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Books > Science & Mathematics > Mathematics
From Euclidian to Hilbert Spaces analyzes the transition from
finite dimensional Euclidian spaces to infinite-dimensional Hilbert
spaces, a notion that can sometimes be difficult for
non-specialists to grasp. The focus is on the parallels and
differences between the properties of the finite and infinite
dimensions, noting the fundamental importance of coherence between
the algebraic and topological structure, which makes Hilbert spaces
the infinite-dimensional objects most closely related to Euclidian
spaces. The common thread of this book is the Fourier transform,
which is examined starting from the discrete Fourier transform
(DFT), along with its applications in signal and image processing,
passing through the Fourier series and finishing with the use of
the Fourier transform to solve differential equations. The
geometric structure of Hilbert spaces and the most significant
properties of bounded linear operators in these spaces are also
covered extensively. The theorems are presented with detailed
proofs as well as meticulously explained exercises and solutions,
with the aim of illustrating the variety of applications of the
theoretical results.
The sixth edition of Meaningful Statistics introduces students to
foundational concepts and demonstrates how statistics are an
integral aspect of their everyday lives-from baseball batting
averages to reports on the median cost of buying a home to the
projected outcomes of an upcoming election. Each chapter begins
with a question and scenario that is then explored through
statistical concepts, demonstrating to students how research and
statistics can help us to answer questions and solve problems. The
opening chapter focuses on the process of collecting data and uses
this information to explore whether multivitamins are a waste of
money. Additional chapters explore linear regression and whether
junk food is harmful to a child's IQ; normal distribution and the
issue of a tie for Olympic downhill gold; confidence intervals and
a simulation of the NBA draft lottery; and more. Students learn
about descriptive measures for populations and samples; probability
and random variables; and sampling distributions, with each concept
corresponding to real-world examples. Closing chapters cover the
testing of hypotheses, tests using the chi-square distribution; and
inferences with two or more populations. For the sixth edition,
exercises and examples have been updated throughout. Designed to
bring key concepts to life, Meaningful Statistics is an ideal
resource for courses in mathematics and statistics.
Physiologically Based Pharmacokinetic (PBPK) Modeling: Methods and
Applications in Toxicology and Risk Assessment presents
foundational principles, advanced techniques and applications of
PBPK modeling. Contributions from experts in PBPK modeling cover
topics such as pharmacokinetic principles, classical physiological
models, the application of physiological models for dose-response
and risk assessment, the use of in vitro information, and in silico
methods. With end-of-chapter exercises that allow readers to
practice and learn the skills associated with PBPK modeling,
dose-response, and its applications to safety and risk assessments,
this book is a foundational resource that provides practical
coverage of PBPK modeling for graduate students, academics,
researchers, and more.
Optimization is a key concept in mathematics, computer science, and
operations research, and is essential to the modeling of any
system, playing an integral role in computer-aided design.
Fundamentals of Optimization Techniques with Algorithms presents a
complete package of various traditional and advanced optimization
techniques along with a variety of example problems, algorithms and
MATLAB (c) code optimization techniques, for linear and nonlinear
single variable and multivariable models, as well as
multi-objective and advanced optimization techniques. It presents
both theoretical and numerical perspectives in a clear and
approachable way. In order to help the reader apply optimization
techniques in practice, the book details program codes and
computer-aided designs in relation to real-world problems. Ten
chapters cover, an introduction to optimization; linear
programming; single variable nonlinear optimization; multivariable
unconstrained nonlinear optimization; multivariable constrained
nonlinear optimization; geometric programming; dynamic programming;
integer programming; multi-objective optimization; and
nature-inspired optimization. This book provides accessible
coverage of optimization techniques, and helps the reader to apply
them in practice.
180 Days of Math is an effective workbook designed to help students
improve their math skills. This easy-to-use first grade workbook is
great for at-home learning or in the classroom. The engaging
standards-based activities cover grade-level skills with easy to
follow instructions and an answer key to quickly assess student
understanding. Each daily practice page includes 8 math problems
covering algebraic thinking, numbers and operations, measurement
and data, and geometry. Watch as student s math confidence grows
with these quick independent learning activities.Parents appreciate
the teacher-approved activity books that keep their child engaged
and learning. Great for homeschooling, to reinforce learning at
school, or prevent learning loss over summer.Teachers rely on the
daily practice workbooks to save them valuable time. The ready to
implement activities are perfect for daily morning review or
homework. The activities can also be used for intervention skill
building to address learning gaps.
Flexible Bayesian Regression Modeling is a step-by-step guide to
the Bayesian revolution in regression modeling, for use in advanced
econometric and statistical analysis where datasets are
characterized by complexity, multiplicity, and large sample sizes,
necessitating the need for considerable flexibility in modeling
techniques. It reviews three forms of flexibility: methods which
provide flexibility in their error distribution; methods which
model non-central parts of the distribution (such as quantile
regression); and finally models that allow the mean function to be
flexible (such as spline models). Each chapter discusses the key
aspects of fitting a regression model. R programs accompany the
methods. This book is particularly relevant to non-specialist
practitioners with intermediate mathematical training seeking to
apply Bayesian approaches in economics, biology, finance,
engineering and medicine.
Classical Mechanics teaches readers how to solve physics problems;
in other words, how to put math and physics together to obtain a
numerical or algebraic result and then interpret these results
physically. These skills are important and will be needed in more
advanced science and engineering courses. However, more important
than developing problem-solving skills and physical-interpretation
skills, the main purpose of this multi-volume series is to survey
the basic concepts of classical mechanics and to provide the reader
with a solid understanding of the foundational content knowledge of
classical mechanics. Classical Mechanics: Conservation Laws and
Rotational Motion covers the conservation of energy and the
conservation of momentum, which are crucial concepts in any physics
course. It also introduces the concepts of center-of-mass and
rotational motion.
In the world of mathematics, the study of fuzzy relations and its
theories are well-documented and a staple in the area of
calculative methods. What many researchers and scientists overlook
is how fuzzy theory can be applied to industries outside of
arithmetic. The framework of fuzzy logic is much broader than
professionals realize. There is a lack of research on the full
potential this theoretical model can reach. Emerging Applications
of Fuzzy Algebraic Structures provides emerging research exploring
the theoretical and practical aspects of fuzzy set theory and its
real-life applications within the fields of engineering and
science. Featuring coverage on a broad range of topics such as
complex systems, topological spaces, and linear transformations,
this book is ideally designed for academicians, professionals, and
students seeking current research on innovations in fuzzy logic in
algebra and other matrices.
This book studies the Dutch mathematician Simon Stevin (1548-1620)
as a new type of 'man of knowledge'. Traditionally, Stevin is best
known for his contributions to the 'Archimedean turn'. This
innovative volume moves beyond this conventional image by bringing
many other aspects of his work into view, by analysing the
connections between the multiple strands of his thinking and by
situating him in a broader European context. Like other
multi-talents ('polymaths') in his time (several of whom are
discussed in this volume), Stevin made an important contribution to
the transformation of the ideal of knowledge in early modern
Europe. This book thus provides new insights into the phenomenon of
'polymaths' in general and in the case of Stevin in particular.
Presents a useful guide for applications of SEM whilst
systematically demonstrating various SEM models using Mplus
Focusing on the conceptual and practical aspects of Structural
Equation Modeling (SEM), this book demonstrates basic concepts and
examples of various SEM models, along with updates on many advanced
methods, including confirmatory factor analysis (CFA) with
categorical items, bifactor model, Bayesian CFA model, item
response theory (IRT) model, graded response model (GRM), multiple
imputation (MI) of missing values, plausible values of latent
variables, moderated mediation model, Bayesian SEM, latent growth
modeling (LGM) with individually varying times of observations,
dynamic structural equation modeling (DSEM), residual dynamic
structural equation modeling (RDSEM), testing measurement
invariance of instrument with categorical variables, longitudinal
latent class analysis (LLCA), latent transition analysis (LTA),
growth mixture modeling (GMM) with covariates and distal outcome,
manual implementation of the BCH method and the three-step method
for mixture modeling, Monte Carlo simulation power analysis for
various SEM models, and estimate sample size for latent class
analysis (LCA) model. The statistical modeling program Mplus
Version 8.2 is featured with all models updated. It provides
researchers with a flexible tool that allows them to analyze data
with an easy-to-use interface and graphical displays of data and
analysis results. Intended as both a teaching resource and a
reference guide, and written in non-mathematical terms, Structural
Equation Modeling: Applications Using Mplus, 2nd edition provides
step-by-step instructions of model specification, estimation,
evaluation, and modification. Chapters cover: Confirmatory Factor
Analysis (CFA); Structural Equation Models (SEM); SEM for
Longitudinal Data; Multi-Group Models; Mixture Models; and Power
Analysis and Sample Size Estimate for SEM. Presents a useful
reference guide for applications of SEM while systematically
demonstrating various advanced SEM models Discusses and
demonstrates various SEM models using both cross-sectional and
longitudinal data with both continuous and categorical outcomes
Provides step-by-step instructions of model specification and
estimation, as well as detailed interpretation of Mplus results
using real data sets Introduces different methods for sample size
estimate and statistical power analysis for SEM Structural Equation
Modeling is an excellent book for researchers and graduate students
of SEM who want to understand the theory and learn how to build
their own SEM models using Mplus.
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