Is the first book on multi-dimensional spectral theory and inverse scattering
on non-compact manifolds
Serves as a comprehensive introductory guide to PDEs, with minimal
preparatory knowledge of mathematics
Presents an abundance of topics, from boundary value problems in a bounded
domain to lattice problems
The aim of this book is to provide basic knowledge of the inverse problems arising in various
areas in mathematics, physics, engineering, and medical science. These practical problems boil
down to the mathematical question in which one tries to recover the operator (coefficients) or
the domain (manifolds) from spectral data. The characteristic properties of the operators in
question are often reduced to those of Schrodinger operators. We start from the 1-dimensional
theory to observe the main features of inverse spectral problems and then proceed to multidimensions.
The first milestone is the Borg?Levinson theorem in the inverse Dirichlet problem
in a bounded domain elucidating basic motivation of the inverse problem as well as the
difference between 1-dimension and multi-dimension. The main theme is the inverse scattering,
in which the spectral data is Heisenberg’s S-matrix defined through the observation of the
asymptotic behavior at infinity of solutions. Significant progress has been made in the past 30
years by using the Faddeev?Green function or the complex geometrical optics solution by
Sylvester and Uhlmann, which made it possible to reconstruct the potential from the S-matrix
of one fixed energy. One can also prove the equivalence of the knowledge of S-matrix and that
of the Dirichlet-to-Neumann map for boundary value problems in bounded domains. We apply
this idea also to the Dirac equation, the Maxwell equation, and discrete Schrodinger operators
on perturbed lattices. Our final topic is the boundary control method introduced by Belishev
and Kurylev, which is for the moment the only systematic method for the reconstruction of the
Riemannian metric from the boundary observation, which we apply to the inverse scattering on
non-compact manifolds.
Mathematics : Mathematical Physics
Due 2020-11-21
1st ed. 2020, XII, 130 p. 2 illus.
Softcover
ISBN 978-981-15-8198-4
Product category : Brief
Series : SpringerBriefs in Mathematical Physics
Interactions between Geometry, Topology, Number Theory and Algebra,
Leicester, UK, June 2018
Explores new connections between algebraic geometry, representation
theory, group theory, number theory, and algebraic topology in connection
with Galois covers, Grothendieck-Teichmuller Theory and Dessins d'Enfants
Combines research and overview articles by prominent international
researchers
Provides a valuable resource for researchers and students in geometry,
topology, and number theory
This book presents original peer-reviewed contributions from the London Mathematical Society
(LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmuller
Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7
June, 2018. Within the theme of the workshop, the collected articles cover a broad range of
topics and explore exciting new links between algebraic geometry, representation theory, group
theory, number theory and algebraic topology. The book combines research and overview
articles by prominent international researchers and provides a valuable resource for
researchers and students alike.
Mathematics : Algebraic Geometry
Due 2020-10-28
1st ed. 2020, VIII, 240 p. 41 illus., 16 illus. in color.
Hardcover
ISBN 978-3-030-51794-6
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistics
Contains many private and work related photographs
Dedicated to George Andrews’ 80 Birthday th
Complemented by special personal contributions
This book presents a printed testimony for the fact that George Andrews, one of the world’s
leading experts in partitions and q-series for the last several decades, has passed the
milestone age of 80.To honor George Andrews on this occasion, the conference “Combinatory
Analysis 2018” was organized at the Pennsylvania State University from June 21 to 24, 2018.
This volume comprises the original articles from the Special Issue “Combinatory Analysis 2018
? In Honor of George Andrews’ 80thBirthday” resulting from the conference and published in
Annals of Combinatorics. In addition to the 37 articles of the Andrews 80 Special Issue, the
book includes two new papers. These research contributions explore new grounds and present
new achievements, research trends, and problems in the area. The volume is complemented by
three special personal contributions: “The Worlds of George Andrews, a daughter’s take” by
Amy Alznauer, “My association and collaboration with George Andrews” by Krishna Alladi, and
“Ramanujan, his Lost Notebook, its importance” by Bruce Berndt. Another aspect which gives
this Andrews volume a truly unique character is the “Photos” collection. In addition to pictures
taken at “Combinatory Analysis 2018”, the editors selected a variety of photos, many of them
not available elsewhere: “Andrews in Austria”, “Andrews in China”, “Andrews in Florida”,
“Andrews in Illinois”, and “Andrews in India”. This volume will be of interest to researchers,
PhD students, and interested practitioners working in the area of Combinatory Analysis, qSeries,
and related fields
Mathematics : Number Theory
Due 2020-12-14
1st ed. 2020, X, 290 p. 39 illus.
Hardcover
ISBN 978-3-030-57049-1
Product category ] Contributed volume
Series : Trends in Mathematics
Motivates readers to understand the connections between different concepts
when transitioning to higher mathematics
Encourages creative and analytical approaches to solving numerous, carefully
chosen problems
Illustrates the many ways in which mathematics is a vibrant human
enterprise by exploring historical perspectives, current trends, and open
questions
This undergraduate textbook promotes an active transition to higher mathematics. Problem
solving is the heart and soul of this book: each problem is carefully chosen to demonstrate,
elucidate, or extend a concept. More than 300 exercises engage the reader in extensive
arguments and creative approaches, while exploring connections between fundamental
mathematical topics. Divided into four parts, this book begins with a playful exploration of the
building blocks of mathematics, such as definitions, axioms, and proofs. A study of the
fundamental concepts of logic, sets, and functions follows, before focus turns to methods of
proof. Having covered the core of a transition course, the author goes on to present a selection
of advanced topics that offer opportunities for extension or further study. Throughout,
appendices touch on historical perspectives, current trends, and open questions, showing
mathematics as a vibrant and dynamic human enterprise. This second edition has been
reorganized to better reflect the layout and curriculum of standard transition courses. It also
features recent developments and improved appendices. An Invitation to Abstract Mathematics
is ideal for those seeking a challenging and engaging transition to advanced mathematics, and
will appeal to both undergraduates majoring in mathematics, as well as non-math majors
interested in exploring higher-level concepts. From reviews of the first edition:Bajnok’s new
book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics.
… The book can be used as a text for traditional transition or structure courses … but since
Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very
little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously
enthusiastic….
Mathematics : Mathematical Logic and Foundations
Due 2020-12-07
2nd ed. 2020, XVI, 440 p. 61 illus.
Hardcover
ISBN 978-3-030-56173-4
Product category : Undergraduate textbook
Series : Undergraduate Texts in Mathematics
Offers a sound statistical background not found in other books for the type of
problems addressed, like an explicit formulation of the regression model and
the proposal of the statistical test for detection of bias
Includes comparisons of more than two methods, and analyses of model
adequacy and sensitivity, topics not commonly found in the current literature
Features R package with implementing techniques and examples to help
practitioners analyze their own data sets
This book provides an updated account of the regression techniques employed in comparing
analytical methods and to test the biases of one method relative to others ? a problem
commonly found in fields like analytical chemistry, biology, engineering, and medicine. Methods
comparison involves a non-standard regression problem; when a method is to be tested in a
laboratory, it may be used on samples of suitable reference material, but frequently it is used
with other methods on a range of suitable materials whose concentration levels are not known
precisely. By presenting a sound statistical background not found in other books for the type of
problem addressed, this book complements and extends topics discussed in the current
literature. It highlights the applications of the presented techniques with the support of
computer routines implemented using the R language, with examples worked out step-by-step.
This book is a valuable resource for applied statisticians, practitioners, laboratory scientists,
geostatisticians, process engineers, geologists and graduate students.
Statistics : Statistical Theory and Methods
Due 2020-11-22
1st ed. 2020, IV, 86 p. 16 illus., 14 illus. in color.
Softcover
ISBN 978-3-030-57934-0
Product category : Brief
Series : SpringerBriefs in Statistics - ABE
Provides an accessible introduction to the finite element method (FEM),
requiring only minimal prerequisites
Emphasizes angle conditions for FEM convergence for elliptic PDEs with
boundary conditions
Presents 0/1-simplicial partitions of higher-dimensional unit cubes and
maximally symmetric manifolds
This monograph focuses on the mathematical and numerical analysis of simplicial partitions
and the finite element method. This active area of research has become an essential part of
physics and engineering, for example in the study of problems involving heat conduction, linear
elasticity, semiconductors, Maxwell's equations, Einstein's equations and magnetic and
gravitational fields. These problems require the simulation of various phenomena and physical
fields over complicated structures in three (and higher) dimensions. Since not all structures can
be decomposed into simpler objects like d-dimensional rectangular blocks, simplicial partitions
are important. In this book an emphasis is placed on angle conditions guaranteeing the
convergence of the finite element method for elliptic PDEs with given boundary conditions. It is
aimed at a general mathematical audience who is assumed to be familiar with only a few
basic results from linear algebra, geometry, and mathematical and numerical analysis.
Mathematics : Numerical Analysis
Due 2020-11-28
1st ed. 2020, XV, 188 p. 99illus., 10 illus. in color.
Hardcover
ISBN 978-3-030-55676-1
Product category : Monograph
Series : Springer Monographs in Mathematics
Provides a unique account of Sce’s work in the context of the modern
development of the theory of hypercomplex variables
Presents English translations of Sce’s papers that are otherwise hard to find
Includes old, very deep results that are not known to a wide readership
Written in a style that will appeal to a wide audience
This book presents English translations of Michele Sce’s most important works, originally
written in Italian during the period 1955-1973, on hypercomplex analysis and algebras of
hypercomplex numbers. Despite their importance, these works are not very well known in the
mathematics community because of the language they were published in. Possibly the most
remarkable instance is the so-called Fueter-Sce mapping theorem, which is a cornerstone of
modern hypercomplex analysis, and is not yet understood in its full generality. This volume is
dedicated to revealing and describing the framework Sce worked in, at an exciting time when
the various generalizations of complex analysis in one variable were still in their infancy. In
addition to faithfully translating Sce’s papers,the authors discusstheir significance and explain
their connections to contemporary research in hypercomplex analysis. They also discuss many
concrete examples that can serve as a basis for further research. The vast majority of the
results presented here will be new to readers, allowing them to finally accessthe original
sources with the benefit of comments from fellow mathematicians active in the field of
hypercomplex analysis. As such, the book offers not only an important chapter in the history of
hypercomplex analysis, but also a roadmap for further exciting research in the field.
Mathematics : Functions of a Complex Variable
Due 2020-11-21
1st ed. 2020, VI, 120 p. 1 illus.
Hardcover
ISBN 978-3-030-50215-7
Product category : Monograph