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

Introduction

Negation of a Proposition

Compound Proposition

Truth Table 1

Truth Table 2

Exam like Question 1

Exam like Question 2

Tautology

Exam like Question 3

Contradiction

Converse Inverse Contrapositive

Exam like Question 4

Exam-like Question 5

Logical Equivalences & De Morgan's Laws

Logical Equivalences & De Morgan's Laws 2

Exam like Question 6

Exam like Question 7

Exam like Question 10

Exam like Question 11

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Nested Quantifiers

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Negation of Nested Quantifiers

Translations

Exam like Question 11

Exam like Question 12

Exam like Question 13

Exam like Question 14

Translation of Mathematical Statements

Translation of Statements With Multiple Variables

Exam like Question 15

Exam like Question 16

Exam like Question 17

Exam like Question 18

Exam like Question 19

Exam like Question 20

Logic Basics 1

Logic Basics 2

Logic Basics 3

Logic Basics 4

Logic Basics 5

Logic Basics 6

Quantifiers 1

Quantifiers 2

Quantifiers 3

Quantifiers 4

Quantifiers 5

Translation 1

Translation 2

Translation 3

Translation 4

Direct Proof

Example 1

Example 2

Example 3

Example 4

Proof by Contrapositive

Example 1

Example 2

Example 3

Proof by Contradiction

Example 1

Example 2

Proof by Counterexample

Example 1

Proof By Cases

Example 1

Example 2

Example 3

Proofs of Equivalence

Example 1

Example 2

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 2

Sum Property of Big-O Notation

Multiplication Property of Big-O Notation

Example 1

Example 2

Big-Omega Notation

Big-Theta Notation

Example 1

Proof Techniques 1

Proof Techniques 2

Proof Techniques 3

Complexity 1

Complexity 2

Complexity 3

Complexity 4

Complexity 5

Complexity 6

Algorithms 1

Algorithms 2

Algorithms 3

Algorithms 4

Algorithms 5

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

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Number Theory 5

Cryptography

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Example 3

Example 4

Proof of Divisibility by Induction

Example 1

Example 2

Proof of Inequality by Induction

Example 1

Example 2

Example 3

Induction Related to Fibonacci

Strong Induction

Introduction

Recursively Defined Functions

Example 1

Recursively Defined Sets

Example 2

Recursively Defined Strings

Example 3

Structural Induction

Example 4

Example 5

Induction 1

Induction 2

Induction 3

Induction 4

Strong Induction 1

Algortithm & Induction

Logic: Basics

Logic: Quantifiers 1

Logic: Quantifiers 2

Logic: Quantifiers 3

Logic: Quantifiers 4

Proof Techniques

Algorithm and Complexity 1

Algorithm and Complexity 2

Complexity 1

Complexity 2

Complexity 3

Complexity 4

Number Theory 1

Number Theory 2

Number Theory 3

Cryptography 1

Cryptography 2

Induction

Induction

Recursion and Induction

Recursive Algorithm and Complexity