CE 215 • Tüm Sınavlar • Discrete Mathematics for Computer Science

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

Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

Exam like Question 1

Nested Quantifiers

Exam like Question 2

Exam like Question 3

Negation of Nested Quantifiers

Exam like Question 4

Exam like Question 5

Translations

Exam like Question 6

Exam like Question 7

Exam like Question 8

Translation of Statements With Multiple Variables

Exam like Question 9

Exam like Question 10

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

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

Logic Basics 1

Logic Basics 2

Logic Basics 3

Logic Basics 4

Logic Basics 5

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

Logic - Translation 4

Logic - Translation 5

Rules of Inferences 1

Rules of Inferences 2

Rules of Inferences 3

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

Proof by Cases 1

Proofs of Equivalence 1

Proofs of Equivalence 2

Definition and Notation

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

Example 5

Proof Example 1

Proof Example 2

Definition

Example 1

Countable Sets

Properties of Countable Sets

Example 1

Uncountable Sets

Definition of Function

Example 1

Number of Functions

Injective Functions

Example 2

Example 3

Example 4

Number of Injective Functions

Surjective Functions

Example 5

Example 6

Example 7

Bijective Function

Inverse Function

Example 8

Example 9

Definition of Sequence

Arithmetique Sequence

Example 1

Geometric Sequence

Example 1

Sum Notation

Example 1

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

Sets 1

Sets 2

Sets 3

Sets 4

Sets 5

Sets 6

Cardinality 1

Cardinality 2

Cardinality 3

Cardinality 4

Functions 1

Functions 2

Functions 3

Functions 4

Functions 5

Sets & Function 1

Sets & Function 2

Sets & Function 3

Sets & Function 4

Sets, Function & Summation 1

Sets, Function & Summation 2

Summation and Function

All Midterm Subjects 1

All Midterm Subjects 2

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Cardinality

Binary & Octal & Hexadecimal Expansions

Summation & Recurrence Relations

Proof by Contradiction

Logical Equivalence

Valid Argument

Nested Quantifiers

Proof of Equivalence

Functions & Quantifiers

Translation

Functions

Functions

Functions

Number Theory

Number Theory

Rules of Inferences

Functions

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Exam-like Question 1

Exam-like Question 2

Proof of Divisibility by Induction

Example 1

Example 2

Exam-like Question 1

Exam-like Question 2

Proof of Inequality by Induction

Example 1

Example 2

Example 3

Exam-like Question 1

Exam-like Question 2

Exam-like Question 3

Induction Related to Fibonacci

Exam-like Question 1

Strong Induction

Example 1

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

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

Pigeonhole Principle

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

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

Induction for Inequalities 1

Induction for Inequalities 2

Induction with Fibonacci 1

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Counting 7

Counting & Binomial Coefficients 1

Principle Inclusion - Exclusion 1

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Pigeonhole Principle 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

Definition

Example 1

Example 2

Example 3

Example 4

Extended Binomial Theorem

Counting Problems with Generating Functions

Example 5

Example 6

Example 7

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

Composition of Relations

Example 13

Example 14

Combining Relations

Inverse and Complementary of a Relation

Example 15

Matrix Representation of a Relation 1

Matrix Representation of a Relation 2

Example 16

Operations on Zero - One Matrices

Example 17

Equivalence Relation

Example 18

Example 19

Example 20

Partially Ordered Set

Example 21

Example 22

Example 23

Totally Ordered Set

Example 24

Hasse Diagram

Example 25

Maximal and Minimal Elements

Greatest and Least Elements

Example 26

Upper and Lower Bound

Least Upper and Greatest Lower Bound

Example 27

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relations 4

Recurrence Relations 5

Recurrence Relations 6 (Hard)

Generating Functions 1

Generating Functions 2

Generating Functions 3

Generating Functions 4

Generating Functions 5

Generating Functions 6

Generating Functions 7

Generating Functions 8

Relations 1

Relations 2

Relations 3

Relations 4

Relations 5

Relations 6

Relations 7

Relations 8

Relations 9

Relations 10

Relations 11

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

Example 10

Planar Graph

Planar Graph - Euler Formula

Example 11

Corollaries about Planar Graph

Example 12

Introduction

Rooted Tree

Terminology for Rooted Trees

Full m-ary Trees

Some Formulas

Adjacency Matrices

Incidence Matrices

Bipartite Graphs & Euler Circuits

Bipartite Graphs, Euler Circuit & Planar Graphs

Euler Path, Induced Subgraph & Incidence Matrix

Chromatic Number 1

Chromatic Number 2

Isomorphism 1

Isomorphism 2

Isomorphism 3

Isomorphism 4

Isomorphism 5

Trees 1

Trees 2

Trees 3

Trees 4

Trees 5

Handshaking Theorem 1

Handshaking Theorem 2

Handshaking Theorem 3

True/False Problems