Recurrence Relations Fibonacci and Catalan Numbers
Author : Ruby L. Edwards
Publisher :
Page : 35 pages
File Size : 26,16 MB
Release : 1992
Category : Combinations
ISBN :
Fibonacci and Catalan Numbers
Author : Ralph Grimaldi
Publisher : John Wiley & Sons
Page : 380 pages
File Size : 11,37 MB
Release : 2012-02-21
Category : Mathematics
ISBN : 1118159764
Book Description
Discover the properties and real-world applications of the Fibonacci and the Catalan numbers With clear explanations and easy-to-follow examples, Fibonacci and Catalan Numbers: An Introduction offers a fascinating overview of these topics that is accessible to a broad range of readers. Beginning with a historical development of each topic, the book guides readers through the essential properties of the Fibonacci numbers, offering many introductory-level examples. The author explains the relationship of the Fibonacci numbers to compositions and palindromes, tilings, graph theory, and the Lucas numbers. The book proceeds to explore the Catalan numbers, with the author drawing from their history to provide a solid foundation of the underlying properties. The relationship of the Catalan numbers to various concepts is then presented in examples dealing with partial orders, total orders, topological sorting, graph theory, rooted-ordered binary trees, pattern avoidance, and the Narayana numbers. The book features various aids and insights that allow readers to develop a complete understanding of the presented topics, including: Real-world examples that demonstrate the application of the Fibonacci and the Catalan numbers to such fields as sports, botany, chemistry, physics, and computer science More than 300 exercises that enable readers to explore many of the presented examples in greater depth Illustrations that clarify and simplify the concepts Fibonacci and Catalan Numbers is an excellent book for courses on discrete mathematics, combinatorics, and number theory, especially at the undergraduate level. Undergraduates will find the book to be an excellent source for independent study, as well as a source of topics for research. Further, a great deal of the material can also be used for enrichment in high school courses.
Fibonacci and Catalan Numbers
Author : Ralph Grimaldi
Publisher : John Wiley & Sons
Page : 380 pages
File Size : 25,58 MB
Release : 2012-03-13
Category : Mathematics
ISBN : 0470631570
Book Description
Discover the properties and real-world applications of the Fibonacci and the Catalan numbers With clear explanations and easy-to-follow examples, Fibonacci and Catalan Numbers: An Introduction offers a fascinating overview of these topics that is accessible to a broad range of readers. Beginning with a historical development of each topic, the book guides readers through the essential properties of the Fibonacci numbers, offering many introductory-level examples. The author explains the relationship of the Fibonacci numbers to compositions and palindromes, tilings, graph theory, and the Lucas numbers. The book proceeds to explore the Catalan numbers, with the author drawing from their history to provide a solid foundation of the underlying properties. The relationship of the Catalan numbers to various concepts is then presented in examples dealing with partial orders, total orders, topological sorting, graph theory, rooted-ordered binary trees, pattern avoidance, and the Narayana numbers. The book features various aids and insights that allow readers to develop a complete understanding of the presented topics, including: Real-world examples that demonstrate the application of the Fibonacci and the Catalan numbers to such fields as sports, botany, chemistry, physics, and computer science More than 300 exercises that enable readers to explore many of the presented examples in greater depth Illustrations that clarify and simplify the concepts Fibonacci and Catalan Numbers is an excellent book for courses on discrete mathematics, combinatorics, and number theory, especially at the undergraduate level. Undergraduates will find the book to be an excellent source for independent study, as well as a source of topics for research. Further, a great deal of the material can also be used for enrichment in high school courses.
Catalan Numbers with Applications
Author : Thomas Koshy
Publisher : OUP USA
Page : 439 pages
File Size : 41,11 MB
Release : 2009
Category : Mathematics
ISBN : 019533454X
Book Description
This book presents a clear and comprehensive introduction to one of the truly fascinating topics in mathematics: Catalan numbers. They crop up in chess, computer programming and even train tracks. In addition to lucid descriptions of the mathematics and history behind Catalan numbers, Koshy includes short biographies of the prominent mathematicians who have worked with the numbers.
Catalan Numbers: Tree-oriented Derivation of Recurrence Relations
Author : C. T. P. Burton
Publisher :
Page : 9 pages
File Size : 39,23 MB
Release : 1988
Category :
ISBN :
Book Description
A Recurrence Relation for Multiple Catalan Numbers
Author : Mersedeh Biglari Sefidi
Publisher :
Page : 92 pages
File Size : 45,98 MB
Release : 2016
Category : Catalan numbers (Mathematics)
ISBN :
Book Description
Commutation Relations, Normal Ordering, and Stirling Numbers
Author : Toufik Mansour
Publisher : CRC Press
Page : 506 pages
File Size : 31,33 MB
Release : 2015-09-18
Category : Mathematics
ISBN : 1466579897
Book Description
Commutation Relations, Normal Ordering, and Stirling Numbers provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. The Weyl algebra is the algebra generated by two letters U and V subject to the commutation relation UV - VU = I. It is a classical result that normal ordering pow
Algorithm Design: A Methodological Approach - 150 problems and detailed solutions
Author : Patrick Bosc
Publisher : CRC Press
Page : 764 pages
File Size : 29,14 MB
Release : 2023-01-31
Category : Computers
ISBN : 1000834840
Book Description
A bestseller in its French edition, this book is original in its construction and its success in the French market demonstrates its appeal. It is based on three principles: (1) An organization of the chapters by families of algorithms: exhaustive search, divide and conquer, etc. On the contrary, there is no chapter devoted only to a systematic exposure of, say, algorithms on strings. Some of these will be found in different chapters. (2) For each family of algorithms, an introduction is given to the mathematical principles and the issues of a rigorous design, with one or two pedagogical examples. (3) For the most part, the book details 150 problems, spanning seven families of algorithms. For each problem, a precise and progressive statement is given. More importantly, a complete solution is detailed, with respect to the design principles that have been presented; often, some classical errors are pointed out. Roughly speaking, two-thirds of the book is devoted to the detailed rational construction of the solutions.
Logic and Discrete Mathematics
Author : Willem Conradie
Publisher : John Wiley & Sons
Page : 456 pages
File Size : 43,51 MB
Release : 2015-04-16
Category : Mathematics
ISBN : 1119000092
Book Description
A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy to understand and use deductive systems of Semantic Tableaux and Resolution. The chapters on set theory, number theory, combinatorics and graph theory combine the necessary minimum of theory with numerous examples and selected applications. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in the accompanying solutions manual. Key Features: Suitable for a variety of courses for students in both Mathematics and Computer Science. Extensive, in-depth coverage of classical logic, combined with a solid exposition of a selection of the most important fields of discrete mathematics Concise, clear and uncluttered presentation with numerous examples. Covers some applications including cryptographic systems, discrete probability and network algorithms. Logic and Discrete Mathematics: A Concise Introduction is aimed mainly at undergraduate courses for students in mathematics and computer science, but the book will also be a valuable resource for graduate modules and for self-study.
Recurrent Sequences
Author : Dorin Andrica
Publisher : Springer Nature
Page : 410 pages
File Size : 36,12 MB
Release : 2020-09-23
Category : Mathematics
ISBN : 3030515028
Book Description
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.
