Notes On The Binomial Transform Theory And Table With Appendix On Stirling Transform

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Notes On The Binomial Transform: Theory And Table With Appendix On Stirling Transform

Author : Boyadzhiev Khristo N
Publisher : World Scientific
ISBN 13 : 9813234997
Total Pages : 208 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Notes On The Binomial Transform: Theory And Table With Appendix On Stirling Transform by : Boyadzhiev Khristo N

Download or read book Notes On The Binomial Transform: Theory And Table With Appendix On Stirling Transform written by Boyadzhiev Khristo N and published by World Scientific. This book was released on 2018-04-10 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The binomial transform is a discrete transformation of one sequence into another with many interesting applications in combinatorics and analysis. This volume is helpful to researchers interested in enumerative combinatorics, special numbers, and classical analysis. A valuable reference, it can also be used as lecture notes for a course in binomial identities, binomial transforms and Euler series transformations. The binomial transform leads to various combinatorial and analytical identities involving binomial coefficients. In particular, we present here new binomial identities for Bernoulli, Fibonacci, and harmonic numbers. Many interesting identities can be written as binomial transforms and vice versa. The volume consists of two parts. In the first part, we present the theory of the binomial transform for sequences with a sufficient prerequisite of classical numbers and polynomials. The first part provides theorems and tools which help to compute binomial transforms of different sequences and also to generate new binomial identities from the old. These theoretical tools (formulas and theorems) can also be used for summation of series and various numerical computations. In the second part, we have compiled a list of binomial transform formulas for easy reference. In the Appendix, we present the definition of the Stirling sequence transform and a short table of transformation formulas. Contents: Theory of the Binomial Transform: Introduction Prerequisite: Special Numbers and Polynomials Euler's Transformation for Series Melzak's Formula and Related Formulas Special Properties. Creating New Identities Binomial Transforms of Products Special Formulas and Power Series with Binomial Sums Table of Binomial Transforms: Assorted Binomial Formulas Identities Involving Harmonic Numbers Transforms of Binomial Coefficients Transforms of Special Numbers and Polynomials Transforms of Trigonometric and Hyperbolic Functions and Applications to Some Trigonometric Integrals Transforms of Some Special Functions Appendix: The Stirling Transform of Sequences Readership: Graduate and researchers in the areas of number theory, discrete mathematics, combinatorics, statistics working with applications using the binomial transform. Keywords: Binomial Coefficients;Binomial Identities;Binomial Sums;Binomial Transform;Euler's Series Transformation;Discrete Mathematics;Finite Differences;Stirling Numbers of the First Kind;Stirling Numbers of the Second Kind;Stirling Transform;Special Numbers and Polynomials;Harmonic Numbers;Bernoulli Numbers;Fibonacci Numbers;Melzak's Formula;Exponential Polynomials;Geometric Polynomials;Laguerre Polynomials;Trigonometric IntegralsReview: Key Features: This is the first, long-overdue book on the subject. (At present, there are no competing books) The book provides interesting new material for researchers in discrete mathematics and will serve as a valuable reference for binomial identities, binomial transform formulas, and Euler series transformations

Analytic Combinatorics

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Analytic Combinatorics by : Philippe Flajolet

Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Probability

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 113949113X
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Probability by : Rick Durrett

Download or read book Probability written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-08-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Biostatistical Analysis

Author : Jerrold H. Zar
Publisher :
ISBN 13 : 9781292024042
Total Pages : 756 pages
Book Rating : 4.0/5 (24 download)

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Book Synopsis Biostatistical Analysis by : Jerrold H. Zar

Download or read book Biostatistical Analysis written by Jerrold H. Zar and published by . This book was released on 2014 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zar's Biostatistncal Analysis, Fifth Edition, is the ideal textbook for graduate and undergraduate students seeking practncal coverage of statistncal analysis methods used by researchers to collect, summarize, analyze and draw conclusnons from biologic E research. The latest editnon of this best-selling textbook is both comprehensive and easy to read. It is suitable as an introductnon for begnnnnng students and as a comprehensive reference book for biologic E researchers and for advanced students. This book is appropriate for a one- or two-semester, junior or graduate-level course in biostatistncs, biometry, quantitatnve biology, or statistics, and assumes a prerequisite ofalgebra.

Combinatorics: The Art of Counting

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
ISBN 13 : 1470460327
Total Pages : 304 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Combinatorics: The Art of Counting by : Bruce E. Sagan

Download or read book Combinatorics: The Art of Counting written by Bruce E. Sagan and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Algebraic Combinatorics

Author : Richard P. Stanley
Publisher : Springer Science & Business Media
ISBN 13 : 1461469988
Total Pages : 226 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Algebraic Combinatorics by : Richard P. Stanley

Download or read book Algebraic Combinatorics written by Richard P. Stanley and published by Springer Science & Business Media. This book was released on 2013-06-17 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.

Numerical Methods for Laplace Transform Inversion

Author : Alan M. Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 0387688552
Total Pages : 262 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis Numerical Methods for Laplace Transform Inversion by : Alan M. Cohen

Download or read book Numerical Methods for Laplace Transform Inversion written by Alan M. Cohen and published by Springer Science & Business Media. This book was released on 2007-06-16 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives background material on the theory of Laplace transforms, together with a fairly comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations.

Generatingfunctionology

Author : Herbert S. Wilf
Publisher : Elsevier
ISBN 13 : 1483276635
Total Pages : 193 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Generatingfunctionology by : Herbert S. Wilf

Download or read book Generatingfunctionology written by Herbert S. Wilf and published by Elsevier. This book was released on 2014-05-10 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

The Analysis of Fractional Differential Equations

Author : Kai Diethelm
Publisher : Springer
ISBN 13 : 3642145744
Total Pages : 247 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm

Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer. This book was released on 2010-08-18 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Analytic Combinatorics in Several Variables

Author : Robin Pemantle
Publisher : Cambridge University Press
ISBN 13 : 1107031575
Total Pages : 395 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Analytic Combinatorics in Several Variables by : Robin Pemantle

Download or read book Analytic Combinatorics in Several Variables written by Robin Pemantle and published by Cambridge University Press. This book was released on 2013-05-31 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.

Complex Analysis

Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 1400831156
Total Pages : 398 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Complex Analysis by : Elias M. Stein

Download or read book Complex Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2010-04-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Combinatorial Identities for Stirling Numbers

Author : Jocelyn Quaintance
Publisher : World Scientific
ISBN 13 : 9814725285
Total Pages : 277 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Combinatorial Identities for Stirling Numbers by : Jocelyn Quaintance

Download or read book Combinatorial Identities for Stirling Numbers written by Jocelyn Quaintance and published by World Scientific. This book was released on 2015-10-27 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."--

Modular Forms, a Computational Approach

Author : William A. Stein
Publisher : American Mathematical Soc.
ISBN 13 : 0821839608
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Modular Forms, a Computational Approach by : William A. Stein

Download or read book Modular Forms, a Computational Approach written by William A. Stein and published by American Mathematical Soc.. This book was released on 2007-02-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.

Foundations of Data Science

Author : Avrim Blum
Publisher : Cambridge University Press
ISBN 13 : 1108617360
Total Pages : 433 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Foundations of Data Science by : Avrim Blum

Download or read book Foundations of Data Science written by Avrim Blum and published by Cambridge University Press. This book was released on 2020-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

Information Theory, Inference and Learning Algorithms

Author : David J. C. MacKay
Publisher : Cambridge University Press
ISBN 13 : 9780521642989
Total Pages : 694 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Information Theory, Inference and Learning Algorithms by : David J. C. MacKay

Download or read book Information Theory, Inference and Learning Algorithms written by David J. C. MacKay and published by Cambridge University Press. This book was released on 2003-09-25 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.

Special Techniques For Solving Integrals: Examples And Problems

Author : Khristo N Boyadzhiev
Publisher : World Scientific
ISBN 13 : 9811235775
Total Pages : 401 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Special Techniques For Solving Integrals: Examples And Problems by : Khristo N Boyadzhiev

Download or read book Special Techniques For Solving Integrals: Examples And Problems written by Khristo N Boyadzhiev and published by World Scientific. This book was released on 2021-12-10 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains techniques of integration which are not found in standard calculus and advanced calculus books. It can be considered as a map to explore many classical approaches to evaluate integrals. It is intended for students and professionals who need to solve integrals or like to solve integrals and yearn to learn more about the various methods they could apply. Undergraduate and graduate students whose studies include mathematical analysis or mathematical physics will strongly benefit from this material. Mathematicians involved in research and teaching in areas related to calculus, advanced calculus and real analysis will find it invaluable.The volume contains numerous solved examples and problems for the reader. These examples can be used in classwork or for home assignments, as well as a supplement to student projects and student research.

The H-Function

Author : A.M. Mathai
Publisher : Springer Science & Business Media
ISBN 13 : 1441909168
Total Pages : 276 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis The H-Function by : A.M. Mathai

Download or read book The H-Function written by A.M. Mathai and published by Springer Science & Business Media. This book was released on 2009-10-10 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.