《斐波那契數和卡塔蘭數：導論》是2020年哈爾濱工業大學出版社出版的圖書。
基本介紹
- 中文名：斐波那契數和卡塔蘭數：導論
- 作者：[美]拉爾夫·P.格里馬爾迪
- 出版時間：2020年10月
- 出版社：哈爾濱工業大學出版社
- ISBN：9787560388878
- 類別：數學理論
- 開本：16 開
- 裝幀：平裝
內容簡介,圖書目錄,
內容簡介
《斐波那契數和卡塔蘭數：導論（英文）》主要介紹了斐波那契數和卡塔蘭數的歷史背景，兔子問題，遞歸定義，斐波那契數的性質，引入性的例子，斐波那契數的可除性，棋盤上的棋子，光學、植物學與斐波那契數列，線性遞歸關係的求解，圖論的例子，盧卡斯數的性質和舉例，矩陣、正切逆函式、無限和，斐波那契數列的gcd屬性等內容。卡特蘭數是組合數學中一個常出現在各種計數問題中的數列，在現代物理、準晶體結構、化學等領域，斐波納契數列都有直接的套用。
《斐波那契數和卡塔蘭數：導論（英文）》適用於數學專業的學生參考閱讀。
圖書目錄
PREFACE
PART ONE THE FIBONACCI NUMBERS
1.Historical Background
2.The Problem of the Rabbitr/>3.The Recursive Definition
4.Properties of the Fibonacci Numberr/>5.Some Introductory Examp
6.Compositions and Palindromer/>7.Tilings: Diviility Properties of the Fibonacci Numberr/>8.Chess Pieces on Cheoardr/>9.Optics, Botany, and the Fibonacci Numberr/>10.Solving Linear Recurrence Relations: The Binet Form for Fn
11.More on ot and B: Applications in Trigonometry, Physics, Continued
Fractions, Probability, the Associative Law, and Computer Science
12.Examp from Graph Theory: An Introduction to the Lucas Numberr/>13.The Lucas Numbers: Further Properties and Examp
14.Matrices, The Inverse Tangent Function, and an Infinite Sum
15.The gcd Property for the Fibonacci Numberr/>16.Alternate Fibonacci Numberr/>17.One Final Example?
PART TWO THE CATALAN NUMBERS
18.Historical Background
19.A First Example: A Formula for the Catalan Numberr/>.Some Further Initial Examp
21.Dyck Paths, Peaks, and Valleyr/>22.Young Tableaux, Compositions, and Vertices and Arcr/>23.Triangulating the Interior of a Convex Polygon
24.Some Examp from Graph Theory
25.Partial Orders, Total Orders, and Topological Sorting
26.Sequences and a Generating Tree
27.Maximal Cliques, a Computer Science Example, and the Tennis Ball
Problem
28.The Catalan Numbers at Sporting Eventr/>29.A Recurrence Relation for the Catalan Numberr/>30.Triangulating the Interior of a Convex Polygon for the Second Time
31.Rooted Ordered Binary Trees, Pattern Avoidance, and Data
Structurer/>32.Strcases, Arrangements of Coins, The Handsh Problem, and
Noncrossing Partitionr/>33.The Narayana Numberr/>34.Related Number Sequences: The Motzkin Numberr/> The Fine Numbers, and The Schr6der Numberr/>35.Generalized Catalan Numberr/>36.One Final Example?
Solutions for the .Numbered Exerciser/>Index
編輯手記
