COMP 106 (Fall 23) • Discrete Mathematics for Computer Science and Engineering • Final

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

Ceasar Cipher

Affine Cipher

Example 1

Example 2

Example 3

Example 4

Transposition Cipher

RSA Algorithm

Example 1

Example 2

Example 3

Exam-like Question 1

Exam-like Question 2

Diffie - Hellman Protocol

Example 1

Definition of Relation

Example 1

Example 2

Example 3

Example 4

Reflexive Relations

Example 5

Example 6

Symmetric Relations

Antisymmetric Relations

Example 7

Transitive Relations

Example 8

Properties of Relations

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14

Composition of Relations

Example 15

Example 16

Combining Relations

Inverse and Complementary of a Relation

Example 17

Matrix Representation of a Relation 1

Matrix Representation of a Relation 2

Example 18

Operations on Zero - One Matrices

Example 19

Reflexive Closure

Symmetric Closure

Example 20

Transitive Closure & Connectivity Relation

Matrix Representation of Transitive Closure

Example 21

Equivalence Relation

Example 22

Example 23

Example 24

Example 25

Example 26

Example 27

Example 28

Example 29

Example 30

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Big-O Notation

Example 1

Example 2

Example 3

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

Example 2

Linear Search Algorithm

Binary Search Algorithm

Bubble Sort Algorithm

Language and Grammar

Phase-Structure Grammar

Grammar -> Language Example 1

Grammar -> Language Example 2

Grammar -> Language Exam Like Question 1

Grammar -> Language Exam Like Question 2

Language -> Grammar Example 1

Language -> Grammar Example 2

Language -> Grammar Exam Like Question 1

Language -> Grammar Exam Like Question 2

Language -> Grammar Exam Like Question 3

Finite State Machines with Output

Example 1

Example 2

Exam Like Question 1

Finite State Machines with NO Output

Example 3

Example 4

Example 5

Exam Like Question 2

Exam Like Question 3

Turing Machine

Example 6

Example 7

Exam Like Question 4

Exam Like Question 1

Exam Like Question 2

Exam Like Question 3

Exam Like Question 4

Exam Like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Exam like Question 9

Exam like Question 10

Exam like Question 11

Exam like Question 12

Exam like Question 13

Exam like Question 14

Exam like Question 15

Exam like Question 16