1st ed. 2017, XIII, 454 p.
Hardcover
ISBN 978-981-10-4252-2
Series: Infosys Science Foundation Series in Mathematical Sciences
* Presents an accessible introduction to the major theorems of modern algebra
* Provides a clear and motivating exposition with numerous examples and exercises
* Is written by an expert with over 43 years of teaching experience of the subject
This is the first in a series of three volumes dealing with important topics in algebra. It
offers an introduction to the foundations of mathematics together with the fundamental
algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for
undergraduate and graduate students of mathematics, it discusses all major topics in
algebra with numerous motivating illustrations and exercises to enable readers to acquire
a good understanding of the basic algebraic structures, which they can then use to find
the exact or the most realistic solutions to their problems.
1st ed. 2017, XIII, 458 p.
Hardcover
ISBN 978-981-10-4255-3
Series: Infosys Science Foundation Series in Mathematical Sciences
* Provides a concise and rigorous introduction to linear algebra
* Includes a large number of motivating illustrations and challenging exercises
* Is written by an expert with over 43 years of teaching experience of the subject
This is the second in a series of three volumes dealing with important topics in algebra.
Volume 2 is an introduction to linear algebra (including linear algebra over rings), Galois
theory, representation theory, and the theory of group extensions. The section on
linear algebra (chapters 1*5) does not require any background material from Algebra
1, except an understanding of set theory. Linear algebra is the most applicable branch
of mathematics, and it is essential for students of science and engineering As such, the
text can be used for one-semester courses for these students. The remaining part of the
volume discusses Jordan and rational forms, general linear algebra (linear algebra over
rings), Galois theory, representation theory (linear algebra over group algebras), and the
theory of extension of groups follow linear algebra, and is suitable as a text for the second
and third year students specializing in mathematics.
1st ed. 2017, VIII, 838 p. 2 volume-set.
Hardcover
ISBN 978-3-319-55860-8
Series: Applied and Numerical Harmonic Analysis
* Exhibits several recently discovered links between traditional
harmonic analysis and modern ideas in areas such as Riemannian geometry and sheaf theory
* Contains both deep theoretical results and innovative applications to
various fields such as medical imagine and data science
* Only publication of its kind extending classical harmonic analysis to
manifolds, graphs, and other general structures
* Comprised of original research and survey papers from well-known experts
A two volume set on novel methods in harmonic analysis, these books draw on a number
of original research and survey papers from well-known specialists detailing the latest
innovations and recently discovered links between various fields. Along with many deep
theoretical results, these volumes contain numerous applications to problems in signal
processing, medical imaging, geodesy, statistics, and data science.
The chapters within cover an impressive range of ideas from both traditional and
modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames,
wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and
sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on
combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological
spaces.
1st ed. 2017, X, 166 p. 13 illus. in color.
Softcover
ISBN 978-3-319-55975-9
Series: Frontiers in Mathematics
* Up-to-date account of KantorovichLs theory for NewtonLs method
* Starts with a detailed presentation of KantorovichLs approach and
ends with new results and alternative approaches
* Contains many numerical examples involving nonlinear integral equations
The book shows the importance of studying semilocal convergence in iterative methods
through Newton's method and addresses the most important aspects of the Kantorovich's
theory including implicated studies. Kantorovich's theory for Newton's method used
techniques of functional analysis to prove the semilocal convergence of the method by
means of the well-known majorant principle. To gain a deeper understanding of these
techniques the authors return to the beginning and present a deep-detailed approach of
Kantorovich's theory for Newton's method, where they include old results, for a historical
perspective and for comparisons with new results, refine old results, and prove their
most relevant results, where alternative approaches leading to new sufficient semilocal
convergence criteria for Newton's method are given. The book contains many numerical
examples involving nonlinear integral equations, two boundary value problems and
systems of nonlinear equations related to numerous physical phenomena. The book is
addressed to researchers in computational sciences, in general, and in approximation of
solutions of nonlinear problems, in particular.
1st ed. 2017, Approx. 350 p.
Hardcover
ISBN 978-3-319-52469-6
Series: Trends in Mathematics
* Introduces the reader to the theory of functions of several complex variables
* Explains geometric ideas
* Presents papers on the border between analysis and geometry
This book is dedicated to the memory of Mikael Passare, an outstanding Swedish
mathematician who devoted his life to developing the theory of analytic functions in
several complex variables and exploring geometric ideas first-hand. It includes several
papers describing Mikaelfs life as well as his contributions to mathematics, written by
friends of Mikaelfs who share his attitude and passion for science. A major section of the
book presents original research articles that further develop Mikaelfs ideas and which
were written by his former students and co-authors. All these mathematicians work at
the interface of analysis and geometry, and Mikaelfs impact on their research cannot
be underestimated. Most of the contributors were invited speakers at the conference
organized at Stockholm University in his honor. This book is an attempt to express our
gratitude towards this great mathematician, who left us full of energy and new creative
mathematical ideas.