Notes

Principles of Mathematical Induction and Well-Ordering

Algorithms for Generating the Fibonacci Sequence

Analysis of the Recursive Algorithm Fib1

Binet's Formula for the Fibonacci Numbers

Probability of No Consecutive Heads

The Fibonacci Numbers and Binomial Coefficients

Cassini's Identity and the Ratio of Fibonacci Numbers

Notes on the Extended Euclidean Algorithm

The Fundamental Theorem of Arithmetic

An Application of the Fundamental Theorem of Arithmetic

Fermat's Little Theorem

Dirichlet's Pigeonhole Principle

Generating Function for Even-Indexed Fibonacci Numbers

Consecutive Fibonacci Numbers and the Euclidean Algorithm

The Method of False Position and Fibonacci Numbers

Average and Worst Case Analysis Example

Asymptotic Growth Rate of Powers and Exponentials

Notes on the Harmonic Numbers

The Josephus Problem

The Binomial Series

Generating Permutations Using a Stack

Division on a Computer

Finding the Smallest and Largest Keys

The Inclusion - Exclusion Principle

The Sieve of Eratosthenes

Bit Strings not Containing the Pattern 010

Homogeneous Linear Difference Equations

Nonhomogeneous Linear Difference Equations

Some Examples of Difference Equations

Characteristic Equation with Complex Roots

Systems of Linear Difference Equations

Decomposition of a Sphere by Great Circles

Implementation of Quick Sort

Implementation of Merge Sort

Implementation of Heap Sort

Sorting Algorithms Demonstration

Merging Sorted Lists

Analysis of Merge Sort

Worst Case Analysis of Heap Sort

Properties of Trees

de Bruijn Sequences

Prim's Algorithm

Kruskal's Algorithm

Counting Spanning Trees: An Example

Examples of DFS Trees and BFS Trees

Connected Components of a Graph Using DFS

2-Colouring a Graph Using BFS

A General Depth First Search Skeleton

The Last Two Examples