MATH 108 • Tüm Sınavlar • Discrete and Combinatorial Mathematics

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

Tautology

Contradiction

Converse Inverse Contrapositive

Practice Problem 1

Practice Problem 2

Logical Equivalences 1

Logical Equivalences 2

De Morgans' Law

Example 1

Practice Problem 3

Practice Problem 4

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Example 2

Nested Quantifiers

Example 3

Negation of Nested Quantifiers

Example 4

Translations

Example 5

Example 6

Translation of Statements With Multiple Variables

Valid Argument

Rules of Inferences

Example 1

Example 2

Example 3

Using Rules of Inferences to Build Arguments

Example 4

Direct Proof

Example 1

Example 2

Example 3

Proof by Contrapositive

Example 4

Proof by Contradiction

Example 5

Proof By Cases

Example 6

Proofs of Equivalence

Example 7

Truth Table & Tautology

Logical Equivalences

Logical Equivalences

Logical Equivalences

Tautology

Quantifiers

Quantifiers

Quantifiers

Nested Quantifiers

Nested Quantifiers

Translations

Translations

Translations

Rules of Inferences 1

Rules of Inferences 2

Rules of Inferences 3

Direct Proof 1

Direct Proof 2

Direct Proof 3

Proof by Contrapositive 1

Proof by Contrapositive 2

Proof by Contradiction 1

Proof by Contradiction 2

Proofs of Equivalence

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 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 (i ve j ŞIKLARI HARİÇ)

Functions 1

Functions 2

Functions 3

Functions 4

Function & Summation (SADECE 2. ve 3. SORULAR)

Functions & Sets

Functions & Sets & Summation (4. ŞIK HARİÇ)

Functions & Summation

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

What is an algorithm?

Algorithm and Pseudocode 1

Algorithm and Pseudocode 2

Algorithm and Pseudocode 3

Linear Search Algorithm

Binary Search Algorithm

Bubble Sort Algorithm

Growth of Functions 1

Growth of Functions 2

Algorithms 1

Algorithms 2

Algorithms 3

Algorithms 4

Algorithms 5

Algorithm and Complexity

Algorithm and Complexity

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

GCD Greatest Common Divisor

LCM Least Commun Multiple

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

Example 2

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Example 4

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

Introduction

Recursively Defined Functions

Example 1

Recursively Defined Sets

Example 2

Recursively Defined Strings

Example 3

Structural Induction

Example 4

Example 5

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Number Theory 5

Number Theory 6

Number Theory 7

Induction for Formulas 1

Induction for Formulas 2

Induction for Formulas 3

Induction for Formulas 4

Induction Proof for Divisibility 1

Induction Proof for Divisibility 2

Induction for Inequalities

Induction with Fibonacci

Recursion and Induction

Recursive Algorithm

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example 1

Identical Objects Example 2

Identical Objects Example 3

Combination

n choose r

Committee Example 1

Committee Example 2

Ball Example 1

Ball Example 2

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Principle Inclusion-Exclusion

Example

Distributing Objects into Boxes 1

Distributing Objects into Boxes 2

Example 1

Example 2

Example 3

Pigeonhole Principle

Example 1

Example 2

Example 3

Generating Functions

Example 1

Example 2

Extended Binomial Theorem

Counting Problems with Generating Functions

Example 1

Example 2

Recurrence Relations

Homogenous Recurrence Relations

Example 1

Example 2

Non Homogenous Recurrence Relations

Example 3

Example 4

Creating Recurrence Relations

Example 5

Example 6

Definition of Relation

Example 1

Example 2

Reflexive Relations

Example 3

Example 4

Symmetric Relations

Antisymmetric Relations

Example 5

Transitive Relations

Example 6

Properties of Relations

Example 7

Example 8

Composition of Relations

Equivalence Relation

Example 9

Principle Inclusion Exclusion 1

Principle Inclusion Exclusion 2

Distributing Objects into Boxes 1

Distributing Objects into Boxes 2

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relations 4

Recurrence Relations 5

Recurrence Relations 6

Generating Functions 1

Generating Functions 2

Generating Functions 3

Properties of Relation

Properties of Relation

Equivalence Relation 1

Equivalence Relation 2

Equivalence Relation 3

Introduction

Graph Terminology

Handshaking Theorem

Example 1

Special Graphs

Example 2

Bipartite Graphs

Example 3

Example 4

Complete Bipartite Graph

Matching

Subgraph

Example 5

Subgraph Induced

Edge Contraction

Example 6

Complementary Graph

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

Introduction

Rooted Tree

Terminology for Rooted Trees

Full m-ary Trees

Some Formulas

Adjacency Matrices

Incidence Matrices

Bipartite Graphs & Euler Circuits

Euler Path, Induced Subgraph & Incidence Matrix

Isomorphism 1

Isomorphism 2

Isomorphism 3

Isomorphism 4

Isomorphism 5