2016, XXII, 756 p. 2 illus.
Hardcover
ISBN 978-3-662-52843-3
* Offers a unique overview of the theme "distance" in mathematics
and science
* Done in a cross-disciplinary fashion
* Comprehensive
This 4-th edition of the leading reference volume on distance metrics is characterized by
updated and rewritten sections on some items suggested by experts and readers, as well
a general streamlining of content and the addition of essential new topics. Though the
structure remains unchanged, the new edition also explores recent advances in the use
of distances and metrics for e.g. generalized distances, probability theory, graph theory,
coding theory, data analysis.
New topics in the purely mathematical sections include e.g. the Vitanyi multiset-metric,
algebraic point-conic distance, triangular ratio metric, Rossi-Hamming metric, Taneja
distance, spectral semimetric between graphs, channel metrization, and Maryland bridge
distance. The multidisciplinary sections have also been supplemented with new topics,
including: dynamic time wrapping distance, memory distance, allometry, atmospheric
depth, elliptic orbit distance, VLBI distance measurements, the astronomical system of
units, and walkability distance.
Leaving aside the practical questions that arise during the selection of a egoodf distance
function, this work focuses on providing the research community with an invaluable
comprehensive listing of the main available distances.
As well as providing standalone introductions and definitions, the encyclopedia facilitates
swift cross-referencing with easily navigable bold-faced textual links to core entries.
In addition to distances themselves, the authors have collated numerous fascinating
curiosities in their Whofs Who of metrics, including distance-related notions and
paradigms that enable applied mathematicians in other sectors to deploy research tools
that non-specialists justly view as arcane. In expanding access to these techniques, and in
many cases enriching the context of distances themselves, this peerless volume is certain
to stimulate fresh research.
1st ed. 2016, XI, 323 p.
Hardcover
ISBN 978-3-319-47719-0
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern
Surveys in Mathematics, Vol. 62
* Provides a self-contained introduction to the products of
independent identically distributed random matrices and to their
Lyapunov exponents
* Explains the relevance of the theory of reductive algebraic groups
and the theory of bounded operators in Banach spaces to the study
of random matrices
* Contains a proof of the Local Limit Theorem for the norm of the
products of independent identically distributed random matrices
The classical theory of Random Walks describes the asymptotic behavior of sums of
independent identically distributed random real variables. This book explains the
generalization of this theory to products of independent identically distributed random
matrices with real coefficients.
Under the assumption that the action of the matrices is semisimple ? or, equivalently,
that the Zariski closure of the group generated by these matrices is reductive - and under
suitable moment assumptions, it is shown that the norm of the products of such random
matrices satisfies a number of classical probabilistic laws.
This book includes necessary background on the theory of reductive algebraic groups,
probability theory and operator theory, thereby providing a modern introduction to the
topic.
1st ed. 2017, Approx. 220 p.
Hardcover
ISBN 978-3-319-47778-7
Series: Progress in Mathematics, Vol. 321
* Provides a friendly introduction to several contemporary research
topics in algebraic geometry and number theory given by leading experts
* Gives a clear and motivating exposition through numerous examples and
exercises
* Presents a modern treatment and new points of view on classical subjects
This lecture notes volume presents significant contributions from the gAlgebraic Geometry
and Number Theoryh Summer School, held at Galatasaray University, Istanbul, June 2-13,
2014.
It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical
projective geometry, birational geometry and equivariant cohomology. Its main aim is to
introduce these contemporary research topics to graduate students who plan to specialize
in the area of algebraic geometry and/or number theory. All contributions combine main
concepts and techniques with motivating examples and illustrative problems for the
covered subjects.
Naturally, the book will also be of interest to researchers working in algebraic geometry,
number theory and related fields.
616pp Nov 2016
ISBN: 978-981-3148-84-0 (hardcover)
This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.
Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.
New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them.
The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity.
The book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading.
The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to sales@wspc.com.
The previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. It was also translated into Korean.
Basic Methods:
Seven is More Than Six. The Pigeon-Hole Principle
One Step at a Time. The Method of Mathematical Induction
Enumerative Combinatorics:
There are a Lot of Them. Elementary Counting Problems
No Matter How You Slice It. The Binomial Theorem and Related Identities
Divide and Conquer. Partitions
Not So Vicious Cycles. Cycles in Permutations
You Shall Not Overcount. The Sieve
A Function is Worth Many Numbers. Generating Functions
Graph Theory:
Dots and Lines. The Origins of Graph Theory
Staying Connected. Trees
Finding a Good Match. Coloring and Matching
Do Not Cross. Planar Graphs
Horizons:
Does It Clique? Ramsey Theory
So Hard to Avoid. Subsequence Conditions on Permutations
Who Knows What It Looks Like, But It Exists. The Probabilistic Method
At Least Some Order. Partial Orders and Lattices
As Evenly as Possible. Block Designs and Error Correcting Codes
Are They Really Different? Counting Unlabeled Structures
The Sooner the Better. Combinatorial Algorithms
Does Many Mean More Than One? Computational Complexity
Upper level undergraduates and graduate students in the field of combinatorics
and graph theory.