Proofs That Really Count The Art Of Combinatorial Proof
Download Proofs That Really Count The Art Of Combinatorial Proof full books in PDF, epub, and Kindle. Read online free Proofs That Really Count The Art Of Combinatorial Proof ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Arthur T. Benjamin |
| Publisher | : American Mathematical Society |
| Total Pages | : 210 |
| Release | : 2022-09-21 |
| Genre | : Mathematics |
| ISBN | : 1470472597 |
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 Soc. |
| Total Pages | : 209 |
| Release | : 2003-11-13 |
| Genre | : Education |
| ISBN | : 0883853337 |
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.
| Author | : Arthur Benjamin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 209 |
| Release | : 2003-12-31 |
| Genre | : Education |
| ISBN | : 1614442088 |
Demonstration of the use of simple counting arguments to describe number patterns; numerous hints and references.
| Author | : Richard H. Hammack |
| Publisher | : |
| Total Pages | : 314 |
| Release | : 2016-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780989472111 |
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
| Author | : Bruce E. Sagan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 304 |
| Release | : 2020-10-16 |
| Genre | : Education |
| ISBN | : 1470460327 |
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.
| Author | : Martin Aigner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 194 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 3662223430 |
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
| Author | : Ethan D. Bloch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461221307 |
The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.
| Author | : Nicholas Loehr |
| Publisher | : CRC Press |
| Total Pages | : 600 |
| Release | : 2011-02-10 |
| Genre | : Computers |
| ISBN | : 1439848866 |
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
| Author | : Philippe Flajolet |
| Publisher | : Cambridge University Press |
| Total Pages | : 825 |
| Release | : 2009-01-15 |
| Genre | : Mathematics |
| ISBN | : 1139477161 |
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.
| Author | : Robert M. Young |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 435 |
| Release | : 1992-10-01 |
| Genre | : Mathematics |
| ISBN | : 1470457202 |
This book explores the rich and elegant interplay between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus.
