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Books > Science & Mathematics > Mathematics
This book demonstrates Microsoft EXCEL-based Fourier transform of
selected physics examples. Spectral density of the auto-regression
process is also described in relation to Fourier transform. Rather
than offering rigorous mathematics, readers will "try and feel"
Fourier transform for themselves through the examples. Readers can
also acquire and analyze their own data following the step-by-step
procedure explained in this book. A hands-on acoustic spectral
analysis can be one of the ideal long-term student projects.
This book is a general introduction to the statistical analysis of
networks, and can serve both as a research monograph and as a
textbook. Numerous fundamental tools and concepts needed for the
analysis of networks are presented, such as network modeling,
community detection, graph-based semi-supervised learning and
sampling in networks. The description of these concepts is
self-contained, with both theoretical justifications and
applications provided for the presented algorithms.Researchers,
including postgraduate students, working in the area of network
science, complex network analysis, or social network analysis, will
find up-to-date statistical methods relevant to their research
tasks. This book can also serve as textbook material for courses
related to thestatistical approach to the analysis of complex
networks.In general, the chapters are fairly independent and
self-supporting, and the book could be used for course composition
"a la carte". Nevertheless, Chapter 2 is needed to a certain degree
for all parts of the book. It is also recommended to read Chapter 4
before reading Chapters 5 and 6, but this is not absolutely
necessary. Reading Chapter 3 can also be helpful before reading
Chapters 5 and 7. As prerequisites for reading this book, a basic
knowledge in probability, linear algebra and elementary notions of
graph theory is advised. Appendices describing required notions
from the above mentioned disciplines have been added to help
readers gain further understanding.
Holographic dualities are at the forefront of contemporary physics
research, peering into the fundamental nature of our universe and
providing best attempt answers to humankind's bold questions about
basic physical phenomena. Yet, the concepts, ideas and mathematical
rigors associated with these dualities have long been reserved for
the specific field researchers and experts. This book shatters this
long held paradigm by bringing several aspects of holography
research into the class room, starting at the college physics level
and moving up from there.
In the context of the Fourth Industrial Revolution, a world of
continuous alterations is glimpsed where science and technology are
at the base of economic competitiveness and where innovation plays
a strategic role in global competition, so that they are forced to
cover a series of requirements to compete successfully in an
increasingly globalized economy, including high investments in both
education and research. Along these lines, the formation of
mathematical learning is important because it is oriented towards
the development of a set of skills with the aim of resolving
situations of daily and professional lives. It focuses on the
acquisition of employing the different ways of representing
information in the form of models, constructions, and graphs to
determine the best decision making. In this sense, it includes the
mastery of the handling of numbers, measures, and structures to
carry out the interpretation of operations and representations of a
quantitative nature on personal and professional situations. For a
society to favor innovation, the use of mathematical information is
an essential condition that allows the development of creativity
and analysis of information. Mathematics education plays a vital
role in this development. Developing Mathematical Literacy in the
Context of the Fourth Industrial Revolution studies the formation
of mathematical abilities in the context of the Fourth Industrial
Revolution regarding its development of both teaching and learning
strategies, as well as the use of ICT and its use in the
development of this discipline in students. It is important that
teachers of any educational level reorient their teaching
strategies and their role as educators. Therefore, the chapters
discuss up-to-date and relevant information on teaching and
didactic tasks in the subject of mathematics. This book highlights
mathematical pedagogies, ICT in mathematics learning, teacher
training, and classroom strategies for mathematics. It is intended
for teachers, pedagogical advisors, business trainers, higher
education staff, administrators, teacher educators, practitioners,
stakeholders, researchers, academicians, and students interested in
mathematical literacy in the fourth industrial revolution.
Energy and power are fundamental concepts in electromagnetism and
circuit theory, as well as in optics, signal processing, power
engineering, electrical machines, and power electronics. However,
in crossing the disciplinary borders, we encounter understanding
difficulties due to (1) the many possible mathematical
representations of the same physical objects, and (2) the many
possible physical interpretations of the same mathematical
entities. The monograph proposes a quantum and a relativistic
approach to electromagnetic power theory that is based on recent
advances in physics and mathematics. The book takes a fresh look at
old debates related to the significance of the Poynting theorem and
the interpretation of reactive power. Reformulated in the
mathematical language of geometric algebra, the new expression of
electromagnetic power reflects the laws of conservation of
energy-momentum in fields and circuits. The monograph offers a
mathematically consistent and a physically coherent interpretation
of the power concept and of the mechanism of power transmission at
the subatomic (mesoscopic) level. The monograph proves
(paraphrasing Heaviside) that there is no finality in the
development of a vibrant discipline: power theory.
This engaging review guide and workbook is the ideal tool for
sharpening your Algebra I skills! This review guide and workbook
will help you strengthen your Algebra I knowledge, and it will
enable you to develop new math skills to excel in your high school
classwork and on standardized tests. Clear and concise explanations
will walk you step by step through each essential math concept. 500
practical review questions, in turn, provide extensive
opportunities for you to practice your new skills. If you are
looking for material based on national or state standards, this
book is your ideal study tool! Features: *Aligned to national
standards, including the Common Core State Standards, as well as
the standards of non-Common Core states and Canada*Designed to help
you excel in the classroom and on standardized tests*Concise, clear
explanations offer step-by-step instruction so you can easily grasp
key concepts*You will learn how to apply Algebra I to practical
situations*500 review questions provide extensive opportunities for
you to practice what you've learned
Assuming no previous study in logic, this informal yet rigorous
text covers the material of a standard undergraduate first course
in mathematical logic, using natural deduction and leading up to
the completeness theorem for first-order logic. At each stage of
the text, the reader is given an intuition based on standard
mathematical practice, which is subsequently developed with clean
formal mathematics. Alongside the practical examples, readers learn
what can and can't be calculated; for example the correctness of a
derivation proving a given sequent can be tested mechanically, but
there is no general mechanical test for the existence of a
derivation proving the given sequent. The undecidability results
are proved rigorously in an optional final chapter, assuming
Matiyasevich's theorem characterising the computably enumerable
relations. Rigorous proofs of the adequacy and completeness proofs
of the relevant logics are provided, with careful attention to the
languages involved. Optional sections discuss the classification of
mathematical structures by first-order theories; the required
theory of cardinality is developed from scratch. Throughout the
book there are notes on historical aspects of the material, and
connections with linguistics and computer science, and the
discussion of syntax and semantics is influenced by modern
linguistic approaches. Two basic themes in recent cognitive science
studies of actual human reasoning are also introduced. Including
extensive exercises and selected solutions, this text is ideal for
students in Logic, Mathematics, Philosophy, and Computer Science.
This book provides a concise introduction to both the special
theory of relativity and the general theory of relativity. The
format is chosen to provide the basis for a single semester course
which can take the students all the way from the foundations of
special relativity to the core results of general relativity: the
Einstein equation and the equations of motion for particles and
light in curved spacetime. To facilitate access to the topics of
special and general relativity for science and engineering students
without prior training in relativity or geometry, the relevant
geometric notions are also introduced and developed from the ground
up. Students in physics, mathematics or engineering with an
interest to learn Einstein's theories of relativity should be able
to use this book already in the second semester of their third
year. The book could also be used as the basis of a graduate level
introduction to relativity for students who did not learn
relativity as part of their undergraduate training.
Developments in the use of game theory have impacted multiple
fields and created opportunities for new applications. With the
ubiquity of these developments, there is an increase in the overall
utilization of this approach. Game Theory: Breakthroughs in
Research and Practice contains a compendium of the latest academic
material on the usage, strategies, and applications for
implementing game theory across a variety of industries and fields.
Including innovative studies on economics, military strategy, and
political science, this multi-volume book is an ideal source for
professionals, practitioners, graduate students, academics, and
researchers interested in the applications of game theory.
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