Series: Universitext
1st ed. 2016, XII, 299 p. 52 illus., 6 illus. in
color.
Softcover
ISBN 978-3-319-50037-9
* Contains 175 exercises including research-oriented problems about
special stochastic processes not covered in traditional textbooks
* Includes detailed simulation programs of the main models
* Covers topics not typically included in traditional textbooks, allowing
for readers to learn quickly on many topics, including researchoriented topics
* Includes a timeline with the main contributors since the origin of probability theory until today
Three coherent parts form the material covered in this text, portions of which have
not been widely covered in traditional textbooks. In this coverage the reader is quickly
introduced to several different topics enriched with 175 exercises which focus on realworld
problems. Exercises range from the classics of probability theory to more exotic
research-oriented problems based on numerical simulations. Intended for graduate
students in mathematics and applied sciences, the text provides the tools and training
needed to write and use programs for research purposes.
The first part of the text begins with a brief review of measure theory and revisits the main
concepts of probability theory, from random variables to the standard limit theorems.
The second part covers traditional material on stochastic processes, including martingales,
discrete-time Markov chains, Poisson processes, and continuous-time Markov chains.
The theory developed is illustrated by a variety of examples surrounding applications
such as the gamblerfs ruin chain, branching processes, symmetric random walks, and
queueing systems.
The third, more research-oriented part of the text, discusses special
stochastic processes of interest in physics, biology, and sociology. Additional emphasis is
placed on minimal models that have been used historically to develop new mathematical
techniques in the field of stochastic processes: the logistic growth process, the Wright-
Fisher model, Kingmanfs coalescent, percolation models, the contact process, and the
voter model.
Further treatment of the material explains how these special processes
are connected to each other from a modeling perspective as well as their simulation
capabilities in C and Matlab.
Series: C.I.M.E. Foundation Subseries, Vol. 2173
VII, 363 p. 55 illus., 44 illus. in color.
Softcover
ISBN 978-3-319-49886-7
* Provides a detailed treatment of the emerging field of hidden or
approximate-structured matrix problems
* Offers different theoretical and application perspectives in a
thorough presentation by leading figures in this areaGives rich
pointers to the state-of-the-art literature on the subject
Focusing on special matrices and matrices which are in some sense `nearf to structured
matrices, this volume covers a broad range of topics of current interest in numerical
linear algebra. Exploitation of these less obvious structural properties can be of great
importance in the design of efficient numerical methods, for example algorithms for
matrices with low-rank block structure, matrices with decay, and structured tensor
computations. Applications range from quantum chemistry to queuing theory.
Structured matrices arise frequently in applications. Examples include banded and sparse
matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable
structure, as well as Hamiltonian and symplectic matrices. The associated literature is
enormous, and many efficient algorithms have been developed for solving problems
involving such matrices.
The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed
to present this fast growing field to young researchers, exploiting the expertise of five
leading lecturers with different theoretical and application perspectives.
1st ed. 2017, Approx. 1750 p. 3 volume-set.
Softcover
ISBN 978-3-319-48262-0
*Three-volume-set
* Standard reference work for researchers in this area
* Features contributions from leading experts
* Presents the most comprehensive work on an explosively growing field
gGratzerfs book General Lattice Theory has become the lattice theoristfs
bible.h (Mathematical Reviews) - In 2009, the author considered updating its second
edition to reflect some exciting new developments. He soon realized that to lay the
foundation, to survey the contemporary field, to pose research problems, would require
more than one volume and more than one person.
This three-volume-set comprises the complete lattice theory project.
Lattice Theory: Foundation is the revised and enlarged third edition of General Lattice
Theory. It focuses on introducing the field and covers the fundamental concepts and results
The two Special Topics and Applications volumes, jointly edited by George Gratzer and
Friedrich Wehrung, update the reader on some of the vast areas not in Foundation.
Volume 1 is divided into three parts. Part I. Topology and Lattices includes two chapters
by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite
Lattices comprises four chapters by Gabor Czedli, George Gratzer and Joseph P. S. Kung.
Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by
Friedrich Wehrung and George Gratzer.
Volume 2 is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese,
P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.
Series: Progress in Mathematics, Vol. 310
1st ed. 2017, Approx. 400 p.
Hardcover
ISBN 978-3-319-49636-8
* Contains contributions by some of the foremost experts
in probability and geometry
* Explains the most recent advances in these subjects with very careful writing
This volume presents original research articles and extended surveys related to the
mathematical interest and work of Jean-Michel Bismut. His outstanding contributions
to probability theory and global analysis on manifolds have had a profound impact on
several branches of mathematics in the areas of control theory, mathematical physics and
arithmetic geometry.
Contributions by:
K. Behrend
N. Bergeron
S. K. Donaldson
J. Dubedat
B. Duplantier
G. Faltings
E. Getzler
G. Kings
R. Mazzeo
J. Millson
C. Moeglin
Series: Progress in Mathematics, Vol. 322
1st ed. 2017, Approx. 530 p.
Hardcover
ISBN 978-3-319-49833-1
* Offers a detailed exposition accessible to students
* Provides numerous figures
* Winner of the 2016 Ferran Sunyer i Balaguer Prize
This monograph focuses on monoidal categories and their connection with threedimensional
topological field theories, guiding readers from basic definitions to the forefront of current research.
Part 1 starts by introducing various important classes of monoidal categories, including
rigid, pivotal, spherical, fusion, braided, and modular categories. It ends by stating two
important theorems of M. Muger, establishing fundamental properties of the center of a
pivotal fusion category. The theorems are proved in Part 2 using Hopf monad techniques.
In the third part the authors introduce the notion of topological quantum field theory
(TQFT) and formulate the Turaev-Viro-type state sum construction of 3-dimensional TQFTs
from spherical fusion categories. Part 4 extends this construction to 3-manifolds with
colored ribbon graphs, which results in a so-called graph TQFT. In the last chapter the
authors present a surgery computation of the graph TQFT and prove the main result of the
monograph: the state sum TQFT derived from a spherical fusion category is isomorphic to
the Reshetikhin-Turaev surgery TQFT derived from the center of that category.
The book is of interest to researchers and students studying monoidal categories, Hopf
algebras, Hopf monads, and 3-dimensional topological field theory.
Series: Operator Theory: Advances and Applications, Vol. 259
1st ed. 2017, Approx. 700 p.
Hardcover
ISBN 978-3-319-49180-6
* Presents a unique source of biographical data and personal
encounters concerning Albrecht Bottcher
* Describes the current state of the spectral theory of Toeplitz
operators, asymptotic behaviour of structured matrices
* Includes a wide range of applications
This book presents a collection of expository and research papers on various topics in
matrix and operator theory, contributed by several experts on the occasion of Albrecht
Bottcherfs 60th birthday. Bottcher himself has made substantial contributions to the
subject in the past. The book also includes a biographical essay, a complete bibliography
of Bottcherfs work and brief informal notes on personal encounters with him.
The book is of interest to graduate and advanced undergraduate students majoring in
mathematics, researchers in matrix and operator theory as well as engineers and applied
mathematicians.
Series: Frontiers in Mathematics
XII, 152 p.
Softcover
ISBN 978-3-319-47939-2
* Presents a popular topic in an original way
* Inspires new ideas in the whole range of applications in analysis
* Contains important notions of multidimensional geometry applied to
Analysis, difficult to be found elsewhere in literature
This book offers a systematic treatment of a classic topic in Analysis. It fills a gap in the
existing literature by presenting in detail the classic É-Holder condition and introducing
the notion of locally Holder-continuous function in an open set ¶ in Rn. Further, it
provides the essential notions of multidimensional geometry applied to analysis.
Written in an accessible style and with proofs given as clearly as possible, it is a valuable
resource for graduate students in Mathematical Analysis and researchers dealing with
Holder-continuous functions and their applications.