Proofs That Really Count
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Proofs That Really Count The Art Of Combinatorial Proof
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Author : Arthur T. Benjamin
language : en
Publisher: American Mathematical Soc.
Release Date : 2003-11-13
Proofs That Really Count The Art Of Combinatorial Proof written by Arthur T. Benjamin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-13 with Education categories.
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2006! 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.
Proofs That Really Count
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Author : Arthur T. Benjamin
language : en
Publisher: American Mathematical Society
Release Date : 2022-09-21
Proofs That Really Count written by Arthur T. Benjamin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-21 with Mathematics categories.
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.
The Art Of Proving Binomial Identities
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Author : Michael Z. Spivey
language : en
Publisher: CRC Press
Release Date : 2019-05-10
The Art Of Proving Binomial Identities written by Michael Z. Spivey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-10 with Mathematics categories.
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.
How To Count
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Author : Robert A. Beeler
language : en
Publisher: Springer
Release Date : 2015-03-14
How To Count written by Robert A. Beeler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-14 with Mathematics categories.
Providing a self-contained resource for upper undergraduate courses in combinatorics, this text emphasizes computation, problem solving, and proof technique. In particular, the book places special emphasis the Principle of Inclusion and Exclusion and the Multiplication Principle. To this end, exercise sets are included at the end of every section, ranging from simple computations (evaluate a formula for a given set of values) to more advanced proofs. The exercises are designed to test students' understanding of new material, while reinforcing a working mastery of the key concepts previously developed in the book. Intuitive descriptions for many abstract techniques are included. Students often struggle with certain topics, such as generating functions, and this intuitive approach to the problem is helpful in their understanding. When possible, the book introduces concepts using combinatorial methods (as opposed to induction or algebra) to prove identities. Students are also asked to prove identities using combinatorial methods as part of their exercises. These methods have several advantages over induction or algebra.
Combinatorics The Art Of Counting
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Author : Bruce E. Sagan
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-16
Combinatorics The Art Of Counting written by Bruce E. Sagan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-16 with Education categories.
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.
Hands On Combinatorics
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Author : Brian Hopkins
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-29
Hands On Combinatorics written by Brian Hopkins and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-29 with Mathematics categories.
This book provides an active-learning approach to combinatorial reasoning and proof through a thoughtful sequence of low threshold, high ceiling activities. A novel feature is its narrative format, with much of the text written from the perspective of a student working through the material with peers. Furthermore, each chapter includes detailed notes for the instructor such as additional scaffolding, extensions, and notation for more advanced students. The exposition is complemented by over 300 colorful illustrations. The main focus of the book is the study of integer compositions with forays into graph theory and recreational mathematics. Befitting the constructive nature of the book, compositions are represented by trains made up of cars. By physically constructing these objects, students become proficient in hands-on verifications of numerous identities. Developed by a recipient of the MAA's Haimo Award for Distinguished Teaching and used in several teacher professional development workshops and college courses, the book has very modest prerequisites. In particular, no prior experience with symbolic formalism is presumed, allowing this material to be used in multiple classroom settings, from enrichment activities for secondary school students through undergraduate classes in discrete mathematics. The structure of the book also makes it conducive to self-study. Get ready to “build some trains” and explore the enlightening world of combinatorial proofs! Hands-On Combinatorics is a wonderful book, cleverly designed for readers of all mathematical levels. With eye-catching illustrations, Brian Hopkins creates beautiful bijections and clever combinatorial arguments with binomial coefficients, Fibonacci numbers, and beyond. —Arthur T. Benjamin, Harvey Mudd College, co-author of Proofs That Really Count
Topics From The 8th Annual Uncg Regional Mathematics And Statistics Conference
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Author : Jan Rychtář
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-20
Topics From The 8th Annual Uncg Regional Mathematics And Statistics Conference written by Jan Rychtář and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-20 with Mathematics categories.
The Annual University of North Carolina Greensboro Regional Mathematics and Statistics Conference (UNCG RMSC) has provided a venue for student researchers to share their work since 2005. The 8th Conference took place on November 3, 2012. The UNCG-RMSC conference established a tradition of attracting active researchers and their faculty mentors from NC and surrounding states. The conference is specifically tailored for students to present the results of their research and to allow participants to interact with and learn from each other. This type of engagement is truly unique. The broad scope of UNCG-RMSC includes topics in applied mathematics, number theory, biology, statistics, biostatistics and computer sciences.
Rediscovering Mathematics
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Author : Shai Simonson
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-30
Rediscovering Mathematics written by Shai Simonson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-30 with Education categories.
Rediscovering Mathematics is aimed at a general audience and addresses the question of how best to teach and study mathematics. The book attempts to bring the exciting and dynamic world of mathematics to a non-technical audience. With so much focus today on how best to educate the new generation and make mathematics less rote and more interactive, this book is an eye-opening experience for many people who suffered with dull math teachers and curricula. Rediscovering Mathematics is an eclectic collection of mathematical topics and puzzles aimed at talented youngsters and inquisitive adults who want to expand their view of mathematics. By focusing on problem solving, and discouraging rote memorization, the book shows how to learn and teach mathematics through investigation, experimentation, and discovery. Rediscovering Mathematics is also an excellent text for training math teachers at all levels. Topics range in difficulty and cover a wide range of historical periods, with some examples demonstrating how to uncover mathematics in everyday life, including: number theory and its application to secure communication over the Internet, the algebraic and combinatorial work of a medieval mathematician Rabbi, and applications of probability to sports, casinos, and gambling. Rediscovering Mathematics provides a fresh view of mathematics for those who already like the subject, and offers a second chance for those who think they don't.
We Reason We Prove For All Mathematics
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Author : Fran Arbaugh
language : en
Publisher: Corwin Press
Release Date : 2018-08-08
We Reason We Prove For All Mathematics written by Fran Arbaugh and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-08 with Education categories.
Sharpen concrete teaching strategies that empower students to reason-and-prove What does reasoning-and-proving instruction look like and how can teachers support students’ capacity to reason-and-prove? Designed as a learning tool for mathematics teachers in grades 6-12, this book transcends all mathematical content areas with a variety of activities for teachers that include Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work Modifying curriculum materials and evaluating learning environments to better support students to reason-and-prove No other book tackles reasoning-and-proving with such breath, depth, and practical applicability.
Wittgensteinian Adj
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Author : Shyam Wuppuluri
language : en
Publisher: Springer Nature
Release Date : 2019-11-22
Wittgensteinian Adj written by Shyam Wuppuluri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-22 with Science categories.
“Tell me," Wittgenstein once asked a friend, "why do people always say, it was natural for man to assume that the sun went round the earth rather than that the earth was rotating?" His friend replied, "Well, obviously because it just looks as though the Sun is going round the Earth." Wittgenstein replied, "Well, what would it have looked like if it had looked as though the Earth was rotating?” What would it have looked like if we looked at all sciences from the viewpoint of Wittgenstein’s philosophy? Wittgenstein is undoubtedly one of the most influential philosophers of the twentieth century. His complex body of work has been analysed by numerous scholars, from mathematicians and physicists, to philosophers, linguists, and beyond. This volume brings together some of his central perspectives as applied to the modern sciences and studies the influence they may have on the thought processes underlying science and on the world view it engenders. The contributions stem from leading scholars in philosophy, mathematics, physics, economics, psychology and human sciences; all of them have written in an accessible style that demands little specialist knowledge, whilst clearly portraying and discussing the deep issues at hand.