professor in the Department of Science Teaching of the Weizmann Institute of Science. He is the author of numerous textbooks on concurrency, programming languages and logic, and has developed software tools for teaching concurrency. In 2004, Ben-Ari received the ACM/SIGCSE Award for Outstanding Contributions to Computer Science Education.

Logic, Symbolic and mathematical --- Logic, Symbolic and mathematical. --- Mathematical logic --- Computer. Automation --- Computers. --- Mathematical logic. --- Theory of Computation. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace

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This book, which is based on Pólya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics. It ends by providing projects for independent study. Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them. Special emphasis is placed on reading carefully and writing well. The authors have included a wide variety of examples, exercises with solutions, problems, and over 40 illustrations, chosen to emphasize these goals. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.

Mathematics --- Technical writing --- Mathematics Teaching & Research --- Physical Sciences & Mathematics --- Study and teaching (Higher) --- 51:37 --- -Technical writing --- -Engineering --- Science --- Scientific writing --- Technology --- Authorship --- Communication of technical information --- Math --- 51:37 Mathematics-:-Opvoeding en onderwijs --(algemeen) --- Mathematics-:-Opvoeding en onderwijs --(algemeen) --- -Study and teaching (Higher) --- -Social aspects --- Mathématiques --- Rédaction technique --- Etude et enseignement (Supérieur) --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical logic. --- Number theory. --- Mathematical Logic and Foundations. --- Analysis. --- Number Theory. --- Engineering --- Logic, Symbolic and mathematical. --- Global analysis (Mathematics). --- Number study --- Numbers, Theory of --- Algebra --- 517.1 Mathematical analysis --- Mathematical analysis --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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Biomolecular computing has emerged as an interdisciplinary ?eld that draws - gether chemistry, computer science, mathematics, molecular biology, and physics. Our knowledge on DNA nanotechnology and biomolecular computing increases exponentially with every passing year. The international meeting on DNA Based Computers has been a forum where scientists with di?erent backgrounds, yet sharing a common interest in biomolecular computing, meet and present their latest results. Continuing this tradition, the 8th International Meeting on DNA Based Computers (DNA8) focuses on the current theoretical and experimental results with the greatest impact. Papers and poster presentations were sought in all areas that relate to b- molecular computing, including (but not restricted to): algorithms and appli- tions, analysis of laboratory techniques/theoretical models, computational p- cesses in vitro and in vivo, DNA-computing-based biotechnological applications, DNA devices, error evaluation and correction, in vitro evolution, models of biomolecular computing (using DNA and/or other molecules), molecular - sign, nucleic acid chemistry, and simulation tools. Papers and posters with new experimental results were particularly encouraged. Authors who wished their work to be considered for either oral or poster presentation were asked to select from one of two submission “tracks”: – Track A - Full Paper – Track B - One-Page Abstract For authors with late-breaking results, or who were submitting their manuscript to a scienti?c journal, a one-page abstract, rather than a full paper, could be submitted in Track B. Authors could (optionally) include a preprint of their full paper, for consideration only by the program committee.

Molecular computers --- Computer Science --- Engineering & Applied Sciences --- Mathematics. --- Computers. --- Algorithms. --- Artificial intelligence. --- Bioinformatics. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Computation by Abstract Devices. --- Algorithm Analysis and Problem Complexity. --- Artificial Intelligence (incl. Robotics). --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Bio-informatics --- Biological informatics --- Biology --- Information science --- Computational biology --- Systems biology --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algorism --- Algebra --- Arithmetic --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Calculators --- Cyberspace --- Math --- Science --- Data processing --- Foundations --- Logic, Symbolic and mathematical. --- Computer science. --- Computer software. --- Artificial Intelligence. --- Software, Computer --- Informatics