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Eulerian Numbers
Within these pages readers will find the complete theory of a renowned class of special numbers, Eulerian numbers, as well as some generalisations and relatives (Eulerian numbers of the second order, factorial numbers, Euler numbers, etc.), their properties, their facts, and their theorems, alongside full proofs.The "names" of many of the special numbers essential to so many aspects of number theory, general mathematics, and numerous applied areas are known to every mathematician: Fermat numbers, Mersenne numbers, Fibonacci numbers, etc. Yet actual information on these numbers is often scattered in the available literature. Those books which do contain such information are often out of date or generalised. It is the goal of this series to remedy this gap.Among the topics covered in this text are the key definitions, the collected main properties of considered mathematical objects, the main questions of Eulerian numbers of the first- and second-orders, the integral main facts of the theory of set partitions, recurrent equations, and generating functions, and much more. A comprehensive and exclusive collection of practice exercises and an expansive mini dictionary are included to support these points of learning. This comes together to provide an accessible guide to the field of Eulerian numbers for not only undergraduate students of Mathematics but also for professionals and the general interested audience.
€ 200,95 -
Catalan Numbers
Catalan numbers, named after the French-Belgian mathematician Eugène Charles Catalan (1814-1894), arise in a variety of combinatorial problems. They have many interesting properties, a rich history, and numerous arithmetic, number-theoretical, analytical, and combinatorial connections, as well as a variety of classical and modern applications. Considering the long list of open problems and questions related to the classical case, its relatives (Bell numbers, Motzkin numbers, Narayana numbers, etc.) and its generalizations, this book provides a broad perspective on the theory of this class of special numbers that will be of interest to professionals, students, and a general audience.The book begins with the history of the problem, before defining the considered numerical sets. The recurrence equation, closed formula, and generating function are then presented, followed by the simplest properties and number-theoretical properties. Later chapters discuss the relationships between Catalan numbers and other special numbers, as well as their applications and open problems.
€ 186,95 -
Stirling Numbers
Stirling numbers are one of the most known classes of special numbers in Mathematics, especially in Combinatorics and Algebra. They were introduced by Scottish mathematician James Stirling (1692-1770) in his most important work, Differential Method with a Tract on Summation and Interpolation of Infinite Series (1730). Stirling numbers have a rich history; many arithmetic, number-theoretical, analytical and combinatorial connections; numerous classical properties; as well as many modern applications.This book collects much of the scattered material on the two subclasses of Stirling numbers to provide a holistic overview of the topic. From the combinatorial point of view, Stirling numbers of the second kind, S(n, k), count the number of ways to partition a set of n different objects (i.e., a given n-set) into k non-empty subsets. Stirling numbers of the first kind, s(n, k), give the number of permutations of n elements with k disjoint cycles. Both subclasses of Stirling numbers play an important role in Algebra: they form the coefficients, connecting well-known sets of polynomials.This book is suitable for students and professionals, providing a broad perspective of the theory of this class of special numbers, and many generalisations and relatives of Stirling numbers, including Bell numbers and Lah numbers. Throughout the book, readers are provided exercises to test and cement their understanding.
€ 200,95 -
Perfect And Amicable Numbers
This book contains a detailed presentation on the theory of two classes of special numbers, perfect numbers, and amicable numbers, as well as some of their generalizations. It also gives a large list of their properties, facts and theorems with full proofs. Perfect and amicable numbers, as well as most classes of special numbers, have many interesting properties, including numerous modern and classical applications as well as a long history connected with the names of famous mathematicians.The theory of perfect and amicable numbers is a part of pure Arithmetic, and in particular a part of Divisibility Theory and the Theory of Arithmetical Functions. Thus, for a perfect number n it holds σ(n) = 2n, where σ is the sum-of-divisors function, while for a pair of amicable numbers (n, m) it holds σ(n) = σ(m) = n + m. This is also an important part of the history of prime numbers, since the main formulas that generate perfect numbers and amicable pairs are dependent on the good choice of one or several primes of special form.Nowadays, the theory of perfect and amicable numbers contains many interesting mathematical facts and theorems, alongside many important computer algorithms needed for searching for new large elements of these two famous classes of special numbers.This book contains a list of open problems and numerous questions related to generalizations of the classical case, which provides a broad perspective on the theory of these two classes of special numbers. Perfect and Amicable Numbers can be useful and interesting to both professional and general audiences.
€ 186,95 -
Mersenne Numbers And Fermat Numbers
This book contains a complete detailed description of two classes of special numbers closely related to classical problems of the Theory of Primes. There is also extensive discussions of applied issues related to Cryptography.In Mathematics, a Mersenne number (named after Marin Mersenne, who studied them in the early 17-th century) is a number of the form Mn = 2n - 1 for positive integer n.In Mathematics, a Fermat number (named after Pierre de Fermat who first studied them) is a positive integer of the form Fn = 2k+ 1, k=2n, where n is a non-negative integer.Mersenne and Fermat numbers have many other interesting properties. Long and rich history, many arithmetic connections (with perfect numbers, with construction of regular polygons etc.), numerous modern applications, long list of open problems allow us to provide a broad perspective of the Theory of these two classes of special numbers, that can be useful and interesting for both professionals and the general audience.
€ 138,50 -
Dictionary of Distances
Suitable for researchers using Mathematics as well as for mathematicians themselves, this book covers a range of subjects in pure and applied mathematics. It provides the distances, as well as distance-related notions and paradigms in ready-to-use fashion.
€ 186,95 -
Figurate Numbers
Figurate numbers have a rich history with many applications. This book provides a complete presentation of the theory of figurate numbers, giving much of their properties, facts and theorems with full proofs.
€ 207,95 -
Encyclopedia of Distances
"The fourth edition of the Encyclopedia of Distances appears barely two years after the third (2014) and contains 76 new entries and 23 additional pages. ... This latest release will be useful mainly to specialists and collections supporting graduate mathematics programs. Summing Up: Recommended. Graduate students through professionals." (L. R. Zellmer, Choice, Vol. 54 (8), April, 2017)
€ 274,95 -
Encyclopedia of Distances
€ 274,95 -
Generalizations Of Finite Metrics And Cuts
This book introduces oriented version of metrics and cuts and their multidimensional analogues, as well as partial metrics and weighted metrics.
€ 146,95 -
Encyclopedia of Distances
This updated and revised third edition of the leading reference volume on distance metrics includes new items from very active research areas in the use of distances and metrics such as geometry, graph theory, probability theory and analysis. Among the new topics included are, for example, polyhedral metric space, nearness matrix problems, distances between belief assignments, distance-related animal settings, diamond-cutting distances, natural units of length, Heidegger¿s de-severance distance, and brain distances. The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval.Leaving aside the practical questions that arise during the selection of a ¿good¿ 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 Whös 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.
€ 117,69