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Books > Academic & Education > Professional & Technical > Mathematics
The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English church-bell music. The latter is facilitated by imbedding the right graph of the right group on an appropriate surface, with suitable symmetries. Throughout the emphasis is on Cayley maps: imbeddings of Cayley graphs for finite groups as (possibly branched) covering projections of surface imbeddings of loop graphs with one vertex. This is not as restrictive as it might sound; many developments in topological graph theory involve such imbeddings.
This book presents what in our opinion constitutes the basis of the
theory of the mu-calculus, considered as an algebraic system rather
than a logic. We have wished to present the subject in a unified
way, and in a form as general as possible. Therefore, our emphasis
is on the generality of the fixed-point notation, and on the
connections between mu-calculus, games, and automata, which we also
explain in an algebraic way.
What is often referred to as industrial mathematics is becoming a
more important focus of applied mathematics. An increased interest
in undergraduate control theory courses for mathematics students is
part of this trend. This is due to the fact that control theory is
both quite mathematical and very important in applications."
Introduction to Feedback Control" provides a rigorous introduction
to input/output, controller design for linear systems to
junior/senior level engineering and mathematics students. All
explanations and most examples are single-input, single-output for
ease of exposition. The student is assumed to have knowledge of
linear ordinary differential equations and complex variables.
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.
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
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
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
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 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.
The TI-85 is the latest and most powerful graphing calculator produced by Texas Instruments. This book describes the use of the TI-85 in courses in precalculus, calculus, linear algebra, differential equations, business mathematics, probability, statistics and advanced engineering mathematics. The book features in-depth coverage of the calculator's use in specific course areas by distinguished experts in each field.
This text is concerned primarily with the theory of linear and nonlinear programming, and a number of closely-related problems, and with algorithms appropriate to those problems. In the first part of the book, the authors introduce the concept of duality which serves as a unifying concept throughout the book. The simplex algorithm is presented along with modifications and adaptations to problems with special structures. Two alternative algorithms, the ellipsoidal algorithm and Karmarker's algorithm, are also discussed, along with numerical considerations. the second part of the book looks at specific types of problems and methods for their solution. This book is designed as a textbook for mathematical programming courses, and each chapter contains numerous exercises and examples.
Scientific Computing and Differential Equations: An Introduction to
Numerical Methods, is an excellent complement to Introduction to
Numerical Methods by Ortega and Poole. The book emphasizes the
importance of solving differential equations on a computer, which
comprises a large part of what has come to be called scientific
computing. It reviews modern scientific computing, outlines its
applications, and places the subject in a larger context. * An introductory chapter gives an overview of scientific
computing, indicating its important role in solving differential
equations, and placing the subject in the larger environment
These edited volumes present new statistical methods in a way that
bridges the gap between theoretical and applied statistics. The
volumes cover general problems and issues and more specific topics
concerning the structuring of change, the analysis of time series,
and the analysis of categorical longitudinal data. The book targets
students of development and change in a variety of fields -
psychology, sociology, anthropology, education, medicine,
psychiatry, economics, behavioural sciences, developmental
psychology, ecology, plant physiology, and biometry - with basic
training in statistics and computing.
These edited volumes present new statistical methods in a way that
bridges the gap between theoretical and applied statistics. The
volumes cover general problems and issues and more specific topics
concerning the structuring of change, the analysis of time series,
and the analysis of categorical longitudinal data. The book targets
students of development and change in a variety of fields -
psychology, sociology, anthropology, education, medicine,
psychiatry, economics, behavioural sciences, developmental
psychology, ecology, plant physiology, and biometry - with basic
training in statistics and computing.
Based on a third-year course for French students of physics, this book is a graduate text in functional analysis emphasizing applications to physics. It introduces Lebesgue integration, Fourier and Laplace transforms, Hilbert space theory, theory of distribution a la Laurent Schwartz, linear operators, and spectral theory. It contains numerous examples and completely worked out exercises. |
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