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The goal of Computer Algebra: Concepts and Techniques is to demystify computer algebra systems for a wide audience including students, faculty, and professionals in scientific fields such as computer science, mathematics, engineering, and physics. Unlike previous books, the only prerequisites are knowledge of first year calculus and a little programming experience - a background that can be assumed of the intended audience. The book is written in a lean and lively style, with numerous examples to illustrate the issues and techniques discussed. It presents the principal algorithms and data structures, while also discussing the inherent and practical limitations of these systems
First Published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.
This volume examines communication processes within the
grandmother-mother-daughter relationship, emphasizing an
intergenerational perspective. Using observations of and extensive
interviews with six sets of middle-income, Caucasian female family
members, this book offers a heuristic account of intergenerational
mother-daughter relational communication.
Originally published in 1988, the purpose of this book was to explore the interrelations among communication, social cognition and affect. The contributors, selected by the editors, were some of the best known in their fields and they significantly added to the knowledge of this interdisciplinary domain at the time. In late April 1986 the authors met at a conference centre at the University of Kentucky. They presented first drafts of their chapters and exchanged ideas. Out of these interactions came this book, which has a broad interest across several areas of psychology and communication. While answering a number of questions, the authors also posed others for future examination.
This book provides a diverse collection of studies reporting the effects of social influence processes in multiple cultures at both the universal and culture-specific levels. The book is characterized by three distinct features. First, the social influence process is considered as a ubiquitous and pervasive feature of human interaction. Second, the book represents a multicultural approach which includes both cross-cultural and culture-focused examinations. Third, the book emphasizes practical implications of the research presented. This volume incorporates theory and research stemming from three different approaches to social influence: social influence principles across cultures, social influence and social change across cultures, and culture and moral perspective in the social influence process. Because each of these three parts encompasses a considerable variety of research methodologies, social contexts, and cultures, each is proceeded by an integrative commentary authored by one of the book editors. These essays provide syntheses of the topics and themes within the corresponding sections and within the book as a whole. They also offer critical commentaries on both theoretical and methodological issues, raise suggestions for future research, and focus on practical applications. This book is intended for both scholars interested in cross- and multicultural research into the mechanisms of the social influence process and for the professional whose mission is to make planned changes in a society. Knowledge about the influence process, especially regarding how it works in different cultures and within several cultural groups, facilitates this goal. The practical implications ending each chapter serve as encouraging instructions for such applications.
This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.
This book explores what social psychology can contribute to our understanding of real-life problems and how it can inform rational interventions in any area of social life. By reviewing some of the most recent achievements in applying social psychology to pressing contemporary problems, Forgas, Crano, and Fiedler convey a fundamentally optimistic message about social psychology's achievements and prospects. The book is organized into four sections. Part I focuses on the basic issues and methods of applying social psychology to real-life problems, discussing evolutionary influences on human sociability, the role of psychological 'mindsets' in interpreting reality, and the use of attitude change techniques to promote adaptive behaviors. Part II explores the applications of social psychology to improve individual health and well-being, including managing aggression, eating disorders, and improving therapeutic interactions. Part III turns to the application of social psychology to improve interpersonal relations and communication, including attachment processes in social relationships, the role of parent-child interaction in preventing adolescent suicide, and analyzing social relations in legal settings and online social networks. Finally, Part IV addresses the question of how social psychology may improve our understanding of public affairs and political behavior. The book will be of interest to students and academics in social psychology, and professionals working in applied settings.
Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne's Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once this embedded manifold, usually of lower codimension, is classified, one tries to reconstruct the original manifold, following a principle appearing also in other areas of geometry such as projective differential geometry or complex geometry.
This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems. In the lectures by Aurelien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament's theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko's unpublished results. The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert's fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin's strict polynomial functors, a conceptual form of modules over the Schur algebra. Roman Mikhailov's lectures highlight topological invariants: homoto py and homology of topological spaces, through derived functors of polynomial functors. In this regard the functor framework makes better use of naturality, allowing it to reach calculations that remain beyond the grasp of classical algebraic topology. Lastly, Antoine Touze's introductory course on homological algebra makes the book accessible to graduate students new to the field. The links between functor homology and the three fields mentioned above offer compelling arguments for pushing the development of the functor viewpoint. The lectures in this book will provide readers with a feel for functors, and a valuable new perspective to apply to their favourite problems.
Exploring Linear Algebra: Labs and Projects with MATLAB (R) is a hands-on lab manual that can be used by students and instructors in classrooms every day to guide the exploration of the theory and applications of linear algebra. For the most part, labs discussed in the book can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems using Mathematica demonstrations (an online tool that can be used with a browser with Java capabilities) and MATLAB (R) coding. This allows students to discover the theory and applications of linear algebra in a meaningful and memorable way. Features: The book's inquiry-based approach promotes student interaction Each chapter contains a project set which consists of application-driven projects emphasizing the chapter's materials Adds a project component to any Linear Algebra course Explores many applications to a variety of fields that can promote research projects Employs MATLAB (R) to calculate and explore concepts and theories of linear algebra
This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems. Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups. The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present.
This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
The conventional wisdom was that biology influenced mathematics and computer science. But a new approach has taken hold: that of transferring methods and tools from computer science to biology. The reverse trend is evident in Grammars and Automata for String Processing: From Mathematics and Computer Science to Biology and Back. The contributors address the structural (syntactical) view of the domain. Mathematical linguistics and computer science can offer various tools for modeling complex macromolecules and for analyzing and simulating biological issues. This collection is valuable for students and researchers in biology, computer science, and applied mathematics.
This book contains several fundamental ideas that are revived time after time in different guises, providing a better understanding of algebraic geometric phenomena. It shows how the field is enriched with loans from analysis and topology and from commutative algebra and homological algebra.
This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many applications of current interest in the theory of nonlinear differential equations are presented to complement the theory. The text is essentially self-contained, so it may also be used as an introduction to topological methods in nonlinear analysis. This volume will appeal to graduate students and researchers in mathematical analysis and its applications.
Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It's main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.
This book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. It presents a breakthrough method for analyzing complex summations. Beautifully written, the book contains practical applications as well as conceptual developments that will have applications in other areas of mathematics. From the table of contents: * Proof Machines * Tightening the Target * The Hypergeometric Database * The Five Basic Algorithms: Sister Celine's Method, Gosper&'s Algorithm, Zeilberger's Algorithm, The WZ Phenomenon, Algorithm Hyper * Epilogue: An Operator Algebra Viewpoint * The WWW Sites and the Software (Maple and Mathematica) Each chapter contains an introduction to the subject and ends with a set of exercises.
Resoundingly popular in its first edition, the second edition of Mechanics of Structures: Variational and Computational Methods promises to be even more so, with broader coverage, expanded discussions, and a streamlined presentation. The authors begin by describing the behavior of deformable solids through the differential equations for the strength of materials and the theory of elasticity. They next introduce variational principles, including mixed or generalized principles, and derive integral forms of the governing equations. Discussions then move to computational methods, including the finite element method, and these are developed to solve the differential and integral equations. New in the second edition: A one-dimensional introduction to the finite element method, complete with illustrations of numerical mesh refinement Expansion of the use of Galerkin's method. Discussion of recent developments in the theory of bending and torsion of thin-walled beams. An appendix summarizing the fundamental equations in differential and variational form Completely new treatment of stability, including detailed examples Discussion of the principal values of geometric properties and stresses Additional exercises As a textbook or as a reference, Mechanics of Structures builds a unified, variational foundation for structure mechanics, which in turn forms the basis for the computational solid mechanics so essential to modern engineering.
This carefully prepared manuscript presents elimination theory in weighted projective spaces over arbitrary noetherian commutative base rings. Elimination theory is a classical topic in commutative algebra and algebraic geometry, and it has become of renewed importance recently in the context of applied and computational algebra. This monograph provides a valuable complement to sparse elimination theory in that it presents in careful detail the algebraic difficulties from working over general base rings. This is essential for applications in arithmetic geometry and many other places. Necessary tools concerning monoids of weights, generic polynomials and regular sequences are treated independently in the first part of the book. Many supplements added to each chapter provide extra details and insightful examples. Necessary tools concerning monoids of weights, generic polynomials and regular sequences are treated independently in the first part of the book. Many supplements added to each chapter provide extra details and insightful examples.
Higher-Order Differential Equations and Elasticity is the third book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This third book consists of two chapters (chapters 5 and 6 of the set). The first chapter in this book concerns non-linear differential equations of the second and higher orders. It also considers special differential equations with solutions like envelopes not included in the general integral. The methods presented include special differential equations, whose solutions include the general integral and special integrals not included in the general integral for myriad constants of integration. The methods presented include dual variables and differentials, related by Legendre transforms, that have application in thermodynamics. The second chapter concerns deformations of one (two) dimensional elastic bodies that are specified by differential equations of: (i) the second-order for non-stiff bodies like elastic strings (membranes); (ii) fourth-order for stiff bodies like bars and beams (plates). The differential equations are linear for small deformations and gradients and non-linear otherwise. The deformations for beams include bending by transverse loads and buckling by axial loads. Buckling and bending couple non-linearly for plates. The deformations depend on material properties, for example isotropic or anisotropic elastic plates, with intermediate cases such as orthotropic or pseudo-isotropic. Discusses differential equations having special integrals not contained in the general integral, like the envelope of a family of integral curves Presents differential equations of the second and higher order, including non-linear and with variable coefficients Compares relation of differentials with the principles of thermodynamics Describes deformations of non-stiff elastic bodies like strings and membranes and buckling of stiff elastic bodies like bars, beams, and plates Presents linear and non-linear waves in elastic strings, membranes, bars, beams, and plates
This book aims to provide an overview of several topics in advanced differential geometry and Lie group theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject.
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.
The concept of the 'ideal city' is, perhaps, more important today - when planners and architects are so firmly confined by considerations of our immediate environment - than ever before. Yet it is a concept which has profoundly influenced the western world throughout history, both as a regulative model and as an inspiration. Rosenau traces the progress of the concept from biblical sources through the hellenistic and Roman empires to the Renaissance and the later Age of Enlightenment, when the emphasis shifted from religious to social considerations. She goes on to discuss the resultant nineteenth-century ideal planning, when the idea of social betterment was approached with a specific and conscious effort. This book was first published in 1983.
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