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Books > Academic & Education > Professional & Technical > Mathematics
General concepts and methods that occur throughout mathematics and
now also in theoretical computer science are the subject of this
book. It is a thorough introduction to Categories, emphasizing the
geometric nature of the subject and explaining its connections to
mathematical logic. The book should appeal to the inquisitive
reader who has seen some basic topology and algebra and would like
to learn and explore further.
Chapter 1 presents theorems on differentiable functions often used
in differential topology, such as the implicit function theorem,
Sard's theorem and Whitney's approximation theorem.
In this book the authors try to bridge the gap between the treatments of matrix theory and linear algebra. It is aimed at graduate and advanced undergraduate students seeking a foundation in mathematics, computer science, or engineering. It will also be useful as a reference book for those working on matrices and linear algebra for use in their scientific work.
Essential Computational Modeling for the Human Body presents key contributions selected from the volume in the Handbook of Numerical Analysis: Computational Modeling for the Human Body Vol. 12 (2005). Computational (Mathematical) Modeling is used by scientists and
researchers with various applications in chemical, biological,
behavioral, environmental sciences, etc. This guide presents
essential research techniques for analysis and essential concrete
examples of computational models, while supplying a wide range of
commonly used methods and applications, followed by various
numerical simulations. Provides various viewpoints of methods and applications are available for researchers to chose and experiment with; Numerical analysis and open problems useful for experimentation; Computational Models useful for surgery simulations;
Essential Numerical Methods for Electromagnetics presents key contributions selected from the volume in the Handbook of Numerical Analysis: Numerical Methods for Electromagnetics Vol. 13 (2005). This reference is an accessible resource on the basics of
modeling. It is designed to assist professionals in the development
of electromagnetic designs for electronic components and devices.
It provides essential numerical methods and applications necessary
for the development of technologies and simulation modeling.
Numerical methods are a key ingredient in a simulation environment
where researchers create virtually simulated experiments versus
physical experiments. This book serves as a useful guide for
scientists, engineers, and researchers providing a quick reference
of commonly used numerical methods to help solve a variety of
problems in the electronic industry. The basics of modeling aspects provide an accessible resource; Numerical solution procedures for quick reference; Special numerical techniques are presented to assist in specialization; Most commonly used methods and applications to create simulation experiments;
Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for over 35 years to introduce junior and senior-level undergraduate engineering students, as well as graduate students, to the basic principles of continuum mechanics and their applications to real engineering problems. The text begins with a detailed presentation of the coordinate invariant quantity, the tensor, introduced as a linear transformation. This is then followed by the formulation of the kinematics of deformation, large as well as very small, the description of stresses and the basic laws of continuum mechanics. As applications of these laws, the behaviors of certain material idealizations (models) including the elastic, viscous and viscoelastic materials, are presented. This new edition offers expanded coverage of the subject matter
both in terms of details and contents, providing greater
flexibility for either a one or two-semester course in either
continuum mechanics or elasticity. Although this current edition
has expanded the coverage of the subject matter, it nevertheless
uses the same approach as that in the earlier editions - that one
can cover advanced topics in an elementary way that go from simple
to complex, using a wealth of illustrative examples and problems.
It is, and will remain, one of the most accessible textbooks on
this challenging engineering subject. New section at the end of Chapter 4 devoted to the integral formulation of the field equations Seven new appendices appear at the end of the relevant chapters to help make each chapter more self-contained Expanded and improved problem sets providing both intellectual challenges and engineering applications
Completely updated guide for scientists, engineers and students who
want to use Microsoft Excel 2007 to its full potential.
This monograph began life as a series of papers documenting five years of research into the logical foundations of Categorial Grammar, a grammatical paradigm which has close analogies with Lambda Calculus and Type Theory. The technical theory presented here stems from the interface between Logic and Linguistics and, in particular, the theory of generalized quantification. A categorical framework with lambda calculus-oriented semantics is a convenient vehicle for generalizing semantic insights (obtained in various corners of natural language) into one coherent theory.
Information Security is usually achieved through a mix of
technical, organizational and legal measures. These may include the
application of cryptography, the hierarchical modeling of
organizations in order to assure confidentiality, or the
distribution of accountability and responsibility by law, among
interested parties.
The material collected in this volume reflects the active present
of this area of mathematics, ranging from the abstract theory of
gradient flows to stochastic representations of non-linear
parabolic PDE's.
This book comes out of need and urgency (expressed especially in
areas of Information Retrieval with respect to Image, Audio,
Internet and Biology) to have a working tool to compare data.
This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.
The Handbook of Mathematical Fluid Dynamics is a compendium of
essays that provides a survey of the major topics in the subject.
Each article traces developments, surveys the results of the past
decade, discusses the current state of knowledge and presents major
future directions and open problems. Extensive bibliographic
material is provided. The book is intended to be useful both to
experts in the field and to mathematicians and other scientists who
wish to learn about or begin research in mathematical fluid
dynamics. The Handbook illuminates an exciting subject that
involves rigorous mathematical theory applied to an important
physical problem, namely the motion of fluids.
Computational Geometry is an area that provides solutions to
geometric problems which arise in applications including Geographic
Information Systems, Robotics and Computer Graphics. This Handbook
provides an overview of key concepts and results in Computational
Geometry. It may serve as a reference and study guide to the field.
Not only the most advanced methods or solutions are described, but
also many alternate ways of looking at problems and how to solve
them.
Volume II of "Classical Recursion Theory" describes the universe
from a local (bottom-up
Topology, for many years, has been one of the most exciting and
influential fields of research in modern mathematics. Although its
origins may be traced back several hundred years, it was Poincare
who "gave topology wings" in a classic series of articles published
around the turn of the century. While the earlier history,
sometimes called the prehistory, is also considered, this volume is
mainly concerned with the more recent history of topology, from
Poincare onwards.
A collection of self contained state-of-the art surveys. The
authors have made an effort to achieve readability for
mathematicians and scientists from other fields, for this series of
handbooks to be a new reference for research, learning and
teaching.
Probability is relevant to so many different subject areas that its
importance as a mathematical technique cannot be underestimated.
This book provides a comprehensive, user-friendly introduction to
the subject. The step-by-step approach taken by the author allows
students to develop knowledge at their own pace and, by working
through the numerous exercises, they are ensured a full
understanding of the material before moving on to more advanced
sections. Traditional examples of probablistic theory, such as
coins and dice, are included but the author has also used many
exercises based on real-life problems. The result is an
introduction to probability that avoids the overly confusing,
theoretical approach often adopted in this area, and provides a
simple and concise text that will be invaluable to all studying
first and second year courses on the subject.
This first part presents chapters on models of computation,
complexity theory, data structures, and efficient computation in
many recognized sub-disciplines of Theoretical Computer Science.
Techniques of physics find wide application in biology, medicine, engineering and technology generally. This series is devoted to techniques which have found and are finding application. The aim is to clarify the principles of each technique, to emphasize and illustrate the applications and to draw attention to new fields of possible employment.
This book is a landmark title in the continuous move from integer
to non-integer in mathematics: from integer numbers to real
numbers, from factorials to the gamma function, from integer-order
models to models of an arbitrary order. For historical reasons, the
word 'fractional' is used instead of the word 'arbitrary'.
This English version of the path-breaking French book on this
subject gives the definitive treatment of the revolutionary
approach to measure theory, geometry, and mathematical physics
developed by Alain Connes. Profusely illustrated and invitingly
written, this book is ideal for anyone who wants to know what
noncommutative geometry is, what it can do, or how it can be used
in various areas of mathematics, quantization, and elementary
particles and fields.
Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.
This book is an exposition of "semi-Riemannian geometry" (also called "pseudo-Riemannian geometry")--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.
Probability theory is a rapidly expanding field and is used in
many areas of science and technology. Beginning from a basis of
abstract analysis, this mathematics book develops the knowledge
needed for advanced students to develop a complex understanding of
probability. The first part of the book systematically presents
concepts and results from analysis before embarking on the study of
probability theory. The initial section will also be useful for
those interested in topology, measure theory, real analysis and
functional analysis. The second part of the book presents the
concepts, methodology and fundamental results of probability
theory. Exercises are included throughout the text, not just at the
end, to teach each concept fully as it is explained, including
presentations of interesting extensions of the theory. The complete
and detailed nature of the book makes it ideal as a reference book
or for self-study in probability and related fields. |
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