MATH 112 • Discrete Mathematics • Final

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Ders Tanıtımı

Binomial Theorem

Example 1

Example 3

Example 2

Pascal Identity

Vandermonde's Identity

Example 1

Combinatorial Proof

Example 1

Discrete Probability

Ücretsiz İçerikler

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Axioms of Probability 5

Intuition of Conditional Probability

Ücretsiz

Conditional Probability 1

Ücretsiz

Conditional Probability 2

Ücretsiz

Conditional Probability and Sets

Ücretsiz

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Exam like Question 19

Ücretsiz

Exam like Question 20

Ücretsiz

Exam like Question 21

Ücretsiz

Exam like Question 22

Ücretsiz

Exam like Question 23

Ücretsiz

Exam like Question 24

Ücretsiz

Recurrence Relations

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

Definition

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

Graph Theory

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 15

Example 16

Incidence Matrices

Example 17

Isomorphism of Graphs

Example 18

Example 19

Example 20

Example 21

Definition of Paths and Circuits

Connected Graphs

Euler Paths and Circuits

Example 22

Hamilton Paths and Circuits

Example 23

Example 24

Planar Graph

Planar Graph - Euler Formula

Example 25

Corollaries about Planar Graph

Example 26

Kuratowski's Theorem

Example 27

Example 28

Example 29

Before Exam Questions

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

Exam like Question 9

Exam like Question 10

Exam like Question 11

Exam like Question 12

Eğitmen

İhsan Altundağ
Eğitmen

2007 yılında Galatasaray Üniversitesi Bilgisayar Mühendisliği bölümünden birincilikle mezun olduktan sonra Fransa'da Kriptoloji üzerine Fransa hükümeti tarafından verilen bursla yüksek lisans yaptım. Devamında ikinci kez sınava girerek Boğaziçi Matematik bölümünü de bitirdim. Yaklaşık 15 yıldır üniversite öğrencilerine dersler vermekteyim.

Ders İçeriği

Ders Tanıtımı

Binomial Theorem

Example 1

Example 3

Example 2

Pascal Identity

Vandermonde's Identity

Example 1

Combinatorial Proof

Example 1

Discrete Probability

Ücretsiz İçerikler

Axioms of Probability 1

Axioms of Probability 2

Axioms of Probability 3

Axioms of Probability 4

Axioms of Probability 5

Intuition of Conditional Probability

Ücretsiz

Conditional Probability 1

Ücretsiz

Conditional Probability 2

Ücretsiz

Conditional Probability and Sets

Ücretsiz

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Exam like Question 19

Ücretsiz

Exam like Question 20

Ücretsiz

Exam like Question 21

Ücretsiz

Exam like Question 22

Ücretsiz

Exam like Question 23

Ücretsiz

Exam like Question 24

Ücretsiz

Recurrence Relations

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

Definition

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

Graph Theory

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 15

Example 16

Incidence Matrices

Example 17

Isomorphism of Graphs

Example 18

Example 19

Example 20

Example 21

Definition of Paths and Circuits

Connected Graphs

Euler Paths and Circuits

Example 22

Hamilton Paths and Circuits

Example 23

Example 24

Planar Graph

Planar Graph - Euler Formula

Example 25

Corollaries about Planar Graph

Example 26

Kuratowski's Theorem

Example 27

Example 28

Example 29

Before Exam Questions

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

Exam like Question 9

Exam like Question 10

Exam like Question 11

Exam like Question 12

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Bu dersin özellikleri:

Okuluna özel hazırlanmış içerikler
Çıkmış sorular
Soruları eğitmenlerimize sorma
Topluluktaki sorulara erişim
İstediğin yerden, dilediğin kadar
Kendi hızında öğrenme

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