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Books > Academic & Education > Professional & Technical > Mathematics
This book introduces interested readers, practitioners, and researchers to "Mathematica methods for solving practical problems in linear algebra. It contains step-by-step solutions of problems in computer science, economics, engineering, mathematics, statistics, and other areas of application. Each chapter contains both elementary and more challenging problems, grouped by fields of application, and ends with a set of exercises. Selected answers are provided in an appendix. The book contains a glossary of definitions and theorem, as well as a summary of relevant "Mathematica tools. Applications of Linear Algebra can be used both in laboratory sessions and as a source of take-home problems and projects. * Concentrates on problem solving and aims to increase the
readers' analytical skills
A Mathematical Introduction to Logic, Second Edition, offers
increased flexibility with topic coverage, allowing for choice in
how to utilize the textbook in a course. The author has made this
edition more accessible to better meet the needs of today's
undergraduate mathematics and philosophy students. It is intended
for the reader who has not studied logic previously, but who has
some experience in mathematical reasoning. Material is presented on
computer science issues such as computational complexity and
database queries, with additional coverage of introductory material
such as sets.
The geometry of power exponents includes the Newton polyhedron,
normal cones of its faces, power and logarithmic transformations.
On the basis of the geometry universal algorithms for
simplifications of systems of nonlinear equations (algebraic,
ordinary differential and partial differential) were developed.
Designed for advanced engineering, physical science, and applied
mathematics students, this innovative textbook is an introduction
to both the theory and practical application of linear algebra and
functional analysis. The book is self-contained, beginning with
elementary principles, basic concepts, and definitions. The
important theorems of the subject are covered and effective
application tools are developed, working up to a thorough treatment
of eigenanalysis and the spectral resolution theorem. Building on a
fundamental understanding of finite vector spaces, infinite
dimensional Hilbert spaces are introduced from analogy. Wherever
possible, theorems and definitions from matrix theory are called
upon to drive the analogy home. The result is a clear and intuitive
segue to functional analysis, culminating in a practical
introduction to the functional theory of integral and differential
operators. Numerous examples, problems, and illustrations highlight
applications from all over engineering and the physical sciences.
Also included are several numerical applications, complete with
"Mathematica" solutions and code, giving the student a "hands-on"
introduction to numerical analysis. Linear Algebra and Linear
Operators in Engineering is ideally suited as the main text of an
introductory graduate course, and is a fine instrument for
self-study or as a general reference for those applying
mathematics.
This book describes a program of research in computable structure
theory. The goal is to find definability conditions corresponding
to bounds on complexity which persist under isomorphism. The
results apply to familiar kinds of structures (groups, fields,
vector spaces, linear orderings Boolean algebras, Abelian p-groups,
models of arithmetic). There are many interesting results already,
but there are also many natural questions still to be answered. The
book is self-contained in that it includes necessary background
material from recursion theory (ordinal notations, the
hyperarithmetical hierarchy) and model theory (infinitary formulas,
consistency properties).
"Introductory Analysis, Second Edition," is intended for the standard course on calculus limit theories that is taken after a problem solving first course in calculus (most often by junior/senior mathematics majors). Topics studied include sequences, function limits, derivatives, integrals, series, metric spaces, and calculus in n-dimensional Euclidean space * Bases most of the various limit concepts on sequential limits,
which is done first
The aim of the present work is two-fold. Firstly it aims at a
giving an account of many existing algorithms for calculating with
finite-dimensional Lie algebras. Secondly, the book provides an
introduction into the theory of finite-dimensional Lie algebras.
These two subject areas are intimately related. First of all, the
algorithmic perspective often invites a different approach to the
theoretical material than the one taken in various other monographs
(e.g., 42], 48], 77], 86]). Indeed, on various occasions the
knowledge of certain algorithms allows us to obtain a
straightforward proof of theoretical results (we mention the proof
of the Poincare-Birkhoff-Witt theorem and the proof of Iwasawa's
theorem as examples). Also proofs that contain algorithmic
constructions are explicitly formulated as algorithms (an example
is the isomorphism theorem for semisimple Lie algebras that
constructs an isomorphism in case it exists). Secondly, the
algorithms can be used to arrive at a better understanding of the
theory. Performing the algorithms in concrete examples, calculating
with the concepts involved, really brings the theory of life.
In this book, fifteen authors from a wide spectrum of disciplines
(ranging from the natural sciences to the arts) offer assessments
of the way time enters their work, the definition and uses of time
that have proved most productive or problematic, and the lessons
their subjects can offer for our understanding of time beyond the
classroom and laboratory walls. The authors have tried, without
sacrificing analytical rigour, to make their contribution
accessible to a cross-disciplinary readership.
Funded by a National Science Foundation grant, "Discovering Higher Mathematics" emphasizes four main themes that are essential components of higher mathematics: experimentation, conjecture, proof, and generalization. The text is intended for use in bridge or transition courses designed to prepare students for the abstraction of higher mathematics. Students in these courses have normally completed the calculus sequence and are planning to take advanced mathematics courses such as algebra, analysis and topology. The transition course is taken to prepare students for these courses by introducing them to the processes of conjecture and proof concepts which are typically not emphasized in calculus, but are critical components of advanced courses. * Constructed around four key themes: Experimentation,
Conjecture, Proof, and Generalization
Mathematical modeling is the art and craft of building a system of
equations that is both sufficiently complex to do justice to
physical reality and sufficiently simple to give real insight into
the situation. Mathematical Modeling: A Chemical Engineer's
Perspective provides an elementary introduction to the craft by one
of the century's most distinguished practitioners. * Describes pitfalls as well as principles of mathematical
modeling
This book treats modal logic as a theory, with several subtheories,
such as completeness theory, correspondence theory, duality theory
and transfer theory and is intended as a course in modal logic for
students who have had prior contact with modal logic and who wish
to study it more deeply. It presupposes training in mathematical or
logic. Very little specific knowledge is presupposed, most results
which are needed are proved in this book.
Hardbound. This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.
"Elements of the Theory of Numbers" teaches students how to
develop, implement, and test numerical methods for standard
mathematical problems. The authors have created a two-pronged
pedagogical approach that integrates analysis and algebra with
classical number theory. Making greater use of the language and
concepts in algebra and analysis than is traditionally encountered
in introductory courses, this pedagogical approach helps to instill
in the minds of the students the idea of the unity of mathematics.
"Elements of the Theory of Numbers" is a superb summary of
classical material as well as allowing the reader to take a look at
the exciting role of analysis and algebra in number theory.
This new edition of Mathematics for Dynamic Modeling updates a
widely used and highly-respected textbook. The text is appropriate
for upper-level undergraduate and graduate level courses in
modeling, dynamical systems, differential equations, and linear
multivariable systems offered in a variety of departments including
mathematics, engineering, computer science, and economics. The text
features many different realistic applications from a wide variety
of disciplines. * Contains a new chapter on stability of dynamic models
The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any "a priori" assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in "H"1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established. In the nonlinear case, again after "ad hoc" scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Karman equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.
The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems. Scientists involved in discrete mathematics, combinatorics, computer science, information theory, geometry, algebra or number theory will find the book of particular significance. It is designed both as an introductory textbook for the beginner and as a reference book for the expert mathematician and engineer. A number of unsolved problems suitable for research projects are also discussed.
The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: - admissible or permissible inference rules - the derivability of the admissible inference rules - the structural completeness of logics - the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and special attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook.
Fourier Analysis and Boundary Value Problems provides a thorough
examination of both the theory and applications of partial
differential equations and the Fourier and Laplace methods for
their solutions. Boundary value problems, including the heat and
wave equations, are integrated throughout the book. Written from a
historical perspective with extensive biographical coverage of
pioneers in the field, the book emphasizes the important role
played by partial differential equations in engineering and
physics. In addition, the author demonstrates how efforts to deal
with these problems have lead to wonderfully significant
developments in mathematics.
Linear models, normally presented in a highly theoretical and
mathematical style, are brought down to earth in this comprehensive
textbook. Linear Models examines the subject from a mean model
perspective, defining simple and easy-to-learn rules for building
mean models, regression models, mean vectors, covariance matrices
and sums of squares matrices for balanced and unbalanced data sets.
The author includes both applied and theoretical discussions of the
multivariate normal distribution, quadratic forms, maximum
likelihood estimation, less than full rank models, and general
mixed models. The mean model is used to bring all of these topics
together in a coherent presentation of linear model theory.
The contributors and their methods are diverse. Their papers deal
with subjects such as anamorphic art, the geometry of Durer,
musical works of Mozart and Beethoven, the history of negative
numbers, the development of mathematical notation, and efforts to
bring mathematics to bear on problems in commerce and engineering.
All papers have English summaries.
This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as "type-free" or "self-referential." These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these theories provide a new outlook on classical topics, such as inductive definitions and predicative mathematics; (iii) they are particularly promising with regard to applications. Research arising from paradoxes has moved progressively closer to the mainstream of mathematical logic and has become much more prominent in the last twenty years. A number of significant developments, techniques and results have been discovered. Academics, students and researchers will find that the book contains a thorough overview of all relevant research in this field.
This volume contains nine essays dealing with historical issues of
mathematics. The topics covered span three different approaches to
the history of mathematics that may be considered both
representative and vital tothe field. The first section, Images of
Mathematics, addresses the historiographical and philosophical
issues involved in determining the meaning of mathematical history.
The second section, Differential Geometry and Analysis, traces the
convoluted development of the ideas of differential geometry and
analysis. The third section, Research Communities and International
Collaboration, discusses the structure and interaction of
mathematical communities through studies of the social fabric of
the mathematical communities of the U.S. and China. |
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