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Combinatorial Identities For Stirling Numbers

Author: Jocelyn Quaintance
Publisher: World Scientific
ISBN: 9814725285
Size: 62.39 MB
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"This book is a unique work which provides an in-depth exploration into the mathematical expertise, philosophy, and knowledge of H W Gould. It is written in a style that is accessible to the reader with basic mathematical knowledge, and yet contains material that will be of interest to the specialist in enumerative combinatorics. This book begins with exposition on the combinatorial and algebraic techniques that Professor Gould uses for proving binomial identities. These techniques are then applied to develop formulas which relate Stirling numbers of the second kind to Stirling numbers of the first kind. Professor Gould's techniques also provide connections between both types of Stirling numbers and Bernoulli numbers. Professor Gould believes his research success comes from his intuition on how to discover combinatorial identities. This book will appeal to a wide audience and may be used either as lecture notes for a beginning graduate level combinatorics class, or as a research supplement for the specialist in enumerative combinatorics."--

The Partition Method For A Power Series Expansion

Author: Victor Kowalenko
Publisher: Academic Press
ISBN: 0128045116
Size: 32.29 MB
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The Partition Method for a Power Series Expansion: Theory and Applications explores how the method known as 'the partition method for a power series expansion', which was developed by the author, can be applied to a host of previously intractable problems in mathematics and physics. In particular, this book describes how the method can be used to determine the Bernoulli, cosecant, and reciprocal logarithm numbers, which appear as the coefficients of the resulting power series expansions, then also extending the method to more complicated situations where the coefficients become polynomials or mathematical functions. From these examples, a general theory for the method is presented, which enables a programming methodology to be established. Finally, the programming techniques of previous chapters are used to derive power series expansions for complex generating functions arising in the theory of partitions and in lattice models of statistical mechanics. Explains the partition method by presenting elementary applications involving the Bernoulli, cosecant, and reciprocal logarithm numbers Compares generating partitions via the BRCP algorithm with the standard lexicographic approaches Describes how to program the partition method for a power series expansion and the BRCP algorithm

The Legacy Of Alladi Ramakrishnan In The Mathematical Sciences

Author: Krishnaswami Alladi
Publisher: Springer Science & Business Media
ISBN: 9781441962638
Size: 26.66 MB
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In the spirit of Alladi Ramakrishnan’s profound interest and contributions to three fields of science — Mathematics, Statistics, and Physics — this volume contains invited surveys and research articles from prominent members of these communities who also knew Ramakrishnan personally and greatly respected his influence in these areas of science. Historical photos, telegrams, and biographical narratives of Alladi Ramakrishnan’s illustrious career of special interest are included as well.

The Craft Of Probabilistic Modelling

Author: J. Gani
Publisher: Springer Science & Business Media
ISBN: 1461386314
Size: 46.73 MB
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This book brings together the personal accounts and reflections of nineteen mathematical model-builders, whose specialty is probabilistic modelling. The reader may well wonder why, apart from personal interest, one should commission and edit such a collection of articles. There are, of course, many reasons, but perhaps the three most relevant are: (i) a philosophicaJ interest in conceptual models; this is an interest shared by everyone who has ever puzzled over the relationship between thought and reality; (ii) a conviction, not unsupported by empirical evidence, that probabilistic modelling has an important contribution to make to scientific research; and finally (iii) a curiosity, historical in its nature, about the complex interplay between personal events and the development of a field of mathematical research, namely applied probability. Let me discuss each of these in turn. Philosophical Abstraction, the formation of concepts, and the construction of conceptual models present us with complex philosophical problems which date back to Democritus, Plato and Aristotle. We have all, at one time or another, wondered just how we think; are our thoughts, concepts and models of reality approxim&tions to the truth, or are they simply functional constructs helping us to master our environment? Nowhere are these problems more apparent than in mathematical model ling, where idealized concepts and constructions replace the imperfect realities for which they stand.

A Distant Light

Author: Henry W. Kendall
Publisher: Springer Science & Business Media
ISBN: 9780387988337
Size: 62.33 MB
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The essays in this collection reveal the far-ranging and enduring contributions to society, of 1990 physics Nobel laureate and longtime environmentalist Henry W. Kendall. Kendall was chairman of the Union of Concerned Scientists for twenty-six years until his death in 1999. Through his work with the UCS, Kendall had a deep impact on a wide spectrum of critical public policy issues, most notably nuclear arms control, U.S. energy policy, and global warming. He was a leading participant on several presidential panels and was often called upon to provide expert advice to the U.S. Congress and various governmental agencies. These essays cover a broad range of efforts by scientists to impact public policy. They illuminate the challenges facing scientists who choose to be actively involved in public matters, with keen insights from Dr. Kendall on what it takes to succeed. Largely non-technical, the essays and papers are arranged in chronological order, organized by topics with new introductions by Dr. Kendall, beginning with the controversies over nuclear power safety in the 1970s, then followed by sections on national security issues, global environmental problems, bio-technology, and other current issues. Kendall's Nobel Prize lecture on the discovery of quarks is included as well. The photos in the book are Kendall's, from a 1992 exhibition of his work.

Concrete Mathematics

Author: Ronald L. Graham
Publisher: Addison-Wesley Professional
ISBN: 9780201558029
Size: 32.57 MB
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This book, updated and improved, introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills--the skills needed to solve complex problems, to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. It is an indispensable text and reference, not only for computer scientists but for all technical professionals in virtually every discipline.

Probabilistic Graphical Models

Author: Daphne Koller
Publisher: MIT Press
ISBN: 0262258358
Size: 10.95 MB
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Most tasks require a person or an automated system to reason -- to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.

Unsolved Problems In Number Theory

Author: Richard Guy
Publisher: Springer Science & Business Media
ISBN: 1489935851
Size: 42.18 MB
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Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.