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Books > Science & Mathematics > Mathematics > Algebra
The most practical, complete, and accessible guide for
understanding algebra If you want to make sense of algebra, check
out Practical Algebra: A Self-Teaching Guide. Written by two
experienced classroom teachers, this Third Edition is completely
revised to align with the Common Core Algebra I math standards used
in many states. You'll get an overview of solving linear and
quadratic equations, using ratios and proportions, decoding word
problems, graphing and interpreting functions, modeling the real
world with statistics, and other concepts found in today's algebra
courses. This book also contains a brief review of pre-algebra
topics, including arithmetic and fractions. It has concrete
strategies that help diverse students to succeed, such as: over 500
images and tables that illustrate important concepts over 200 model
examples with complete solutions almost 1,500 exercises with
answers so you can monitor your progress Practical Algebra
emphasizes making connections to what you already know and what
you'll learn in the future. You'll learn to see algebra as a
logical and consistent system of ideas and see how it connects to
other mathematical topics. This book makes math more accessible by
treating it as a language. It has tips for pronouncing and using
mathematical notation, a glossary of commonly used terms in
algebra, and a glossary of symbols. Along the way, you'll discover
how different cultures around the world over thousands of years
developed many of the mathematical ideas we use today. Since
students nowadays can use a variety of tools to handle complex
modeling tasks, this book contains technology tips that apply no
matter what device you're using. It also describes strategies for
avoiding common mistakes that students make. By working through
Practical Algebra, you'll learn straightforward techniques for
solving problems, and understand why these techniques work so
you'll retain what you've learned. You (or your students) will come
away with better scores on algebra tests and a greater confidence
in your ability to do math.
Complex analysis is found in many areas of applied mathematics,
from fluid mechanics, thermodynamics, signal processing, control
theory, mechanical and electrical engineering to quantum mechanics,
among others. And of course, it is a fundamental branch of pure
mathematics. The coverage in this text includes advanced topics
that are not always considered in more elementary texts. These
topics include, a detailed treatment of univalent functions,
harmonic functions, subharmonic and superharmonic functions,
Nevanlinna theory, normal families, hyperbolic geometry, iteration
of rational functions, and analytic number theory. As well, the
text includes in depth discussions of the Dirichlet Problem,
Green's function, Riemann Hypothesis, and the Laplace transform.
Some beautiful color illustrations supplement the text of this most
elegant subject.
The Linear Algebra Survival Guide offers a concise introduction to
the difficult core topics of linear algebra, guiding you through
the powerful graphic displays and visualization of Mathematica that
make the most abstract theories seem simple - allowing you to
tackle realistic problems using simple mathematical manipulations.
This resource is therefore a guide to learning the content of
Mathematica in a practical way, enabling you to manipulate
potential solutions/outcomes, and learn creatively. No starting
knowledge of the Mathematica system is required to use the book.
Desktop, laptop, web-based versions of Mathematica are available on
all major platforms. Mathematica Online for tablet and smartphone
systems are also under development and increases the reach of the
guide as a general reference, teaching and learning tool.
Numerical Linear Algebra with Applications is designed for those
who want to gain a practical knowledge of modern computational
techniques for the numerical solution of linear algebra problems,
using MATLAB as the vehicle for computation. The book contains all
the material necessary for a first year graduate or advanced
undergraduate course on numerical linear algebra with numerous
applications to engineering and science. With a unified
presentation of computation, basic algorithm analysis, and
numerical methods to compute solutions, this book is ideal for
solving real-world problems. The text consists of six introductory
chapters that thoroughly provide the required background for those
who have not taken a course in applied or theoretical linear
algebra. It explains in great detail the algorithms necessary for
the accurate computation of the solution to the most frequently
occurring problems in numerical linear algebra. In addition to
examples from engineering and science applications, proofs of
required results are provided without leaving out critical details.
The Preface suggests ways in which the book can be used with or
without an intensive study of proofs. This book will be a useful
reference for graduate or advanced undergraduate students in
engineering, science, and mathematics. It will also appeal to
professionals in engineering and science, such as practicing
engineers who want to see how numerical linear algebra problems can
be solved using a programming language such as MATLAB, MAPLE, or
Mathematica.
Spaces of homogeneous type were introduced as a generalization to
the Euclidean space and serve as a suffi cient setting in which one
can generalize the classical isotropic Harmonic analysis and
function space theory. This setting is sometimes too general, and
the theory is limited. Here, we present a set of fl exible
ellipsoid covers of n that replace the Euclidean balls and support
a generalization of the theory with fewer limitations.
This book is devoted to the structure of the absolute Galois groups
of certain algebraic extensions of the field of rational numbers.
Its main result, a theorem proved by the authors and Florian Pop in
2012, describes the absolute Galois group of distinguished
semi-local algebraic (and other) extensions of the rational numbers
as free products of the free profinite group on countably many
generators and local Galois groups. This is an instance of a
positive answer to the generalized inverse problem of Galois
theory. Adopting both an arithmetic and probabilistic approach, the
book carefully sets out the preliminary material needed to prove
the main theorem and its supporting results. In addition, it
includes a description of Melnikov's construction of free products
of profinite groups and, for the first time in book form, an
account of a generalization of the theory of free products of
profinite groups and their subgroups. The book will be of interest
to researchers in field arithmetic, Galois theory and profinite
groups.
This book presents the latest findings on statistical inference in
multivariate, multilinear and mixed linear models, providing a
holistic presentation of the subject. It contains pioneering and
carefully selected review contributions by experts in the field and
guides the reader through topics related to estimation and testing
of multivariate and mixed linear model parameters. Starting with
the theory of multivariate distributions, covering identification
and testing of covariance structures and means under various
multivariate models, it goes on to discuss estimation in mixed
linear models and their transformations. The results presented
originate from the work of the research group Multivariate and
Mixed Linear Models and their meetings held at the Mathematical
Research and Conference Center in Bedlewo, Poland, over the last 10
years. Featuring an extensive bibliography of related publications,
the book is intended for PhD students and researchers in modern
statistical science who are interested in multivariate and mixed
linear models.
This is the fourth in a series of proceedings of the Combinatorial
and Additive Number Theory (CANT) conferences, based on talks from
the 2019 and 2020 workshops at the City University of New York. The
latter was held online due to the COVID-19 pandemic, and featured
speakers from North and South America, Europe, and Asia. The 2020
Zoom conference was the largest CANT conference in terms of the
number of both lectures and participants. These proceedings contain
25 peer-reviewed and edited papers on current topics in number
theory. Held every year since 2003 at the CUNY Graduate Center, the
workshop surveys state-of-the-art open problems in combinatorial
and additive number theory and related parts of mathematics. Topics
featured in this volume include sumsets, zero-sum sequences,
minimal complements, analytic and prime number theory, Hausdorff
dimension, combinatorial and discrete geometry, and Ramsey theory.
This selection of articles will be of relevance to both researchers
and graduate students interested in current progress in number
theory.
Optimization is the act of obtaining the "best" result under given
circumstances. In design, construction, and maintenance of any
engineering system, engineers must make technological and
managerial decisions to minimize either the effort or cost required
or to maximize benefits. There is no single method available for
solving all optimization problems efficiently. Several optimization
methods have been developed for different types of problems. The
optimum-seeking methods are mathematical programming techniques
(specifically, nonlinear programming techniques). Nonlinear
Optimization: Models and Applications presents the concepts in
several ways to foster understanding. Geometric interpretation: is
used to re-enforce the concepts and to foster understanding of the
mathematical procedures. The student sees that many problems can be
analyzed, and approximate solutions found before analytical
solutions techniques are applied. Numerical approximations: early
on, the student is exposed to numerical techniques. These numerical
procedures are algorithmic and iterative. Worksheets are provided
in Excel, MATLAB(R), and Maple(TM) to facilitate the procedure.
Algorithms: all algorithms are provided with a step-by-step format.
Examples follow the summary to illustrate its use and application.
Nonlinear Optimization: Models and Applications: Emphasizes process
and interpretation throughout Presents a general classification of
optimization problems Addresses situations that lead to models
illustrating many types of optimization problems Emphasizes model
formulations Addresses a special class of problems that can be
solved using only elementary calculus Emphasizes model solution and
model sensitivity analysis About the author: William P. Fox is an
emeritus professor in the Department of Defense Analysis at the
Naval Postgraduate School. He received his Ph.D. at Clemson
University and has taught at the United States Military Academy and
at Francis Marion University where he was the chair of mathematics.
He has written many publications, including over 20 books and over
150 journal articles. Currently, he is an adjunct professor in the
Department of Mathematics at the College of William and Mary. He is
the emeritus director of both the High School Mathematical Contest
in Modeling and the Mathematical Contest in Modeling.
This book is about Lie group analysis of differential equations for
physical and engineering problems. The topics include: --
Approximate symmetry in nonlinear physical problems -- Complex
methods for Lie symmetry analysis -- Lie group classification,
Symmetry analysis, and conservation laws -- Conservative difference
schemes -- Hamiltonian structure and conservation laws of
three-dimensional linear elasticity -- Involutive systems of
partial differential equations This collection of works is written
in memory of Professor Nail H. Ibragimov (1939-2018). It could be
used as a reference book in differential equations in mathematics,
mechanical, and electrical engineering.
Noncommutative geometry studies an interplay between spatial forms
and algebras with non-commutative multiplication. This book covers
the key concepts of noncommutative geometry and its applications in
topology, algebraic geometry, and number theory. Our presentation
is accessible to the graduate students as well as nonexperts in the
field. The second edition includes two new chapters on arithmetic
topology and quantum arithmetic.
This book presents material in two parts. Part one provides an
introduction to crossed modules of groups, Lie algebras and
associative algebras with fully written out proofs and is suitable
for graduate students interested in homological algebra. In part
two, more advanced and less standard topics such as crossed modules
of Hopf algebra, Lie groups, and racks are discussed as well as
recent developments and research on crossed modules.
This book includes discussions related to solutions of such tasks
as: probabilistic description of the investment function;
recovering the income function from GDP estimates; development of
models for the economic cycles; selecting the time interval of
pseudo-stationarity of cycles; estimating
characteristics/parameters of cycle models; analysis of accuracy of
model factors. All of the above constitute the general principles
of a theory explaining the phenomenon of economic cycles and
provide mathematical tools for their quantitative description. The
introduced theory is applicable to macroeconomic analyses as well
as econometric estimations of economic cycles.
This book provides a broad, interdisciplinary overview of
non-Archimedean analysis and its applications. Featuring new
techniques developed by leading experts in the field, it highlights
the relevance and depth of this important area of mathematics, in
particular its expanding reach into the physical, biological,
social, and computational sciences as well as engineering and
technology. In the last forty years the connections between
non-Archimedean mathematics and disciplines such as physics,
biology, economics and engineering, have received considerable
attention. Ultrametric spaces appear naturally in models where
hierarchy plays a central role - a phenomenon known as
ultrametricity. In the 80s, the idea of using ultrametric spaces to
describe the states of complex systems, with a natural hierarchical
structure, emerged in the works of Fraunfelder, Parisi, Stein and
others. A central paradigm in the physics of certain complex
systems - for instance, proteins - asserts that the dynamics of
such a system can be modeled as a random walk on the energy
landscape of the system. To construct mathematical models, the
energy landscape is approximated by an ultrametric space (a finite
rooted tree), and then the dynamics of the system is modeled as a
random walk on the leaves of a finite tree. In the same decade,
Volovich proposed using ultrametric spaces in physical models
dealing with very short distances. This conjecture has led to a
large body of research in quantum field theory and string theory.
In economics, the non-Archimedean utility theory uses probability
measures with values in ordered non-Archimedean fields. Ultrametric
spaces are also vital in classification and clustering techniques.
Currently, researchers are actively investigating the following
areas: p-adic dynamical systems, p-adic techniques in cryptography,
p-adic reaction-diffusion equations and biological models, p-adic
models in geophysics, stochastic processes in ultrametric spaces,
applications of ultrametric spaces in data processing, and more.
This contributed volume gathers the latest theoretical developments
as well as state-of-the art applications of non-Archimedean
analysis. It covers non-Archimedean and non-commutative geometry,
renormalization, p-adic quantum field theory and p-adic quantum
mechanics, as well as p-adic string theory and p-adic dynamics.
Further topics include ultrametric bioinformation, cryptography and
bioinformatics in p-adic settings, non-Archimedean spacetime,
gravity and cosmology, p-adic methods in spin glasses, and
non-Archimedean analysis of mental spaces. By doing so, it
highlights new avenues of research in the mathematical sciences,
biosciences and computational sciences.
This book is the second edition of the first complete study and
monograph dedicated to singular traces. The text offers, due to the
contributions of Albrecht Pietsch and Nigel Kalton, a complete
theory of traces and their spectral properties on ideals of compact
operators on a separable Hilbert space. The second edition has been
updated on the fundamental approach provided by Albrecht Pietsch.
For mathematical physicists and other users of Connes'
noncommutative geometry the text offers a complete reference to
traces on weak trace class operators, including Dixmier traces and
associated formulas involving residues of spectral zeta functions
and asymptotics of partition functions.
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