The Fibonacci Numbers. Historical Background
The Problem of the Rabbits
Properties of the Fibonacci Numbers
Some Introductory Examples
Compositions and Palindromes
Tilings: Divisibility Properties of the Fibonacci Numbers
Chess Pieces on Chessboards
Optics, Botany, and the Fibonacci Numbers
Solving Linear Recurrence Relations: The Binet Form for
More on and : Applications in Trigonometry, Physics, Continued Fractions, Probability, the Associative Law, and Computer Science
Examples from Graph Theory: An Introduction to the Lucas Numbers
The Lucas Numbers: Further Properties and Examples
Matrices, The Inverse Tangent Function, and an Infinite Sum
The gcd Property for the Fibonacci Numbers
Alternate Fibonacci Numbers
The Catalan Numbers. Historical Background
A First Example: A Formula for the Catalan Numbers
Some Further Initial Examples
Dyck Paths, Peaks, and Valleys
Young Tableaux, Compositions, and Vertices and Arcs
Triangulating the Interior of a Convex Polygon
Some Examples from Graph Theory
Partial Orders, Total Orders, and Topological Sorting
Sequences and a Generating Tree
Maximal Cliques, a Computer Science Example, and the Tennis Ball Problem
The Catalan Numbers at Sporting Events
A Recurrence Relation for the Catalan Numbers
Triangulating the Interior of a Convex Polygon for the Second Time
Rooted Ordered Binary Trees, Pattern Avoidance, and Data Structures
Staircases, Arrangements of Coins, The Handshaking Problem, and Noncrossing Partitions
Related Number Sequences: The Motzkin Numbers, The Fine Numbers, and the Schr̲der Numbers
Generalized Catalan Numbers
Solutions for the Odd-Numbered Exercises