MATH 132 • Tüm Sınavlar • Discrete Mathematics

Injective Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Surjective Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Bijective Function

Image of a Set

Example 1

Proof Example For Image of a Function

Preimage of a Set

Example 1

Example 2

Proof Example for Preimage of a Function

Example 1

Definition

Example 1

Countable Sets

Properties of Countable Sets

Example 1

Uncountable Sets

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

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

Sets and Functions 1

Cardinality 1

Cardinality 2

Cardinality 3

Cardinality 4

Cardinality 5

Cardinality 6

Cardinality 7

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

Induction 1

Induction 2

Induction 3

Induction 4

Induction 5

Induction 6

Induction 7

Induction 8

Induction & Number Theory

Number Theory

Number Theory

Induction

Cardinality

Pigeonhole Principle (SINAVA DAHİL DEĞİL)

Number Theory - Modular Arithmetic

Number Theory - Chinese Remainder Theorem

Number Theory - Euclidian Algorithm

Cardinality

Induction for Formulas

Induction for Divisibility

Pigeonhole Principle

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 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 2

Example 3

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

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

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Pigeonhole Principle 5

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Binomial Coefficients and Identities 1

Binomial Coefficients and Identities 2

Generalized Permutations and Combinations 1

Generalized Permutations and Combinations 2

Generalized Permutations and Combinations 3

Generalized Permutations and Combinations 4

Generalized Permutations and Combinations 5

Generalized Permutations and Combinations 6

Generalized Permutations and Combinations 7

Generalized Permutations and Combinations 8

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relations 4

Recurrence Relations & Generalized Permutations and Combinations

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Principle Inclusion-Exclusion

Example 1

Example 2

Exam like Question 1

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

Example 13

Example 14

Composition of Relations

Example 15

Example 16

Combining Relations

Inverse and Complementary of a Relation

Example 17

Matrix Representation of Relation: Part 1

Matrix Representation of Relation: Part 2

Example 18

Operations on Zero - One Matrices

Example 19

Equivalence Relation

Example 22

Example 23

Example 24

Example 25

Example 26

Example 27

Example 28

Example 29

Example 30

Exam like Question 1

Partially Ordered Set

Example

Example

Example

Totally Ordered Set

Example

Hasse Diagram

Example

Maximal and Minimal Elements

Greatest and Least Elements

Example

Upper and Lower Bound

Least Upper and Greatest Lower Bound

Example

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relation & Advanced Counting Techniques

Principle Inclusion Exclusion 1

Principle Inclusion Exclusion 2

Principle Inclusion Exclusion 3

Principle Inclusion Exclusion 4

Principle Inclusion Exclusion 5

Relations 1

Relations 2

Relations 3

Relations 4

Relations 5

Relations 6

Relations 7

Relations 8

Relations 9

Relations 10

Generating Functions

Generating Functions

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Relations

Relations

Relations

Relations

Counting & Derangement

Counting & Derangement