Obtaining Generating Functions

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Obtaining Generating Functions

Author : Elna B. McBride
Publisher : Springer Science & Business Media
ISBN 13 : 364287682X
Total Pages : 109 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Obtaining Generating Functions by : Elna B. McBride

Download or read book Obtaining Generating Functions written by Elna B. McBride and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the study of methods of obtaining generating functions. It is an expository work at the level of the beginning graduate student. The first part of Chapter I gives the reader the necessary definitions and basic concepts. The fundamental method of direct summation is explained and illustrated. The second part of Chapter I deals with the methods developed by Rainville. These methods are based principally on inventive manipulation of power series. Weisner's group-theoretic method is explained in detail in Chapter II and is further illustrated in Chapter III. When this method is applicable, it yields a set of at least three generating functions. In Chapter II for the Laguerre polynomials six generating functions were found. Truesdell's method is studied in Chapter IV. For a given set of functions {fez, an the success of this method depends on the existence of certain transformations. If fez, a) can be transformed into F(z, a) such that a a-; F(z, a)=F(z, a+ 1), or if fez, a) can be transformed into G(z, a) such that a a-; G(z, a)=G(z, a-I), then from each transformed function a generating function can be obtained. Truesdell's method for obtaining the transformed functions does not require any ingenuity on the user's part. Truesdell has shown how these simple results may be exploited to generate more complicated results by means of specified, systematic, and general processes. His method of obtaining generating functions is only one of these results.

Discrete Mathematics

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781724572639
Total Pages : 238 pages
Book Rating : 4.5/5 (726 download)

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Book Synopsis Discrete Mathematics by : Oscar Levin

Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2018-07-30 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.

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.

generatingfunctionology

Author : Herbert S. Wilf
Publisher : CRC Press
ISBN 13 : 143986439X
Total Pages : 192 pages
Book Rating : 4.4/5 (398 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 CRC Press. This book was released on 2005-12-20 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in - Combinatorics - Probability Theory - Statistics - Theory of Markov Chains - Number Theory One of the most important and

Obtaining Generating Functions

Author : Elna Browning McBride
Publisher : Springer
ISBN 13 : 9780387052557
Total Pages : 100 pages
Book Rating : 4.0/5 (525 download)

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Book Synopsis Obtaining Generating Functions by : Elna Browning McBride

Download or read book Obtaining Generating Functions written by Elna Browning McBride and published by Springer. This book was released on 1971-01-01 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

A Treatise on Generating Functions

Author : H. M. Srivastava
Publisher : Ellis Horwood
ISBN 13 :
Total Pages : 580 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis A Treatise on Generating Functions by : H. M. Srivastava

Download or read book A Treatise on Generating Functions written by H. M. Srivastava and published by Ellis Horwood. This book was released on 1984 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Generating Functions in Engineering and the Applied Sciences

Author : Rajan Chattamvelli
Publisher : Springer Nature
ISBN 13 : 3031794109
Total Pages : 99 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Generating Functions in Engineering and the Applied Sciences by : Rajan Chattamvelli

Download or read book Generating Functions in Engineering and the Applied Sciences written by Rajan Chattamvelli and published by Springer Nature. This book was released on 2022-05-31 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on generating functions (GFs) and their applications. It discusses commonly encountered generating functions in engineering and applied sciences, such as ordinary generating functions (OGF), exponential generating functions (EGF), probability generating functions (PGF), etc. Some new GFs like Pochhammer generating functions for both rising and falling factorials are introduced in Chapter 2. Two novel GFs called "mean deviation generating function" (MDGF) and "survival function generating function" (SFGF), are introduced in Chapter 3. The mean deviation of a variety of discrete distributions are derived using the MDGF. The last chapter discusses a large number of applications in various disciplines including algebra, analysis of algorithms, polymer chemistry, combinatorics, graph theory, number theory, reliability, epidemiology, bio-informatics, genetics, management, economics, and statistics. Some background knowledge on GFs is often assumed for courses in analysis of algorithms, advanced data structures, digital signal processing (DSP), graph theory, etc. These are usually provided by either a course on "discrete mathematics" or "introduction to combinatorics." But, GFs are also used in automata theory, bio-informatics, differential equations, DSP, number theory, physical chemistry, reliability engineering, stochastic processes, and so on. Students of these courses may not have exposure to discrete mathematics or combinatorics. This book is written in such a way that even those who do not have prior knowledge can easily follow through the chapters, and apply the lessons learned in their respective disciplines. The purpose is to give a broad exposure to commonly used techniques of combinatorial mathematics, highlighting applications in a variety of disciplines.

Applied Discrete Structures

Author : Ken Levasseur
Publisher : Lulu.com
ISBN 13 : 1105559297
Total Pages : 574 pages
Book Rating : 4.1/5 (55 download)

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Book Synopsis Applied Discrete Structures by : Ken Levasseur

Download or read book Applied Discrete Structures written by Ken Levasseur and published by Lulu.com. This book was released on 2012-02-25 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.

Generating Functionology

Author : Herbert S. Wilf
Publisher : Elsevier
ISBN 13 : 0080571514
Total Pages : 239 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Generating Functionology by : Herbert S. Wilf

Download or read book Generating Functionology written by Herbert S. Wilf and published by Elsevier. This book was released on 2013-10-22 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica(r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter. Provides new applications on the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences Features an Appendix on using MAPLE(r) and Mathematica (r) to generate functions Includes many new exercises with complete solutions at the end of each chapter

A STUDY OF METHODS OF OBTAINING GENERATING FUNCTIONS.

Author : ELNA BROWNING MCBRIDE
Publisher :
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.:/5 (28 download)

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Book Synopsis A STUDY OF METHODS OF OBTAINING GENERATING FUNCTIONS. by : ELNA BROWNING MCBRIDE

Download or read book A STUDY OF METHODS OF OBTAINING GENERATING FUNCTIONS. written by ELNA BROWNING MCBRIDE and published by . This book was released on 1966 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inquiry-Based Enumerative Combinatorics

Author : T. Kyle Petersen
Publisher : Springer
ISBN 13 : 3030183084
Total Pages : 238 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Inquiry-Based Enumerative Combinatorics by : T. Kyle Petersen

Download or read book Inquiry-Based Enumerative Combinatorics written by T. Kyle Petersen and published by Springer. This book was released on 2019-06-28 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers the opportunity to create a uniquely engaging combinatorics classroom by embracing Inquiry-Based Learning (IBL) techniques. Readers are provided with a carefully chosen progression of theorems to prove and problems to actively solve. Students will feel a sense of accomplishment as their collective inquiry traces a path from the basics to important generating function techniques. Beginning with an exploration of permutations and combinations that culminates in the Binomial Theorem, the text goes on to guide the study of ordinary and exponential generating functions. These tools underpin the in-depth study of Eulerian, Catalan, and Narayana numbers that follows, and a selection of advanced topics that includes applications to probability and number theory. Throughout, the theory unfolds via over 150 carefully selected problems for students to solve, many of which connect to state-of-the-art research. Inquiry-Based Enumerative Combinatorics is ideal for lower-division undergraduate students majoring in math or computer science, as there are no formal mathematics prerequisites. Because it includes many connections to recent research, students of any level who are interested in combinatorics will also find this a valuable resource.

Lectures on Generating Functions

Author : Sergei K. Lando
Publisher : American Mathematical Soc.
ISBN 13 : 9780821884492
Total Pages : 170 pages
Book Rating : 4.8/5 (844 download)

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Book Synopsis Lectures on Generating Functions by : Sergei K. Lando

Download or read book Lectures on Generating Functions written by Sergei K. Lando and published by American Mathematical Soc.. This book was released on with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces readers to the language of generating functions, which is the main language of enumerative combinatorics. This book starts with definitions, simple properties, and many examples of generating functions. It discusses topics such as formal grammars, generating functions in several variables, and the exclusion-inclusion principle.

Abel’s Theorem in Problems and Solutions

Author : V.B. Alekseev
Publisher : Springer Science & Business Media
ISBN 13 : 1402021879
Total Pages : 278 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Abel’s Theorem in Problems and Solutions by : V.B. Alekseev

Download or read book Abel’s Theorem in Problems and Solutions written by V.B. Alekseev and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.

Recurrent Sequences

Author : Dorin Andrica
Publisher : Springer Nature
ISBN 13 : 3030515028
Total Pages : 410 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Recurrent Sequences by : Dorin Andrica

Download or read book Recurrent Sequences written by Dorin Andrica and published by Springer Nature. This book was released on 2020-09-23 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics. It is designed to appeal to a wide readership, ranging from scholars and academics, to undergraduate students, or advanced high school and college students training for competitions. The content of the book is very recent, and focuses on areas where significant research is currently taking place. Among the new approaches promoted in this book, the authors highlight the visualization of some recurrences in the complex plane, the concurrent use of algebraic, arithmetic, and trigonometric perspectives on classical number sequences, and links to many applications. It contains techniques which are fundamental in other areas of math and encourages further research on the topic. The introductory chapters only require good understanding of college algebra, complex numbers, analysis and basic combinatorics. For Chapters 3, 4 and 6 the prerequisites include number theory, linear algebra and complex analysis. The first part of the book presents key theoretical elements required for a good understanding of the topic. The exposition moves on to to fundamental results and key examples of recurrences and their properties. The geometry of linear recurrences in the complex plane is presented in detail through numerous diagrams, which lead to often unexpected connections to combinatorics, number theory, integer sequences, and random number generation. The second part of the book presents a collection of 123 problems with full solutions, illustrating the wide range of topics where recurrent sequences can be found. This material is ideal for consolidating the theoretical knowledge and for preparing students for Olympiads.

Combinatorics

Author : Pavle Mladenović
Publisher : Springer
ISBN 13 : 3030008312
Total Pages : 365 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Combinatorics by : Pavle Mladenović

Download or read book Combinatorics written by Pavle Mladenović and published by Springer. This book was released on 2019-03-13 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability. A number of examples are given with explanations while the book also provides more than 300 exercises of different levels of difficulty that are arranged at the end of each chapter, and more than 130 additional challenging problems, including problems from mathematical olympiads. Solutions or hints to all exercises and problems are included. The book can be used by secondary school students preparing for mathematical competitions, by their instructors, and by undergraduate students. The book may also be useful for graduate students and for researchers that apply combinatorial methods in different areas.

Mathematics for Computer Science

Author : Eric Lehman
Publisher :
ISBN 13 : 9789888407064
Total Pages : 988 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Mathematics for Computer Science by : Eric Lehman

Download or read book Mathematics for Computer Science written by Eric Lehman and published by . This book was released on 2017-03-08 with total page 988 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.