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Books > Science & Mathematics > Mathematics
Over the last number of years powerful new methods in analysis and
topology have led to the development of the modern global theory of
symplectic topology, including several striking and important
results. The first edition of Introduction to Symplectic Topology
was published in 1995. The book was the first comprehensive
introduction to the subject and became a key text in the area. A
significantly revised second edition was published in 1998
introducing new sections and updates on the fast-developing area.
This new third edition includes updates and new material to bring
the book right up-to-date.
The book contains a detailed account of numerical solutions of
differential equations of elementary problems of Physics using
Euler and 2nd order Runge-Kutta methods and Mathematica 6.0. The
problems are motion under constant force (free fall), motion under
Hooke's law force (simple harmonic motion), motion under
combination of Hooke's law force and a velocity dependent damping
force (damped harmonic motion) and radioactive decay law. Also
included are uses of Mathematica in dealing with complex numbers,
in solving system of linear equations, in carrying out
differentiation and integration, and in dealing with matrices.
Few artworks have been the subject of more extensive modern
interpretation than Melencolia I by renowned artist, mathematician,
and scientist Albrecht Durer (1514). And yet, did each of these art
experts and historians miss a secret manifesto that Durer included
within the engraving? This is the first work to decrypt secrets
within Melencolia I based not on guesswork, but Durer's own
writings, other subliminal artists that inspired him (i.e.,
Leonardo da Vinci), the Jewish and Christian Bibles, and books that
inspired Durer (De Occulta Philosophia and the Hieorglyphica). To
read the covert message of Melencolia I is to understand that Durer
was a humanist in his interests in mathematics, science, poetry,
and antiquity. This book recognizes his unparalleled power with the
burin, his mathematical skill in perspective, his dedication to
precise language, and his acute observation of nature. Melencolia I
may also be one of the most controversial (and at the time most
criminal) pieces of art as it hid Durer's disdain for the hierarchy
of the Catholic Church, the Kaiser, and the Holy Roman Empire from
the general public for centuries. This book closely ties the
origins of philosophy (science) and the work of a Renaissance
master together, and will be of interest for anyone who loves
scientific history, art interpretation, and secret manifestos.
Theory and Computation of Tensors: Multi-Dimensional Arrays
investigates theories and computations of tensors to broaden
perspectives on matrices. Data in the Big Data Era is not only
growing larger but also becoming much more complicated. Tensors
(multi-dimensional arrays) arise naturally from many engineering or
scientific disciplines because they can represent multi-relational
data or nonlinear relationships.
Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition,
is the first systematic exposition of the theory of local iterated
function systems, local fractal functions and fractal surfaces, and
their connections to wavelets and wavelet sets. The book is based
on Massopust's work on and contributions to the theory of fractal
interpolation, and the author uses a number of tools-including
analysis, topology, algebra, and probability theory-to introduce
readers to this exciting subject. Though much of the material
presented in this book is relatively current (developed in the past
decades by the author and his colleagues) and fairly specialized,
an informative background is provided for those entering the field.
With its coherent and comprehensive presentation of the theory of
univariate and multivariate fractal interpolation, this book will
appeal to mathematicians as well as to applied scientists in the
fields of physics, engineering, biomathematics, and computer
science. In this second edition, Massopust includes pertinent
application examples, further discusses local IFS and new fractal
interpolation or fractal data, further develops the connections to
wavelets and wavelet sets, and deepens and extends the pedagogical
content.
Lie superalgebras are a natural generalization of Lie algebras,
having applications in geometry, number theory, gauge field theory,
and string theory. Introduction to Finite and Infinite Dimensional
Lie Algebras and Superalgebras introduces the theory of Lie
superalgebras, their algebras, and their representations. The
material covered ranges from basic definitions of Lie groups to the
classification of finite-dimensional representations of semi-simple
Lie algebras. While discussing all classes of finite and infinite
dimensional Lie algebras and Lie superalgebras in terms of their
different classes of root systems, the book focuses on Kac-Moody
algebras. With numerous exercises and worked examples, it is ideal
for graduate courses on Lie groups and Lie algebras.
Science Without Numbers caused a stir in philosophy on its original
publication in 1980, with its bold nominalist approach to the
ontology of mathematics and science. Hartry Field argues that we
can explain the utility of mathematics without assuming it true.
Part of the argument is that good mathematics has a special feature
("conservativeness") that allows it to be applied to "nominalistic"
claims (roughly, those neutral to the existence of mathematical
entities) in a way that generates nominalistic consequences more
easily without generating any new ones. Field goes on to argue that
we can axiomatize physical theories using nominalistic claims only,
and that in fact this has advantages over the usual axiomatizations
that are independent of nominalism. There has been much debate
about the book since it first appeared. It is now reissued in a
revised contains a substantial new preface giving the author's
current views on the original book and the issues that were raised
in the subsequent discussion of it.
Biostatistics and Computer-Based Analysis of Health Data Using the
R Software addresses the concept that many of the actions performed
by statistical software comes back to the handling, manipulation,
or even transformation of digital data. It is therefore of primary
importance to understand how statistical data is displayed and how
it can be exploited by software such as R. In this book, the
authors explore basic and variable commands, sample comparisons,
analysis of variance, epidemiological studies, and censored data.
With proposed applications and examples of commands following each
chapter, this book allows readers to apply advanced statistical
concepts to their own data and software.
The Mathematical Brain Across the Lifespan is the latest volume in
the Progress in Brain Research series that focuses on new trends
and developments. This established international series examines
major areas of basic and clinical research within the
neurosciences, as well as popular and emerging subfields.
The UK's most trusted A level Mathematics resources With over
900,000 copies sold (plus 1.3 million copies sold of the previous
edition), Pearson's own resources for Pearson Edexcel are the
market-leading and most trusted for AS and A level Mathematics.
This book covers all the content needed for the optional Edexcel AS
and A level Further Mechanics 1 exams Enhanced focus on
problem-solving and modelling, as well as supporting the large data
set and calculators Packed with worked examples with guidance, lots
of exam-style questions, practice papers, and plenty of mixed and
review exercises Full worked solutions to every question available
free and online for quick and easy access. Plus free additional
online content with GeoGebra interactives and Casio calculator
tutorials Practice books also available offering the most
comprehensive and flexible AS/A level Maths practice with over 2000
extra questions Includes access to an online digital edition (valid
for 3 years once activated) Pearson Edexcel AS and A level Further
Mathematics Further Statistics 2 Textbook + e-book matches the
Pearson Edexcel exam structure and is fully integrated with Pearson
Edexcel's interactive scheme of work. All of the books in this
series focus on problem-solving and modelling, as well as
supporting the large data set and calculators. They are packed with
worked examples with guidance, lots of exam-style questions,
practice papers, and plenty of mixed and review exercises. There
are full worked solutions to every question available free and
online for quick and easy access. You will also have access to lots
of free additional online content with GeoGebra interactives and
Casio calculator tutorials. There are separate Pure and Applied
textbooks for AS and A level Maths, and a textbook per option for
AS and A level Further Maths. Practice books are also available
offering the most comprehensive and flexible AS/A level Maths
practice with over 2000 extra questions. Pearson's revision
resources are the smart choice for those revising for Pearson
Edexcel AS and A level Mathematics - there is a Revision Workbook
for exam practice and a Revision Guide for classroom and
independent study. Practice Papers Plus+ books contain additional
full length practice papers, so you can practice answering
questions by writing straight into the book and perfect your
responses with targeted hints, guidance and support for every
question, including fully worked solutions.
Semihypergroup Theory is the first book devoted to the
semihypergroup theory and it includes basic results concerning
semigroup theory and algebraic hyperstructures, which represent the
most general algebraic context in which reality can be modelled.
Hyperstructures represent a natural extension of classical
algebraic structures and they were introduced in 1934 by the French
mathematician Marty. Since then, hundreds of papers have been
published on this subject.
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