Combinatorial Identities PDF Download
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Author | : Jocelyn Quaintance |
Publisher | : World Scientific |
Total Pages | : 277 |
Release | : 2015-10-27 |
Genre | : Mathematics |
ISBN | : 9814725293 |
Download Combinatorial Identities For Stirling Numbers: The Unpublished Notes Of H W Gould Book in PDF, ePub and Kindle
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.
Author | : John Riordan |
Publisher | : |
Total Pages | : 280 |
Release | : 1979 |
Genre | : Mathematics |
ISBN | : |
Download Combinatorial Identities Book in PDF, ePub and Kindle
Author | : Arthur T. Benjamin |
Publisher | : American Mathematical Society |
Total Pages | : 210 |
Release | : 2022-09-21 |
Genre | : Mathematics |
ISBN | : 1470472597 |
Download Proofs that Really Count Book in PDF, ePub and Kindle
Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.
Author | : Oscar Levin |
Publisher | : Createspace Independent Publishing Platform |
Total Pages | : 238 |
Release | : 2018-07-30 |
Genre | : |
ISBN | : 9781724572639 |
Download Discrete Mathematics Book in PDF, ePub and Kindle
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.
Author | : Jocelyn Quaintance |
Publisher | : World Scientific |
Total Pages | : 277 |
Release | : 2015-10-27 |
Genre | : Mathematics |
ISBN | : 9814725285 |
Download Combinatorial Identities for Stirling Numbers Book in PDF, ePub and Kindle
"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."--
Author | : Henry Wadsworth Gould |
Publisher | : |
Total Pages | : 250 |
Release | : 1972 |
Genre | : Analyse combinatoire |
ISBN | : |
Download Combinatorial Identities Book in PDF, ePub and Kindle
Author | : W.D. Wallis |
Publisher | : CRC Press |
Total Pages | : 398 |
Release | : 2011-06-30 |
Genre | : Computers |
ISBN | : 1439806233 |
Download Introduction to Combinatorics Book in PDF, ePub and Kindle
Accessible to undergraduate students, Introduction to Combinatorics presents approaches for solving counting and structural questions. It looks at how many ways a selection or arrangement can be chosen with a specific set of properties and determines if a selection or arrangement of objects exists that has a particular set of properties. To give students a better idea of what the subject covers, the authors first discuss several examples of typical combinatorial problems. They also provide basic information on sets, proof techniques, enumeration, and graph theory—topics that appear frequently throughout the book. The next few chapters explore enumerative ideas, including the pigeonhole principle and inclusion/exclusion. The text then covers enumerative functions and the relations between them. It describes generating functions and recurrences, important families of functions, and the theorems of Pólya and Redfield. The authors also present introductions to computer algebra and group theory, before considering structures of particular interest in combinatorics: graphs, codes, Latin squares, and experimental designs. The last chapter further illustrates the interaction between linear algebra and combinatorics. Exercises and problems of varying levels of difficulty are included at the end of each chapter. Ideal for undergraduate students in mathematics taking an introductory course in combinatorics, this text explores the different ways of arranging objects and selecting objects from a set. It clearly explains how to solve the various problems that arise in this branch of mathematics.
Author | : Michael Z. Spivey |
Publisher | : CRC Press |
Total Pages | : 231 |
Release | : 2019-05-10 |
Genre | : Mathematics |
ISBN | : 1351215809 |
Download The Art of Proving Binomial Identities Book in PDF, ePub and Kindle
The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton’s binomial series), differentiation (Leibniz’s generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.
Author | : Russell Merris |
Publisher | : John Wiley & Sons |
Total Pages | : 572 |
Release | : 2003-09-24 |
Genre | : Mathematics |
ISBN | : 047145849X |
Download Combinatorics Book in PDF, ePub and Kindle
A mathematical gem–freshly cleaned and polished This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course. Features retained from the first edition: Lively and engaging writing style Timely and appropriate examples Numerous well-chosen exercises Flexible modular format Optional sections and appendices Highlights of Second Edition enhancements: Smoothed and polished exposition, with a sharpened focus on key ideas Expanded discussion of linear codes New optional section on algorithms Greatly expanded hints and answers section Many new exercises and examples
Author | : Chuan-Chong Chen |
Publisher | : World Scientific |
Total Pages | : 314 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 9789810211394 |
Download Principles and Techniques in Combinatorics Book in PDF, ePub and Kindle
A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.