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The aim of the book is to give a smooth analytic continuation from
basic subjects including linear algebra, group theory, Hilbert
space theory, etc. to number theory. With plenty of practical
examples and worked-out exercises, and the scope ranging from these
basic subjects made applicable to number-theoretic settings to
advanced number theory, this book can then be read without tears.
It will be of immense help to the reader to acquire basic sound
skills in number theory and its applications.Number theory used to
be described as the queen of mathematics, that is, there is no
practical use. However, with the development of computers and the
security of internet communications, the importance of number
theory has been exponentially increasing daily. The raison d'etre
of the present book in this situation is that it is extremely
reader-friendly while keeping the rigor of serious mathematics and
in-depth analysis of practical applications to various subjects
including control theory and pseudo-random number generation. The
use of operators is prevailing rather abundantly in anticipation of
applications to electrical engineering, allowing the reader to
master these skills without much difficulty. It also delivers a
very smooth bridging between elementary subjects including linear
algebra and group theory (and algebraic number theory) for the
reader to be well-versed in an efficient and effortless way. One of
the main features of the book is that it gives several different
approaches to the same topic, helping the reader to gain deeper
insight and comprehension. Even just browsing through the materials
would be beneficial to the reader.
This book emphasizes the role of symmetry and presents as many
viewpoints as possible of an important phenomenon - the functional
equation of the associated zeta-function. It starts from the basics
before warping into the space of new interest; from the ground
state to the excited state. For example, the celebrated Gauss
quadratic reciprocity law is proved in four independent ways, which
are in some way or other dependent on the functional equation. The
proofs rest on finite fields, representation theory of nilpotent
groups, reciprocity law for the Dedekind sums, and the translation
formula for the theta-series, respectively. Likewise, for example,
the Euler function is treated in several different places.One of
the important principles of learning is to work with the material
many times. This book presents many worked-out examples and
exercises to enhance the reader's comprehension on the topics
covered in an in-depth manner. This is done in a different setting
each time such that the reader will always be challenged. For the
keen reader, even browsing the text alone, without solving the
exercises, will yield some knowledge and enjoyment.
This book paves the way for a proper understanding of current and
future issues on global warming, air pollution, depletion of
natural resources, cyberattacks on smart grids, amongst others, by
unifying various diverse disciplines of science to focus on a
sustainable green society of the future.Readers will find
applications of science described through the practical use of
mobilities, in this case, the electric vehicles.The book could be
used to teach and study on issues of global warming through the
window of electric vehicles. The first three chapters can be used
for teaching applications of mechanics, quantum mechanics,
thermodynamics, and fluid mechanics. Chapter 5 provides rudiments
of control theory in anticipation of control theory through number
theory and algebraic geometry. Chapters 6 and 7 contain aspects of
climatology, global warming, and electric vehicles to green grid.
This is the only such comprehensive introductory book in the market
that provides the readers hints, suggestions and directions to
ponder for a sustainable future through renewable sources.
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