Fibonacci and Catalan Numbers (PDF)
An Introduction
(Sprache: Englisch)
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...
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...
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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 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.
Autoren-Porträt von Ralph Grimaldi
RALPH P. GRIMALDI, PHD, is Professor of Mathematics at Rose-Hulman Institute of Technology. With more than forty years of experience in academia, Dr. Grimaldi has published numerous articles in discrete mathematics, combinatorics, and graph theory. Over the past twenty years, he has developed and led mini-courses and workshops examining the Fibonacci and the Catalan numbers.
Bibliographische Angaben
- Autor: Ralph Grimaldi
- 2011, 1. Auflage, 380 Seiten, Englisch
- Verlag: John Wiley & Sons
- ISBN-10: 1118159772
- ISBN-13: 9781118159774
- Erscheinungsdatum: 21.12.2011
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- Größe: 4.75 MB
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Sprache:
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