1st ed. 2017, Approx. 1230p. 2 volume-set.
Printed book
Hardcover
ISBN 978-3-319-68580-9
A textbook pair that provides a landmark unified treatment of the field
Introduces readers from mathematics, computer science, and beyond to the
increasingly relevant field of relation algebras
Advances readers with foundations in relation algebras to the frontiers of active research
Engages the reader with numerous examples, exercises, and historical remarks
Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in
1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly
relevant field of relation algebras. Clear and insightful prose guides the reader through
material previously only available in scattered, highly-technical journal articles.
Students and experts alike will appreciate the work as both a textbook and invaluable reference for the
community. This set charts relation algebras from novice to expert level.
The first volume,Introduction to Relation Algebras, offers a comprehensive grounding for readers new to the topic.
The second, Advanced Topics in Relation Algebras, build on this foundation and advances
the reader into the deeper mathematical results of the past few decades. Such material offers
an ideal preparation for research in relation algebras and Boolean algebras with operators.
Note that the second volume contains numerous, essential references to the first. Readers of
the advanced material are encouraged to purchase the pair as a set, as access to the first
book is necessary to make use of the second.
Due 2017-12-12
1st ed. 2017, IX, 137 p. 25
illus., 11 illus. in color.
Printed book
Softcover ISBN 978-981-10-6792-1
SpringerBriefs in Mathematics
Shows how the quandle has been evaluated in relation to mathematics or
topology while the quandle was often considered to be something combinatorial
Constitutes a guide on quandles at a time when few surveys of quandles and
few topological books on quandles exist
Emphasizes the geometric advantages of quandles at a high level
mathematically while the quandle is used as an algebraic method in many books
This book surveys quandle theory, starting from basic motivations and going on to introduce
recent developments of quandles with topological applications and related topics.
The book is written from topological aspects, but it illustrates how esteemed quandle theory is in
mathematics, and it constitutes a crash course for studying quandles.
More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for
the study of lowdimensional topology (e.g., knot theory) and relative objects with symmetry.
The direction of research is summarized as gWe shall thoroughly (re)interpret the previous studies
of relative symmetry in terms of the quandleh.
The perspectives contained herein can be summarized by the following topics. T
he first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and
symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups,
and some geometric anomalies.
The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e
.g., knot theory, relative cup products, and relative group cohomology.
For applications in topology, it is shown that from the perspective that some existing results in topology
can be recovered from some quandles, a method is provided to diagrammatically compute some grelative homologyh.
(Such classes since have been considered to be uncomputable and speculative). Furthermore,
the book provides a perspective that unifies some previous studies of quandles.
The former part of the book explains motivations for studying quandles and discusses basic properties of quandles.
Due 2018-01-21
VI, 247 p. 33 illus., 28 illus. in color.
Printed book
Hardcover ISBN 978-1-4939-7542-6
Series
Fields Institute Communications
Comprises a mosaic of multiple aspects of approximation theory
Highlights interesting connections between aspects of approximation theory
and important contemporary areas of analysis
Contains contributions by well-established mathematicians
The international conference entitled "New Trends in Approximation Theory" was held at the
Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly
dedicated to the memory of our unique friend and colleague, Andre Boivin, who gave tireless
service in Canada until his very last moment of his life in October 2014. The impact of his
warm personality and his fine work on Complex Approximation Theory was reflected by the
mathematical excellence and the wide research range of the 37 participants. In total there
were 27 talks, delivered by well-established mathematicians and young researchers. In
particular, 19 invited lectures were delivered by leading experts of the field, from 8 different
countries. The wide variety of presentations composed a mosaic of aspects of approximation
theory, highlighting interesting connections with important contemporary areas of Analysis.
Primary topics discussed include application of approximation theory (isoperimetric inequalities,
construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic
and holomorphic functions (especially uniform and tangential approximation), polynomial and
rational approximation; zeros of approximants and zero-free approximation; tools used in
approximation theory; approximation on complex manifolds, in product domains, and in
function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.
Due 2018-01-08
1st ed. 2017, VII, 180 p. 5
illus., 1 illus. in color.
Printed book
Softcover ISBN 978-3-319-69433-7
Series
Lecture Notes in Mathematics
Provides self-contained, introductory texts to some advanced topics in
modern algebraic topology
Includes various topics in homotopical algebra and stable homotopy
Leads quickly to open and concrete problems
Held during algebraic topology special sessions at the Vietnam Institute for Advanced Studies
in Mathematics (VIASM, Hanoi), this set of notes consists of expanded versions of three courses
given by G. Ginot, H.-W. Henn and G. Powell. They are all introductory texts and can be used by
PhD students and experts in the field. Among the three contributions, two concern stable
homotopy of spheres: Henn focusses on the chromatic point of view, the Morava K(n)-
localization and the cohomology of the Morava stabilizer groups. Powellfs chapter is concerned
with the derived functors of the destabilization and iterated loop functors and provides a small
complex to compute them. Indications are given for the odd prime case. Providing an
introduction to some aspects of string and brane topology, Ginotfs contribution focusses on
Hochschild homology and its generalizations. It contains a number of new results and fills a
gap in the literature.
Due 2018-01-19
1st ed. 2017, X, 310 p. 25
illus., 14 illus. in color.
Printed book
Hardcover ISBN 978-3-319-70153-0
Series
Trends in Mathematics
Contains expositions of numerous open problems in such important areas as
complex dynamical systems, geometric function theory and harmonic analysis
Provides relevant background and historical remarks concerning these problems and their interrelationships
Dedicated to the memory of Alexander Vasiliev
This book focuses on developments in complex dynamical systems and geometric function
theory over the past decade, showing strong links with other areas of mathematics and the
natural sciences. Traditional methods and approaches surface in physics and in the life and
engineering sciences with increasing frequency ? the SchrammLoewner evolution, Laplacian
growth, and quadratic differentials are just a few typical examples. This book provides a
representative overview of these processes and collects open problems in the various areas,
while at the same time showing where and how each particular topic evolves. This volume is
dedicated to the memory of Alexander Vasiliev.