COMP 106 • Final • Discrete Mathematics for Computer Science and Engineering

What is an algorithm?

Algorithm and Pseudocode 1

Algorithm and Pseudocode 2

Algorithm and Pseudocode 3

Algorithm and Pseudocode 4

Exam Like Question 1

Exam Like Question 2

Big-O Notation

Example 1

Example 4

Sum Property of Big-O Notation

Multiplication Property of Big-O Notation

Example 1

Example 2

Big-Omega Notation

Big-Theta Notation

Example 1

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Example 3

Example 4

Exam-like Question 1

Exam-like Question 2

Proof of Divisibility by Induction

Example 1

Example 2

Exam-like Question 1

Proof of Inequality by Induction

Example 1

Example 2

Example 3

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Induction Related to Fibonacci

Strong Induction

Definition of Divisibility

Example 1

Example 2

Example 3

Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

Example 1

Example 2

Prime Numbers

Example 1

Example 2

Example 3

GCD Greatest Common Divisor

LCM Least Commun Multiple

Example 1

Euclidian Algorithm

Example 1

Bézout Identity

Example 1

Example 2

Example 3

Inverse of a Number in Modular Arithmetic

Primitive Root

Discrete Logarithm

Fermat's Little Theorem

Solving Linear Congruences

Example 1

Example 2

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Example 4

RSA Algorithm

Example 1

Example 2

Example 3

Exam-like Question 1

Exam-like Question 2

Diffie - Hellman Protocol

Example 1

Complexity 1

Complexity 2

Complexity 3

Complexity 4

Complexity 5

Complexity 6

Algorithms 1

Algorithms 2

Algorithms 3

Algorithms 4

Algorithms 5

Induction 1

Induction 2

Induction 3

Induction 4

Strong Induction 1

Algortithm & Induction

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Number Theory 5

Number Theory & Induction

Cryptography

Language and Grammar

Phase-Structure Grammar

Grammar -> Language Example 1

Grammar -> Language Example 2

Language -> Grammar Example 1

Language -> Grammar Example 2

Finite State Machines with Output

Example 1

Example 2

Finite State Machines with NO Output

Example 3

Example 4

Example 5

Turing Machine

Example 6

Example 7

Grammar -> Language 1

Grammar -> Language 2

Language -> Grammar 1

Language -> Grammar 2

Language -> Grammar 3

Finite State Machines with Output

Finite State Machines with NO Output 1

Finite State Machines with NO Output 2

Turing Machine

Induction 1

Algorithm and Complexity 1

Algorithm and Complexity 2

Complexity 1

Complexity 2

Complexity 3

Number Theory 1

Number Theory 2

Cryptography 1