Category: Science & Math

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Combinatorics: A Problem-Based Approach

Description This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside’s lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability. A number of examples are given with explanations while the book also provides more than 300 exercises of different levels of difficulty that are arranged at the end of each chapter, and more than 130 additional challenging problems, including problems from mathematical olympiads. Solutions or hints to all exercises and problems are included. The book can be used by secondary school students preparing for mathematical competitions, by their instructors, and...

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Stochastic Disorder Problems

Description This monograph focuses on those stochastic quickest detection tasks in disorder problems that arise in the dynamical analysis of statistical data. These include quickest detection of randomly appearing targets, of spontaneously arising effects, and of arbitrage (in financial mathematics). There is also currently great interest in quickest detection methods for randomly occurring intrusions in information systems and in the design of defense methods against cyber-attacks. The author shows that the majority of quickest detection problems can be reformulated as optimal stopping problems where the stopping time is the moment the occurrence of disorder is signaled. Thus, considerable attention is devoted to the general theory of optimal stopping rules,...

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Introduction to Mathematical Logic, 6th Edition

Description The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. 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. This appendix last appeared in the first edition. It is offered in the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which...

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The Logic of Infinity

Description Few mathematical results capture the imagination like Georg Cantor’s groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status...

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Photosynthesis in the Marine Environment

Description “Marine photosynthesis provides for at least half of the primary production worldwide…” Photosynthesis in the Marine Environment constitutes a comprehensive explanation of photosynthetic processes as related to the special environment in which marine plants live. The first part of the book introduces the different photosynthesising organisms of the various marine habitats: the phytoplankton (both cyanobacteria and eukaryotes) in open waters, and macroalgae, marine angiosperms and photosymbiont-containing invertebrates in those benthic environments where there is enough light for photosynthesis to support growth, and describes how these organisms evolved. The special properties of seawater for sustaining primary production are then considered, and the two main differences between...

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Computer-Supported Calculus

Description This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledge of one of the most important mathematical software systems, namely, MACSYMA. This will equip them with the mathematical competence they need for science and engi­ neering and the competitive workplace. The choice of MACSYMA is not essential for the didactic goal of the book. In fact, any of the other major mathematical software systems, e. g. , AXIOM, MATHEMATICA, MAPLE, DERIVE, or REDUCE, could have been taken for the examples and for acquiring the skill in using...

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The Mathematical Theory of Elasticity, 2nd Edition

Description Through its inclusion of specific applications, The Mathematical Theory of Elasticity, Second Edition continues to provide a bridge between the theory and applications of elasticity. It presents classical as well as more recent results, including those obtained by the authors and their colleagues. Revised and improved, this edition incorporates additional examples and the latest research results. New to the Second Edition Exposition of the application of Laplace transforms, the Dirac delta function, and the Heaviside function Presentation of the Cherkaev, Lurie, and Milton (CLM) stress invariance theorem that is widely used to determine the effective moduli of elastic composites The Cauchy relations in elasticity A body...

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Participatory Mapping: New Data, New Cartography

Description This book is intended for applications of online digital mapping, called mashups (or composite application), and to analyze the mapping practices in online socio-technical controversies. The hypothesis put forward is that the ability to create an online map accompanies the formation of online audience and provides support for a position in a debate on the Web. The first part provides a study of the map: – a combination of map and statistical reason – crosses between map theories and CIS theories – recent developments in scanning the map, from Geographic Information Systems (GIS) to Web map. The second part is based on a corpus...

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Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Description These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was “Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications”. The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These...

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Proof Theory: The First Step into Impredicativity

Description The kernel of this book consists of a series of lectures on in?nitary proof theory which I gave during my time at the Westfalische ¨ Wilhelms–Universitat ¨ in Munster ¨ . It was planned as a successor of Springer Lecture Notes in Mathematics 1407. H- ever, when preparing it, I decided to also include material which has not been treated in SLN 1407. Since the appearance of SLN 1407 many innovations in the area of – dinal analysis have taken place. Just to mention those of them which are addressed in this book: Buchholz simpli?ed local predicativity by the invention of operator controlled derivations...