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Fibonacci and Catalan Numbers

Author: Ralph Grimaldi

Publisher: John Wiley & Sons

Published: 2012-02-21

Total Pages: 380

ISBN-13: 1118159764

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 Lucas Numbers with Applications

Author: Thomas Koshy

Publisher: John Wiley & Sons

Published: 2011-10-24

Total Pages: 676

ISBN-13: 1118031318

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The first comprehensive survey of mathematics' most fascinatingnumber sequences Fibonacci and Lucas numbers have intrigued amateur and professionalmathematicians for centuries. This volume represents the firstattempt to compile a definitive history and authoritative analysisof these famous integer sequences, complete with a wealth ofexciting applications, enlightening examples, and fun exercisesthat offer numerous opportunities for exploration andexperimentation. The author has assembled a myriad of fascinating properties of bothFibonacci and Lucas numbers-as developed by a wide range ofsources-and catalogued their applications in a multitude of widelyvaried disciplines such as art, stock market investing,engineering, and neurophysiology. Most of the engaging anddelightful material here is easily accessible to college and evenhigh school students, though advanced material is included tochallenge more sophisticated Fibonacci enthusiasts. A historicalsurvey of the development of Fibonacci and Lucas numbers,biographical sketches of intriguing personalities involved indeveloping the subject, and illustrative examples round out thisthorough and amusing survey. Most chapters conclude with numericand theoretical exercises that do not rely on long and tediousproofs of theorems. Highlights include: * Balanced blend of theory and real-world applications * Excellent reference material for student reports andprojects * User-friendly, informal, and entertaining writing style * Historical interjections and short biographies that add a richerperspective to the topic * Reference sections providing important symbols, problemsolutions, and fundamental properties from the theory of numbersand matrices Fibonacci and Lucas Numbers with Applications providesmathematicians with a wealth of reference material in oneconvenient volume and presents an in-depth and entertainingresource for enthusiasts at every level and from any background.

Catalan Numbers with Applications

Author: Thomas Koshy

Publisher: OUP USA

Published: 2009

Total Pages: 439

ISBN-13: 019533454X

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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.

Fibonacci and Catalan Numbers

Author: Ralph Grimaldi

Publisher: John Wiley & Sons

Published: 2012-03-13

Total Pages: 380

ISBN-13: 0470631570

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Blockhead

Author: Joseph D'Agnese

Publisher: Macmillan

Published: 2010-03-30

Total Pages: 52

ISBN-13: 0805063056

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A biography of Leonardo Fibonacci, the 12th century mathematician who discovered the numerical sequence named for him.

Pell and Pell–Lucas Numbers with Applications

Author: Thomas Koshy

Publisher: Springer

Published: 2014-11-11

Total Pages: 444

ISBN-13: 1461484898

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Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis, geometry, trigonometry, and various areas of discrete mathematics, number theory, graph theory, linear algebra, and combinatorics. Pell and Pell–Lucas numbers belong to an extended Fibonacci family as a powerful tool for extracting numerous interesting properties of a vast array of number sequences. A key feature of this work is the historical flavor that is interwoven into the extensive and in-depth coverage of the subject. An interesting array of applications to combinatorics, graph theory, geometry, and intriguing mathematical puzzles is another highlight engaging the reader. The exposition is user-friendly, yet rigorous, so that a broad audience consisting of students, math teachers and instructors, computer scientists and other professionals, along with the mathematically curious will all benefit from this book. Finally, Pell and Pell–Lucas Numbers provides enjoyment and excitement while sharpening the reader’s mathematical skills involving pattern recognition, proof-and-problem-solving techniques.

Fibonacci and Lucas Numbers, and the Golden Section

Author: Steven Vajda

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 194

ISBN-13: 0486462765

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This survey of the use of Fibonacci and Lucas numbers and the ancient principle of the Golden Section covers areas relevant to operational research, statistics, and computational mathematics. 1989 edition.

Inquiry-Based Enumerative Combinatorics

Author: T. Kyle Petersen

Publisher: Springer

Published: 2019-06-28

Total Pages: 238

ISBN-13: 3030183084

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This textbook offers the opportunity to create a uniquely engaging combinatorics classroom by embracing Inquiry-Based Learning (IBL) techniques. Readers are provided with a carefully chosen progression of theorems to prove and problems to actively solve. Students will feel a sense of accomplishment as their collective inquiry traces a path from the basics to important generating function techniques. Beginning with an exploration of permutations and combinations that culminates in the Binomial Theorem, the text goes on to guide the study of ordinary and exponential generating functions. These tools underpin the in-depth study of Eulerian, Catalan, and Narayana numbers that follows, and a selection of advanced topics that includes applications to probability and number theory. Throughout, the theory unfolds via over 150 carefully selected problems for students to solve, many of which connect to state-of-the-art research. Inquiry-Based Enumerative Combinatorics is ideal for lower-division undergraduate students majoring in math or computer science, as there are no formal mathematics prerequisites. Because it includes many connections to recent research, students of any level who are interested in combinatorics will also find this a valuable resource.

Applications of Fibonacci Numbers

Author: G.E. Bergum

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 633

ISBN-13: 9401120587

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This book contains 58 papers from among the 68 papers presented at the Fifth International Conference on Fibonacci Numbers and Their Applications which was held at the University of St. Andrews, St. Andrews, Fife, Scotland from July 20 to July 24, 1992. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its four predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. June 5, 1993 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U.S.A. Alwyn F. Horadam University of New England Armidale, N.S.W., Australia Andreas N. Philippou Government House Z50 Nicosia, Cyprus xxv THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Campbell, Colin M., Co-Chair Horadam, A.F. (Australia), Co-Chair Phillips, George M., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Foster, Dorothy M.E. Ando, S. (Japan) McCabe, John H. Bergum, G.E. (U.S.A.) Filipponi, P. (Italy) O'Connor, John J.

A Handbook of Integer Sequences

Author: N.J.A. Sloane

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 221

ISBN-13: 148326467X

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A Handbook of Integer Sequences contains a main table of 2300 sequences of integers that are collected from all branches of mathematics and science. This handbook describes how to use the main table and provides methods for analyzing and describing unknown and important sequences. This compilation also serves as an index to the literature for locating references on a particular problem and quickly finds numbers such as 712, number of partitions of 30, 18th Catalan number, or expansion of ? to 60 decimal places. Other topics include the method of differences, self-generating sequences, polyominoes, permutations, and puzzle sequences. This publication is a good source for students and researchers who are confronted with strange and important sequences.