Proofs that Really Count PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Proofs that Really Count PDF full book. Access full book title Proofs that Really Count by Arthur T. Benjamin. Download full books in PDF and EPUB format.
Author: Arthur T. Benjamin
Publisher: American Mathematical Society
ISBN: 1470472597
Category : Mathematics
Languages : en
Pages : 210
Get Book Here
Book Description
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: Arthur T. Benjamin
Publisher: American Mathematical Society
ISBN: 1470472597
Category : Mathematics
Languages : en
Pages : 210
Get Book Here
Book Description
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: John Riordan
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 280
Get Book Here
Book Description
Author: Jocelyn Quaintance
Publisher: World Scientific
ISBN: 9814725285
Category : Mathematics
Languages : en
Pages : 277
Get Book Here
Book Description
"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: Oscar Levin
Publisher: Createspace Independent Publishing Platform
ISBN: 9781534970748
Category :
Languages : en
Pages : 342
Get Book Here
Book Description
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. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. 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: Antonio Giambruno
Publisher: CRC Press
ISBN: 9780203911549
Category : Mathematics
Languages : en
Pages : 442
Get Book Here
Book Description
Polynomial Identities and Combinatorial Methods presents a wide range of perspectives on topics ranging from ring theory and combinatorics to invariant theory and associative algebras. It covers recent breakthroughs and strategies impacting research on polynomial identities and identifies new concepts in algebraic combinatorics, invariant and representation theory, and Lie algebras and superalgebras for novel studies in the field. It presents intensive discussions on various methods and techniques relating the theory of polynomial identities to other branches of algebraic study and includes discussions on Hopf algebras and quantum polynomials, free algebras and Scheier varieties.
Author: Russell Merris
Publisher: John Wiley & Sons
ISBN: 047145849X
Category : Mathematics
Languages : en
Pages : 572
Get Book Here
Book Description
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: Titu Andreescu
Publisher: Springer Science & Business Media
ISBN: 0817682228
Category : Mathematics
Languages : en
Pages : 125
Get Book Here
Book Description
"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.
Author: J. Siemons
Publisher: Cambridge University Press
ISBN: 9780521378239
Category : Mathematics
Languages : en
Pages : 232
Get Book Here
Book Description
Many areas of current research activity in combinatorics and its applications, including graph theory, designs and probabilistic graphs, are surveyed in lectures presented at the 12th British Combinatorial Conference.
Author: Krishnaswami Alladi
Publisher: Springer Nature
ISBN: 3030570509
Category : Mathematics
Languages : en
Pages : 802
Get Book Here
Book Description
This book presents a printed testimony for the fact that George Andrews, one of the world’s leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the conference “Combinatory Analysis 2018” was organized at the Pennsylvania State University from June 21 to 24, 2018. This volume comprises the original articles from the Special Issue “Combinatory Analysis 2018 – In Honor of George Andrews’ 80th Birthday” resulting from the conference and published in Annals of Combinatorics. In addition to the 37 articles of the Andrews 80 Special Issue, the book includes two new papers. These research contributions explore new grounds and present new achievements, research trends, and problems in the area. The volume is complemented by three special personal contributions: “The Worlds of George Andrews, a daughter’s take” by Amy Alznauer, “My association and collaboration with George Andrews” by Krishna Alladi, and “Ramanujan, his Lost Notebook, its importance” by Bruce Berndt. Another aspect which gives this Andrews volume a truly unique character is the “Photos” collection. In addition to pictures taken at “Combinatory Analysis 2018”, the editors selected a variety of photos, many of them not available elsewhere: “Andrews in Austria”, “Andrews in China”, “Andrews in Florida”, “Andrews in Illinois”, and “Andrews in India”. This volume will be of interest to researchers, PhD students, and interested practitioners working in the area of Combinatory Analysis, q-Series, and related fields.
Author: Nicholas Loehr
Publisher: CRC Press
ISBN: 1439848866
Category : Computers
Languages : en
Pages : 600
Get Book Here
Book Description
Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical
