Graduate Studies in Mathematics Volume: 194
2018; 490 pp; Hardcover
MSC: Primary 62; 14; 13; 52; 60; 90; 92;
Print ISBN: 978-1-4704-3517-2
Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.
Graduate students and researchers interested in algebraic statistics and its applications.
Graduate Studies in Mathematics Volume: 195
2018; Hardcover
MSC: Primary 05; 11; 52; 68;
Print ISBN: 978-1-4704-2200-4
Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics.
Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.
Advanced undergraduate students and graduate students learning combinatorics; instructors teaching such courses.
Pure and Applied Undergraduate Texts Volume: 33
2019; Hardcover
MSC: Primary 42; 65; 94; 46;
Print ISBN: 978-1-4704-4191-3
This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques?all of which are important in many areas of engineering and science?the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page.
The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.
Undergraduate students and graduate students (engineering students and math majors) and researchers (practicing engineers) interested in Fourier analysis.
ISBN: 978-1-4704-3914-9
Contemporary Mathematics, Volume 719
Published: 29 November 2018; Copyright Year: 2018
Pages: 211; Softcover;
Probability and Statistics
Discrete Mathematics and Combinatorics
Graduate students and research mathematicians interested in ergodic theory, dynamical
systems, random graphs and applications.
This volume contains the proceedings of the AMS Special Session on
Unimodularity in Randomly Generated Graphs, held from October 8?9, 2016, in Denver,Colorado.
Unimodularity, a term initially used in locally compact topological groups, is one of the main
examples in which the generalization from groups to graphs is successful. The grandomly generated
graphsh, which include percolation graphs, random Erdo?s?Renyi graphs, and graphings
of equivalence relations, are much easier to describe if they result as random objects in the
context of unimodularity, with respect to either a vertex-transient ghosth-graph or a probability
measure.
This volume tries to give an impression of the various fields in which the notion currently
finds strong development and application: percolation theory, point processes, ergodic theory,
and dynamical systems.
A co-publication of the AMS and Centre de Recherches Mathematiques.
ISBN: 978-1-4704-3556-1
Contemporary Mathematics, Volume 720
Published: 29 November 2018; Copyright Year: 2018
Pages: 240; Softcover
Analysis
Mathematical Physics
Graduate students and research mathematicians interested in special theory and
mathematical physics.
This book is a collection of lecture notes and survey papers based on the minicourses
given by leading experts at the 2016 CRM Summer School on Spectral Theory and
Applications, held from July 4?14, 2016, at Universite Laval, Quebec City, Quebec, Canada.
The papers contained in the volume cover a broad variety of topics in spectral theory, starting
from the fundamentals and highlighting its connections to PDEs, geometry, physics, and
numerical analysis.
ISBN: 978-1-4704-4868-4
Graduate Studies in Mathematics, Volume 196
13 December 2018; Copyright Year: 2018;
Pages: 156; Hardcover;
Applications
Graduate students and researchers interested in singular perturbation theory and
appropriate numerical methods.
Many physical problems involve diffusive and convective (transport) processes.
When diffusion dominates convection, standard numerical methods work satisfactorily. But
when convection dominates diffusion, the standard methods become unstable, and special
techniques are needed to compute accurate numerical approximations of the unknown solution.
This convection-dominated regime is the focus of the book. After discussing at length the
nature of solutions to convection-dominated convection-diffusion problems, the authors motivate
and design numerical methods that are particularly suited to this class of problems.
At first they examine finite-difference methods for two-point boundary value problems, as
their analysis requires little theoretical background. Upwinding, artificial diffusion, uniformly
convergent methods, and Shishkin meshes are some of the topics presented. Throughout, the
authors are concerned with the accuracy of solutions when the diffusion coefficient is close to
zero. Later in the book they concentrate on finite element methods for problems posed in one
and two dimensions.
This lucid yet thorough account of convection-dominated convection-diffusion problems and
how to solve them numerically is meant for beginning graduate students, and it includes a
large number of exercises. An up-to-date bibliography provides the reader with further reading.
This book is published in cooperation with Atlantic Association for Research in the
Mathematical Sciences.
ISBN: 978-1-4704-4890-5
Translations of Mathematical Monographs, Volume 247
Published: 17 December 2018; Copyright Year: 2018
Pages: 176; Hardcover
Analysis
Differential Equations
Graduate students and researchers interested in inverse problems and scattering theory.
Inverse problems of spectral analysis deal with the reconstruction of operators of
the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An
interest in spectral problems was initially inspired by quantum mechanics. The main inverse
spectral problems have been solved already for Schrodinger operators and for their finite-difference
analogues, Jacobi matrices.
This book treats inverse problems in the theory of small oscillations of systems with finitely
many degrees of freedom, which requires finding the potential energy of a system from the
observations of its oscillations. Since oscillations are small, the potential energy is given by a
positive definite quadratic form whose matrix is called the matrix of potential energy. Hence,
the problem is to find a matrix belonging to the class of all positive definite matrices. This
is the main difference between inverse problems studied in this book and the inverse problems
for discrete analogues of the Schrodinger operators, where only the class of tridiagonal
Hermitian matrices are considered.