The first book treating minimal surfaces in Euclidean spaces by complex
analytic methods, many of which have been developed only recently
Treats the global theory of minimal surfaces with a given complex structure,
providing new results
Offers new directions in the theory of minimal surfaces and exposes several
challenging open problems
This monograph offers the first systematic treatment of the theory of minimal surfaces in
Euclidean spaces by complex analytic methods, many of which have been developed in recent
decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places
particular emphasis on the study of the global theory of minimal surfaces with a given
complex structure. Advanced methods of holomorphic approximation, interpolation, and
homotopy classification of manifold-valued maps, along with elements of convex integration
theory, are implemented for the first time in the theory of minimal surfaces. The text also
presents newly developed methods for constructing minimal surfaces in minimally convex
domains of Rn, based on the Riemann?Hilbert boundary value problem adapted to minimal
surfaces and holomorphic null curves. These methods also provide major advances in the
classical Calabi?Yau problem, yielding in particular minimal surfaces with the conformal
structure of any given bordered Riemann surface. Offering new directions in the field and
several challenging open problems, the primary audience of the book are researchers
(including postdocs and PhD students) in differential geometry and complex analysis. Although
not primarily intended as a textbook, two introductory chapters surveying background material
and the classical theory of minimal surfaces also make it suitable for preparing Masters or
PhD level courses.
1st ed. 2021, XIII, 430 p.
24 illus., 21 illus. in color.
Hardcover
IProduct category : Monograph
Series : Springer Monographs in Mathematics
Mathematics : Global Analysis and Analysis on Manifolds
Covers important topics in quantum computing and its applications
Offers a valuable quantum computing textbook
Encourages readers to pursue a career in the STEM (science, technology,
engineering, and mathematics) fields
This book discusses the application of quantum mechanics to computing. It explains the
fundamental concepts of quantum mechanics and then goes on to discuss various elements of
mathematics required for quantum computing. Quantum cryptography, waves and Fourier
analysis, measuring quantum systems, comparison to classical mechanics, quantum gates, and
important algorithms in quantum computing are among the topics covered. The book offers a
valuable resource for graduate and senior undergraduate students in STEM (science,
technology, engineering, and mathematics) fields with an interest in designing quantum
algorithms. Readers are expected to have a firm grasp of linear algebra and some familiarity
with Fourier analysis.
1st ed. 2020, XVII, 265 p.
28 illus., 7 illus. in color.
Hardcover
ISBN 978-981-15-2470-7
Softcover
ISBN 978-981-15-2473-8
Product category : Graduate/advanced undergraduate textbook
Series : Undergraduate Lecture Notes in Physics
Mathematics : Quantum Computing
This book contains two parts: The first six chapters present the modern
mathematical theory of boundary integral equations with applications on
fundamental problems in continuum mechanics and electromagnetics, while
the second six chapters present an introduction to the basic theory of
classical pseudo-differential operators so that the particular boundary
integral equations arising in the aforementioned applications can be recast as
pseudo-differential equations which serve as concrete examples illustrating
the basic ideas how one may apply the theory of pseudo-differential operators
and their calculus to obtain basic properties for the corresponding boundary
integral operators. The book is unique in the sense
This is the second edition of the book which has two additional new chapters on Maxwell?fs
equations as well as a section on properties of solution spaces of Maxwell?fs equations and
their trace spaces. These two new chapters, which summarize the most up-to-date results in
the literature for the Maxwell?fs equations, are sufficient enough to serve as a self-contained
introductory book on the modern mathematical theory of boundary integral equations in
electromagnetics. The book now contains 12 chapters and is divided into two parts. The first
six chapters present modern mathematical theory of boundary integral equations that arise in
fundamental problems in continuum mechanics and electromagnetics based on the approach
of variational formulations of the equations. The second six chapters present an introduction to
basic classical theory of the pseudo-differential operators. The aforementioned corresponding
boundary integral operators can now be recast as pseudo-differential operators. These serve as
concrete examples that illustrate the basic ideas of how one may apply the theory of pseudodifferential
operators and their calculus to obtain additional properties for the corresponding
boundary integral operators. These two different approaches are complementary to each other.
2nd ed. 2021, XX, 783 p. 16
illus., 5 illus. in color.
Hardcover
ISBN 978-3-030-71126-9
Product category : Monograph
Series : Applied Mathematical Sciences
Mathematics : Computational Mathematics and Numerical Analysis
Presents a high-level topic in an accessible style Includes exercises
Leads the reader from the theory basics to more advanced results
This textbook is an introduction to the theory of infinity-categories, a tool used in many aspects
of modern pure mathematics. It treats the basics of the theory and supplies all the necessary
details while leading the reader along a streamlined path from the basic definitions to more
advanced results such as the very important adjoint functor theorems. The book is based on
lectures given by the author on the topic. While the material itself is well-known to experts, the
presentation of the material is, in parts, novel and accessible to non-experts. Exercises
complement this textbook that can be used both in a classroom setting at the graduate level
and as an introductory text for the interested reader.
Due 2021-05-26
1st ed. 2021, X, 296 p.
Softcover
ISBN 978-3-030-61523-9
Product category : Graduate/advanced undergraduate textbook
Series : Compact Textbooks in Mathematics
Mathematics : Category Theory, Homological Algebra
Explores the fascinating and intimate relationship between physics and music
Provides an accessible introduction to a ubiquitous yet complex phenomenon
of daily life
Combines the acoustic aspects of music with visualized dynamics
This book explores the fascinating and intimate relationship between music and physics. Over
millennia,the playing of, and listening to music have stimulated creativity and curiosity in
people all around the globe. Beginning with the basics, the authors first address the tonal
systems of European-type music, comparing them with those of other, distant cultures. They
analyze the physical principles of common musical instruments with emphasis on sound
creation and particularly charisma. Modern research on the psychology of musical perception ?
the field known as psychoacoustics ? is also described. The sound of orchestras in concert
halls is discussed,and its psychoacoustic effects are explained. Finally, the authors touch upon
the role of music for our mind and society. Throughout the book, interesting stories and
anecdotes give insights into the musical activities of physicists and their interaction with
composers and musicians.
Due 2021-06-06
1st ed. 2021, XVIII, 428 p.
310 illus., 185 illus. in color.
Hardcover
ISBN 978-3-030-68675-8
Product category : Popular science
Physics : Acoustics
A thorough introduction to B-series, written by its originator
Contains a self-contained analysis of Runge-Kutta methods
Includes a detailed study of trees and related constructs
Applies B-series to general linear methods and structure-preserving methods
B-series, also known as Butcher series, are an algebraic tool for analysing solutions to ordinary
differential equations, including approximate solutions. Through the formulation and
manipulation of these series, properties of numerical methods can be assessed. Runge?Kutta
methods, in particular, depend on B-series for a clean and elegant approach to the derivation
of high order and efficient methods. However, the utility of B-series goes much further and
opens a path to the design and construction of highly accurate and efficient multivalue
methods. This book offers a self-contained introduction to B-series by a pioneer of the subject.
After a preliminary chapter providing background on differential equations and numerical
methods, a broad exposition of graphs and trees is presented. This is essential preparation for
the third chapter, in which the main ideas of B-series are introduced and developed. In chapter
four, algebraic aspects are further analysed in the context of integration methods, a
generalization of Runge?Kutta methods to infinite index sets. Chapter five, on explicit and
implicit Runge?Kutta methods, contrasts the B-series and classical approaches. Chapter six, on
multivalue methods, gives a traditional review of linear multistep methods and expands this to
general linear methods, for which the B-series approach is both natural and essential. The final
chapter introduces some aspects of geometric integration, from a B-series point of view.
Placing B-series at the centre of its most important applications makes this book an invaluable
resource for scientists, engineers and mathematicians who depend on computational
modelling, not to mention computational scientists who carry out research on numerical
methods in differential equations. In addition to exercises with solutions and study notes, a
number of open-ended projects are suggested.
1st ed. 2021, X, 310 p. 50 illus.
Hardcover
ISBN 978-3-030-70955-6
Product category : Monograph
Series : Springer Series in Computational Mathematics
Mathematics : Computational Mathematics and Numerical Analysis
Assumes no background in abstract algebra or real analysis
Contains a number of examples and exercises
Is based on years of classroom testing
Algebraic Topologyis an introductory textbook based on a class for advanced high-school
students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught
for many years. Each chapter, or lecture, corresponds to one day of class at SUMaC. The book
begins with the preliminaries needed for the formal definition of a surface. Other topics
covered in the book include the classification of surfaces, group theory, the fundamental group,
and homology. This book assumes no background in abstract algebra or real analysis, and the
material from those subjects is presented as needed in the text. This makes the book readable
to undergraduates or high-school students who do not have the background typically assumed
in an algebraic topology book or class. The book contains many examples and exercises,
allowing it to be used for both self-study and for an introductory undergraduate topology course.
Due 2021-06-06
1st ed. 2021, XIII, 221 p.
66 illus., 28 illus. in color.
Hardcover
ISBN 978-3-030-70607-4
Product category : Undergraduate textbook
Mathematics : Algebraic Topology
Theory, Models, and Applications to Finance, Biology, and Medicine
Introduces readers to the theory of continuous-time stochastic processes
using real-life examples in medicine, finance, and biology
Includes updated exercises, examples, and material based on advances in
recent literature
Illustrates the ways that similar stochastic methods can be applied broadly
across different fields
This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the
theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential
equations. Expertly balancing theory and applications, it features concrete examples of
modeling real-world problems from biology, medicine, finance, and insurance using stochastic
methods. No previous knowledge of stochastic processes is required. Unlike other books on
stochastic methods that specialize in a specific field of applications, this volume examines the
ways in which similar stochastic methods can be applied across dierent elds. Beginning with
the fundamentals of probability, the authors go on to introduce the theory of stochastic
processes, the Ito Integral, and stochastic differential equations. The following chapters then
explore stability, stationarity, and ergodicity. The second half of the book is dedicated to
applications to a variety of fields, including finance, biology, and medicine. Some highlights of
this fourth edition include a more rigorous introduction to Gaussian white noise, additional
material on the stability of stochastic semigroups used in models of population dynamics and
epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic
dierential equations.
Due 2021-05-16
4th ed. 2021, XXII, 560 p. 13 illus.
Hardcover
ISBN 978-3-030-69652-8
Product category : Graduate/advanced undergraduate textbook
Series : Modeling and Simulation in Science, Engineering and Technology
Mathematics : Probability Theory and Stochastic Processes