MATH 204 • Tüm Sınavlar • Discrete Mathematics

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Tautology

Example 1

Contradiction

Converse Inverse Contrapositive

Example 2

Logical Equivalences 1

Logical Equivalences 2

Example 3

Example 4

Example 5

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Example 1

Example 2

Nested Quantifiers

Example 3

Example 4

Negation of Nested Quantifiers

Example 5

Example 6

Translations - Introduction

Translation: English to Logic

Translation: Logic to English

Translation with Quantifiers 1

Translation with Quantifiers 2

Translation of Mathematical Statements

Example 7

Translation of Statements With Multiple Variables

Example 8

Example 9

Logic Basics 1

Logic Basics 2

Logic Basics 3

Logic Basics 4

Logic - Quantifiers 1

Logic - Quantifiers 2

Logic - Quantifiers 3

Logic - Quantifiers 4

Logic - Quantifiers 5

Logic - Quantifiers 6

Logic - Translation 1

Logic - Translation 2

Logic - Translation 3

Direct Proof

Example 1

Example 2

Example 3

Example 4

Proof by Contrapositive

Example 5

Example 6

Proof by Contradiction

Example 7

Example 8

Proof by Counterexample

Example 9

Proof By Cases

Example 10

Proofs of Equivalence

Example 11

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

Induction Related to Fibonacci

Strong Induction

Direct Proof 1

Direct Proof 2

Proof by Contrapositive 1

Proof by Contrapositive 2

Proof by Contradiction 1

Proof by Contradiction 2

Proof by Contradiction 3

Proof by Contradiction 4

Proof by Contradiction 5

Proofs of Equivalence 1

Proofs of Equivalence 2

Induction for Formulas 1

Induction for Formulas 2

Induction for Formulas 3

Induction for Formulas 4

Induction for Formulas 5

Induction Proof for Divisibility 1

Induction Proof for Divisibility 2

Direct Proof & Induction 1

Direct Proof & Induction 2

Induction for Inequalities 1

Induction for Inequalities 2

Induction for Inequalities 3

Induction with Fibonacci 1

Induction with Fibonacci 2

Definition and Notation of a Set

Subset

Example 1

Union and Intersection of Two Sets

Difference of Two Sets

Set Identities

Example 2

Power Set

Example 3

Cartesian Product

Example 4

Proof Example 1

Definition of Function

Example 5

Number of Functions

Injective Functions

Example 6

Example 7

Number of Injective Functions

Surjective Functions

Example 8

Example 9

Bijective Function

Inverse Function

Example 10

Example 11

Definition

Example 1

Countable Sets

Properties of Countable Sets

Example 1

Uncountable Sets

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 1

Sum Notation

Example 1

Sets 1

Sets 2

Sets 3

Sets 4

Functions 1

Functions 2

Functions 3

Functions 4

Functions & Sets

Function & Summation

Functions & Sets & Summation

Functions & Summation

Cardinality 1

Cardinality 2

Cardinality 3

Cardinality 4

Cardinality 5

Cardinality 6

Propositional Logic (Spring 2025)

Tautology by Truth Table (Fall 2024)

Quantifiers (Spring 2025)

Nested Quantifiers (Fall 2024)

Negation of Nested Quantifiers (Fall 2024)

Translation (Fall 2024)

Translation (Spring 2025)

Direct Proof (Fall 2024)

Proof Techniques and Sets (Spring 2025)

Induction (Spring 2025)

Induction (Fall 2024)

Functions - Bijection Proof (Spring 2025)

Cardinality (Spring 2024)

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

Growth of Functions 1

Growth of Functions 2

Growth of Functions 3

Algorithms 1

Algorithms 2

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

Fermat's Little Theorem

Solving Linear Congruences

Example 1

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Example 4

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example

Combination

n choose r

Committee Example

Ball Example

Binomial Theorem

Example 1

Example 3

Example 2

Pascal Identity

Vandermonde's Identity

Example 1

Combinatorial Proof

Example 1

Principle Inclusion-Exclusion

Example 1

Example 2

Distributing Objects into Boxes 1

Distributing Objects into Boxes 2

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Pigeonhole Principle

Example 1

Example 2

Example 3

Example 4

Example 5

Introduction

Homogenous Recurrence Relations

Example 1

Example 2

Example 3

Example 4

Non Homogenous Recurrence Relations

Example5

Example 6

Creating Recurrence Relations

Example 7

Example 8

Example 9

Generating Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Extended Binomial Theorem

Counting Problems with Generating Functions

Example 6

Example 7

Example 8

Example 9

Example 10

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

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Counting 7

Counting 8

Principle Inclusion - Exclusion 1

Principle Inclusion - Exclusion 2

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Pigeonhole Principle 5

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relations 4

Recurrence Relations 5

Recurrence Relations 6

Recurrence Relations 7

Recurrence Relations 8

Recurrence Relations 9

Generating Functions 1

Generating Functions 2

Generating Functions 3

Generating Functions 4

Generating Functions 5

Generating Functions 6

Generating Functions 7

Generating Functions 8

Generating Functions 9

Generating Functions 10

Generating Functions 11

Generating Functions 12

Generating Functions 13

Generating Functions 14

Generating Functions 15

Generating Functions 16

Algorithms (Spring 2019)

Growth of Functions (Spring 2024)

Growth of Functions & Number Theory (Spring 2025)

Modular Arithmetic- True False (Spring 2019)

Modular Arithmetic - Proof (Spring 2019)

Modular Arithmetic - Proof (Spring 2024)

Euclidian Algorithm (Spring 2024)

Euclidian Algorithm (Spring 2025)

Number Theory (Fall 2024)

Number Theory (Fall 2024)

Binomial Coefficient (Spring 2024)

Binomial Identities (Spring 2024)

Binomial Identities (Spring 2025)

Counting (Spring 2019)

Counting (Spring 2019)

Counting (Fall 2024)

Counting (Spring 2024)

Counting (Spring 2025)

Counting (Spring 2025)

Counting (Spring 2025)

Pigeonhole Principle (Fall 2024)

Pigeonhole Principle (Spring 2024)

Short Mixed Questions 1 (Spring 2025)

Short Mixed Questions 2 (Spring 2025)

Recurrence Relations (Spring 2025)

Generating Functions (Spring 2025)

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

Equivalence Relation

Example 13

Example 14

Example 15

Composition of Relations

Example 16

Example 17

Generating Functions 1

Generating Functions 2

Generating Functions 3

Generating Functions 4

Generating Functions 5

Generating Functions 6

Generating Functions 7

Generating Functions 8

Generating Functions 9

Generating Functions 10

Generating Functions 11

Generating Functions 12

Generating Functions 13

Generating Functions 14

Generating Functions 15

Generating Functions 16

Properties of Relation 1

Properties of Relation 2

Equivalence Relation 1

Equivalence Relation 2

Equivalence Relation 3

Equivalence Relation 4

Equivalence Relation 5

Equivalence Relation 6

Equivalence Relation - Proof

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relations 4

Recurrence Relations 5

Recurrence Relations 6

Recurrence Relations 7

Recurrence Relations 8

Recurrence Relations 9

Recurrence Relations 10

Recurrence Relations 11

Recurrence Relations 12

Recurrence Relations 13

Recurrence Relations 14

Recurrence Relations 15

Introduction

Example 1

Graph Terminology

Example 2

Handshaking Theorem

Example 3

Example 4

Special Graphs

Example 5

Example 6

Bipartite Graphs

Example 7

Example 8

Complete Bipartite Graph

Matching

Example 9

Subgraph

Example 10

Subgraph Induced

Edge Contraction

Example 11

Complementary Graph

Example 12

Example 13

Example 14

Adjacency Matrices - Undirected Graphs

Adjacency Matrices - Directed Graphs

Example 1

Example 2

Incidence Matrices

Example 3

Isomorphism of Graphs

Example 4

Example 5

Example 6

Example 7

Definition of Paths and Circuits

Connected Graphs

Euler Paths and Circuits

Example 8

Hamilton Paths and Circuits

Example 9

Example 10

Graphs 1

Graphs 2

Graphs 3

Graphs 4

Graphs 5

Graphs 6

Graphs 7

Graphs 8

Graphs 9

Graphs 10

Graphs 11

Graphs 12

Graphs 13

Graphs 14

Graphs 15

Short Mixed Questions 1

Short Mixed Questions 2

Generating Functions

Recurrence Relations

Graph Theory - Euler Path and Circuit

Graph Theory - Isomorphism

Propositional Logic & Sets - Proof

Relations