MAT 1006 (Spring 24) • Engineering Mathematics I • Midterm

Introduction

Negation of a Proposition

Compound Propositions

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 8

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

Exam like Question 9

Exam like Question 10

Translation of Mathematical Statements

Translation of Statements With Multiple Variables

Exam like Question 11

Exam like Question 12

Exam like Question 13

Exam like Question 14

Logic Basics 1

Logic Basics 2

Logic Basics 3

Logic Basics 4

Logic Basics 5

Logic Basics 6

Logic - Quantifiers 1

Logic - Quantifiers 2

Logic - Quantifiers 3

Logic - Quantifiers 4

Logic - Quantifiers 5

Logic - Quantifiers 6

Logic - Quantifiers 7

Logic - Translation 1

Logic - Translation 2

Logic - Translation 3

Logic - Translation 4

Logic - Translation 5

Definition and Notation

Subset

Example 1

Union and Intersection of Two Sets

Difference of Two Sets

Example 1

Symmetric Difference

Example 1

Set Identities

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Power Set

Example 1

Example 2

Cartesian Product

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Generalized Intersections and Unions

Example 1

Example 2

Example 3

Definition of Function

Example 1

Number of Functions

Injective Functions

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Surjective Functions

Example 10

Example 11

Example 12

Example 13

Example 14

Example 15

Example 16

Bijective Function

Inverse Function

Example 17

Example 18

Image of a Set

Proof Example For Image of a Function

Preimage of a Set

Example 19

Proof Example for Preimage of a Function

Example 20

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 1

Sum Notation

Example 1

Proofs & Sets 1

Proofs & Sets 2

Proofs & Sets 3

Proofs & Sets 4

Proofs & Sets 5

Proofs & Sets 6

Proofs & Sets 7

Functions 1

Functions 2

Functions 3

Functions 4

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

Diffie - Hellman Protocol

Example 1

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Number Theory 5

Number Theory 6

Number Theory 7

Number Theory 8

Number Theory 9

Number Theory 10

Number Theory 11

Number Theory 12

Cryptography 1

Cryptography 2