Mathematics

Model Theory

Author: Wilfrid Hodges

Publisher: Cambridge University Press

ISBN: 9780521304429

Category: Mathematics

Page: 772

View: 2789

Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.
Mathematics

The Theory of Partitions

Author: George E. Andrews

Publisher: Cambridge University Press

ISBN: 9780521637664

Category: Mathematics

Page: 255

View: 4727

Discusses mathematics related to partitions of numbers into sums of positive integers.
Computers

Relational Mathematics

Author: Gunther Schmidt

Publisher: Cambridge University Press

ISBN: 0521762685

Category: Computers

Page: 567

View: 9754

A modern, comprehensive 2010 overview providing an easy introduction for applied scientists who are not versed in mathematics.
Mathematics

Boolean Functions

Theory, Algorithms, and Applications

Author: Yves Crama,Peter L. Hammer

Publisher: Cambridge University Press

ISBN: 1139498630

Category: Mathematics

Page: N.A

View: 1158

Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.
Mathematics

Purity, Spectra and Localisation

Author: Mike Prest

Publisher: Cambridge University Press

ISBN: 0521873088

Category: Mathematics

Page: 769

View: 9622

A unified, coherent account of the algebraic aspects and uses of the Ziegler spectrum. It may be used as an introductory graduate-level text, providing relevant background material and a wealth of illustrated examples. An extensive index and thorough referencing also make this book an ideal reference.
Mathematics

A Shorter Model Theory

Author: Wilfrid Hodges

Publisher: Cambridge University Press

ISBN: 9780521587136

Category: Mathematics

Page: 310

View: 3706

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.
Mathematics

Matroid Applications

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521381659

Category: Mathematics

Page: 363

View: 5712

This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).
Mathematics

Graph Structure and Monadic Second-Order Logic

A Language-Theoretic Approach

Author: Bruno Courcelle,Joost Engelfriet

Publisher: Cambridge University Press

ISBN: 1139644009

Category: Mathematics

Page: N.A

View: 4327

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
Mathematics

Building Models by Games

Author: Wilfrid Hodges

Publisher: Courier Corporation

ISBN: 0486450171

Category: Mathematics

Page: 318

View: 3322

This volume introduces a general method for building infinite mathematical structures and surveys applications in algebra and model theory. It covers basic model theory and examines a variety of algebraic applications, including completeness for Magidor-Malitz quantifiers, Shelah's recent and sophisticated omitting types theorem for L(Q), and applications to Boolean algebras. Over 160 exercises. 1985 edition.
Computers

Finite Model Theory and Its Applications

Author: Erich Grädel,Phokion G. Kolaitis,Leonid Libkin,Maarten Marx,Joel Spencer,Moshe Y. Vardi,Yde Venema,Scott Weinstein

Publisher: Springer Science & Business Media

ISBN: 3540688048

Category: Computers

Page: 437

View: 926

Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.
Mathematics

Stochastic Control and Mathematical Modeling

Applications in Economics

Author: Hiroaki Morimoto

Publisher: Cambridge University Press

ISBN: 9780521195034

Category: Mathematics

Page: 340

View: 1419

This is a concise and elementary introduction to stochastic control and mathematical modeling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and non-linear PDE theory. Contents include the basics of analysis and probability, the theory of stochastic differential equations, variational problems, problems in optimal consumption and in optimal stopping, optimal pollution control, and solving the HJB equation with boundary conditions. Major mathematical requisitions are contained in the preliminary chapters or in the appendix so that readers can proceed without referring to other materials.
Mathematics

Dynamic Data Assimilation

A Least Squares Approach

Author: John M. Lewis,S. Lakshmivarahan,Sudarshan Dhall

Publisher: Cambridge University Press

ISBN: 0521851556

Category: Mathematics

Page: 654

View: 1916

Dynamic data assimilation is the assessment, combination and synthesis of observational data, scientific laws and mathematical models to determine the state of a complex physical system, for instance as a preliminary step in making predictions about the system's behaviour. The topic has assumed increasing importance in fields such as numerical weather prediction where conscientious efforts are being made to extend the term of reliable weather forecasts beyond the few days that are presently feasible. This book is designed to be a basic one-stop reference for graduate students and researchers. It is based on graduate courses taught over a decade to mathematicians, scientists, and engineers, and its modular structure accommodates the various audience requirements. Thus Part I is a broad introduction to the history, development and philosophy of data assimilation, illustrated by examples; Part II considers the classical, static approaches, both linear and nonlinear; and Part III describes computational techniques. Parts IV to VII are concerned with how statistical and dynamic ideas can be incorporated into the classical framework. Key themes covered here include estimation theory, stochastic and dynamic models, and sequential filtering. The final part addresses the predictability of dynamical systems. Chapters end with a section that provides pointers to the literature, and a set of exercises with instructive hints.
Mathematics

Mathematical and Computational Modeling

With Applications in Natural and Social Sciences, Engineering, and the Arts

Author: Roderick Melnik

Publisher: John Wiley & Sons

ISBN: 1118853857

Category: Mathematics

Page: 336

View: 9264

Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-the-art achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts also features: Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, industrial, and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.
Mathematics

Encyclopedia of Mathematics

Author: James Stuart Tanton

Publisher: Infobase Publishing

ISBN: 1438110081

Category: Mathematics

Page: 577

View: 8066

Encyclopedia of Mathematics is a comprehensive one-volume encyclopedia designed for high school through early college students. More than 1,000 entries, numerous essays, and more than 125 photographs and illustrations cover the principal areas and issues that characterize this "new" area of science. This valuable resource unites disparate ideas and provides the meaning, history, context, and relevance behind each one. The easy-to-use format makes finding straightforward and natural answers to questions within arithmetic simple. Encyclopedia of Mathematics also gives historical context to mathematical concepts, with entries discussing ancient Arabic, Babylonian, Chinese, Egyptian, Greek, Hindu, and Mayan mathematics, as well as entries providing biographical descriptions of important people in the development of mathematics.
Mathematics

A Course in Model Theory

Author: Katrin Tent,Martin Ziegler

Publisher: Cambridge University Press

ISBN: 052176324X

Category: Mathematics

Page: 248

View: 5920

This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.
Mathematics

The Foundations of Mathematics in the Theory of Sets

Author: John P. Mayberry

Publisher: Cambridge University Press

ISBN: 9780521770347

Category: Mathematics

Page: 424

View: 5975

This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.
Business & Economics

Essentials of Stochastic Finance

Facts, Models, Theory

Author: Albert N. Shiryaev

Publisher: World Scientific

ISBN: 9810236050

Category: Business & Economics

Page: 834

View: 3530

Readership: Undergraduates and researchers in probability and statistics; applied, pure and financial mathematics; economics; chaos.
Mathematics

Andrzej Mostowski and Foundational Studies

Author: A. Ehrenfeucht,V.W. Marek,M. Srebrny

Publisher: IOS Press

ISBN: 1607502720

Category: Mathematics

Page: 460

View: 5739

Andrzej Mostowski was one of the leading 20th century logicians. His legacy is examined in this volume of papers devoted both to his extraordinary scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and person. Professor Mostowski pioneered and mastered many areas of mathematical logic. His contributions spanned set theory, recursion theory, and model theory - the backbone of the foundations of mathematics. The complete detailed bibliography of Mostowski's writings is included. For many years after WWII and especially in the late sixties and until his untimely death in 1975, Warsaw, where he led the centre of foundational studies, was a place where many leading logicians visited, studied, and started their career. Their memories form an important part of this volume, attempting to bring back the extraordinary achievements and personality of Mostowski.
Computers

Instruction Sequences for Computer Science

Author: Jan A Bergstra,Cornelis A. Middelburg

Publisher: Springer Science & Business Media

ISBN: 9491216651

Category: Computers

Page: 232

View: 7588

This book demonstrates that the concept of an instruction sequence offers a novel and useful viewpoint on issues relating to diverse subjects in computer science. Selected issues relating to well-known subjects from the theory of computation and the area of computer architecture are rigorously investigated in this book thinking in terms of instruction sequences. The subjects from the theory of computation, to wit the halting problem and non-uniform computational complexity, are usually investigated thinking in terms of a common model of computation such as Turing machines and Boolean circuits. The subjects from the area of computer architecture, to wit instruction sequence performance, instruction set architectures and remote instruction processing, are usually not investigated in a rigorous way at all.
Computers

Encyclopedia of Information Science and Technology, Third Edition

Author: Khosrow-Pour, Mehdi

Publisher: IGI Global

ISBN: 1466658894

Category: Computers

Page: 10384

View: 4648

"This 10-volume compilation of authoritative, research-based articles contributed by thousands of researchers and experts from all over the world emphasized modern issues and the presentation of potential opportunities, prospective solutions, and future directions in the field of information science and technology"--Provided by publisher.