1st ed. 2019, XVIII, 280 p.
41 illus., 22 illus. in color.
Printed book
Hardcover
ISBN 978-3-030-18471-1
Presents an advanced and systematic approach for analyzing the stationary
or non-stationary time series
Provides an inverse method on how to construct stochastic evolution equation
from given time series
Offers a non-parametric approach: all functions and parameters of the
constructed stochastic evolution equation are determined directly from the
measured time series
This book focuses on a central question in the field of complex systems: Given a fluctuating (in
time or space), uni- or multi-variant sequentially measured set of experimental data (even
noisy data), how should one analyse non-parametrically the data, assess underlying trends,
uncover characteristics of the fluctuations (including diffusion and jump contributions), and
construct a stochastic evolution equation?Here, the term "non-parametrically" exemplifies that
all the functions and parameters of the constructed stochastic evolution equation can be
determined directly from the measured data. The book provides an overview of methods that
have been developed for the analysis of fluctuating time series and of spatially disordered
structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating
time series and spatially disordered structures of complex systems studied in scientific fields
such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and
the neurosciences, and has led to a number of important results. The book also includes the
numerical and analytical approaches to the analyses of complex time series that are most
common in the physical and natural sciences.
1st ed. 2019, XXXII, 386 p.
1 illus.
Printed book
Hardcover
ISBN 978-3-030-26901-2
Introduces real analysis to students with an emphasis on accessibility and clarity
Adapts the authorfs successful, classroom-tested lecture notes to motivate a
thorough exploration of real analysis
Includes numerous exercises, definitions, and theorems, which are both easy
to understand and rigorous
Reinforces the material with numerous additional online resources
Developed over years of classroom use, this textbook provides a clear and accessible approach
to real analysis. This modern interpretation is based on the authorfs lecture notes and has
been meticulously tailored to motivate students and inspire readers to explore the material,
and to continue exploring even after they have finished the book. The definitions, theorems,
and proofs contained within are presented with mathematical rigor, but conveyed in an
accessible manner and with language and motivation meant for students who have not taken a
previous course on this subject. The text covers all of the topics essential for an introductory
course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation,
absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter,
challenging exercises are presented, and the end of each section includes additional problems.
Such an inclusive approach creates an abundance of opportunities for readers to develop their
understanding, and aids instructors as they plan their coursework. Additional resources are
available online, including expanded chapters, enrichment exercises, a detailed course outline,
and much more. Introduction to Real Analysis is intended for first-year graduate students
taking a first course in real analysis, as well as for instructors seeking detailed lecture material
with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D.
students in any scientific or engineering discipline who have taken a standard upper-level
undergraduate real analysis course.
Due 2019-10-15
1st ed. 2019, IX, 128 p. 56
illus.
Printed book
Softcover
ISBN 978-3-030-26695-0
Introduces a unique technique to count lattice paths by using the discrete
Fourier transform
Explores the interconnection between combinatorics and Fourier methods
Motivates students to move from one-dimensional problems to higher dimensions
Presents numerous exercises with selected solutions appearing at the end
This monograph introduces a novel and effective approach to counting lattice paths by using
the discrete Fourier transform (DFT) as a type of periodic generating function. Utilizing a
previously unexplored connection between combinatorics and Fourier analysis, this method will
allow readers to move to higher-dimensional lattice path problems with ease. The technique is
carefully developed in the first three chapters using the algebraic properties of the DFT, moving
from one-dimensional problems to higher dimensions. In the following chapter, the discussion
turns to geometric properties of the DFT in order to study the corridor state space. Each
chapter poses open-ended questions and exercises to prompt further practice and future
research. Two appendices are also provided, which cover complex variables and nonrectangular
lattices, thus ensuring the text will be self-contained and serve as a valued
reference. Counting Lattice Paths Using Fourier Methods is ideal for upper-undergraduates and
graduate students studying combinatorics or other areas of mathematics, as well as computer
science or physics. Instructors will also find this a valuable resource for use in their seminars.
Readers should have a firm understanding of calculus, including integration, sequences, and
series, as well as a familiarity with proofs and elementary linear algebra.
Due 2019-10-30
1st ed. 2019, XIII, 621 p.
58 illus., 52 illus. in color.
Printed book
Hardcover
ISBN 978-0-387-84807-5
Subject matter connects several different branches of mathematics and has
myriad applications to the physical and biological sciences
Book is rich with attractive, full color images
Self-contained book, accessible to both research professionals and graduate students
This book aims to provide an introduction to the broad and dynamic subject of discrete energy
problems and point configurations. Written by leading authorities on the topic, this treatise is
designed with the graduate student and further explorers in mind. The presentation includes a
chapter of preliminaries and an extensive Appendix that augments a course in Real Analysis
andmakes the text self-contained. Along with numerous attractive full-color images, the
exposition conveys the beauty of the subject and its connection to several branches of
mathematics, computational methods, and physical/biological applications. This work is
destined to be a valuable research resource for such topics as packing and covering problems,
generalizations of the famous Thomson Problem, andclassical potential theory in Rd. It
features three chapters dealing with point distributions on the sphere, including an extensive
treatment of Delsarte?Yudin?Levenshtein linear programming methods for lower bounding
energy, a thorough treatment of Cohn?Kumar universality, and a comparison of 'popular
methods' for uniformly distributing points on the two-dimensional sphere. Some unique
features of the work are its treatment of Gauss-type kernels for periodic energy problems, its
asymptotic analysis of minimizing point configurations for non-integrable Riesz potentials (the
so-called Poppy-seed bagel theorems), its applications to the generation of non-structured
grids of prescribed densities, and its closing chapter on optimal discrete measures
forChebyshev (polarization) problems.
Due 2019-10-02
1st ed. 2019, Approx. 230 p.
Printed book
Softcover
ISBN 978-3-030-29015-3
Complete, self-contained presentation with proofs
Low-level prerequisites
Matter is presented from a decidedly geometric viewpoint, updating classical
approaches
Exercises at the end of each chapter
The book presents the central facts of the local, projective and intrinsic theories of complex
algebraic plane curves, with complete proofs and starting from low-level prerequisites. It
includes Puiseux series, branches, intersection multiplicity, Bezout theorem, rational functions,
Riemann-Roch theorem and rational maps. It is aimed at graduate and advanced
undergraduate students, and also at anyone interested in algebraic curves or in an introduction
to algebraic geometry via curves.
Due 2019-10-22
1st ed. 2019, X, 120 p. 5
illus.
Printed book
Softcover
ISBN 978-3-030-27229-6
First introduction to a systematic analysis of the Hybridizable Discontinuous
Galerkin Method
Presentation of new simplified techniques to prove estimates using the wellestablished
projection-based analysis of HDG methods
Covers applications to diffusion process (steady-state and evolutionary) and
wave propagation (time-harmonic and transient)
This monograph requires basic knowledge of the variational theory of elliptic PDEand the
techniques used for the analysis of the Finite Element Method. However, all the tools for
theanalysis of FEM (scaling arguments, finite dimensional estimates in the reference
configuration, Piolatransforms) are carefully introduced before being used, so that the reader
does not need to go overlongforgotten textbooks. Readers include: computational
mathematicians, numerical analysts, engineersand scientists interested in new and
computationally competitive Discontinuous Galerkin methods. Theintended audience includes
graduate students in computational mathematics, physics, and engineering,since the
prerequisites are quite basic for a second year graduate student who has already taken a
nonnecessarily advanced class in the Finite Element method.
Due 2019-10-09
1st ed. 2019, XII, 134 p.
Printed book
Softcover
ISBN 978-3-030-27226-5
Self-contained treatment of equivariant cohomology
Treatment of moduli spaces of flat connections (a topic of considerable current interest)
The only background required is a course on differential manifolds (a
standard offering at the advanced undergraduate or introductory graduate
level)
This monograph could be used for a graduate course on symplectic geometry as well as for
independent study. The monograph starts with an introduction of symplectic vector spaces,
followed by symplectic manifolds and then Hamiltonian group actions and the Darboux
theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients
are studied. The convexity theorem and toric manifolds come next and we give a
comprehensive treatment of Equivariant cohomology. The monograph also contains detailed
treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections
on 2-manifolds. Finally, there is an appendix which provides background material on Lie
groups. A course on differential topology is an essential prerequisite for this course. Some of
the later material will be more accessible to readers who have had a basic course on algebraic
topology. For some of the later chapters, it would be helpful to have some background on
representation theory and complex geometry.