MATH 112 (Fall 23) • Discrete Mathematics • Part II

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Ders Tanıtımı

Sets

Ücretsiz İçerikler

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

Ücretsiz

Functions

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

Sample Exam Problems I

Ücretsiz İçerikler

Proofs & Sets 1

Proofs & Sets 2

Proofs & Sets 3 (Spring 2023)

Proofs & Sets 4

Proofs & Sets 5

Proofs & Sets 6

Proofs & Sets 7 (Spring 2023 - Make Up)

Ücretsiz

Functions 1

Functions 2

Functions 3 (Spring 2023)

Ücretsiz

Functions 4 (Spring 2023 - Make Up)

Counting: Standard Models

Introduction to Counting

Combination & Permutation: Intuition

Combination

Permutation 1

Permutation 2

Binomial Coefficients

Binomial Theorem

Example 1

Example 2

Example 3

Pascal Identity

Combinatorial Proof

Sample Exam Problems II

Ücretsiz İçerikler

Counting Standard Models 1

Counting Standard Models 2

Counting Standard Models 3

Ücretsiz

Counting Standard Models 4

Counting Standard Models 5

Counting Standard Models 6 (Spring 2023)

Counting Standard Models 7 (Spring 2023 - Make Up)

Counting Standard Models & Binomial Coefficients 1

Combinatorial Proof 1

Counting: Inclusion and Exclusion Principle

Principle Inclusion-Exclusion

Example 1

Example 2

Counting: Distributing Objects into the Boxes

Distributing Objects into Boxes 1

Distributing Objects into Boxes 2

Example 1

Example 2

Example 3

Example 4

Example 5

Exam Like Question 1

Exam Like Question 2

Exam Like Question 3

Counting: The Pigeonhole Principle

Ücretsiz İçerikler

Pigeonhole Principle

Ücretsiz

Example 1

Example 2

Example 3

Example 4

Example 5

Advanced Counting: 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

Sample Exam Problems III

Inclusion-Exclusion Principle 1

Inclusion-Exclusion Principle 2

Inclusion-Exclusion Principle & Distributing Objects 1

Distributing Objects into Boxes 1 (Spring 2023)

Distributing Objects into Boxes 2

Distributing Objects into Boxes 3

Distributing Objects into Boxes 4

Distributing Objects into Boxes 5

Distributing Objects into Boxes 6 (Spring 2023 - Make up)

Pigeonhole Principle 1

Pigeonhole Principle 2 (Spring 2023)

Pigeonhole Principle 3

Recurrence Relations 1 (Fall 2022)

Recurrence Relations 2 (Fall 2022)

Recurrence Relations 3 (Fall 2022)

Recurrence Relations 4

Recurrence Relations 5 (Spring 2023)

Recurrence Relations 6 (Fall 2022)

Recurrence Relations 7 (Fall 2022)

Recurrence Relations 8 (Spring 2023)

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

Sets

Ücretsiz İçerikler

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

Ücretsiz

Functions

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

Sample Exam Problems I

Ücretsiz İçerikler

Proofs & Sets 1

Proofs & Sets 2

Proofs & Sets 3 (Spring 2023)

Proofs & Sets 4

Proofs & Sets 5

Proofs & Sets 6

Proofs & Sets 7 (Spring 2023 - Make Up)

Ücretsiz

Functions 1

Functions 2

Functions 3 (Spring 2023)

Ücretsiz

Functions 4 (Spring 2023 - Make Up)

Counting: Standard Models

Introduction to Counting

Combination & Permutation: Intuition

Combination

Permutation 1

Permutation 2

Binomial Coefficients

Binomial Theorem

Example 1

Example 2

Example 3

Pascal Identity

Combinatorial Proof

Sample Exam Problems II

Ücretsiz İçerikler

Counting Standard Models 1

Counting Standard Models 2

Counting Standard Models 3

Ücretsiz

Counting Standard Models 4

Counting Standard Models 5

Counting Standard Models 6 (Spring 2023)

Counting Standard Models 7 (Spring 2023 - Make Up)

Counting Standard Models & Binomial Coefficients 1

Combinatorial Proof 1

Counting: Inclusion and Exclusion Principle

Principle Inclusion-Exclusion

Example 1

Example 2

Counting: Distributing Objects into the Boxes

Distributing Objects into Boxes 1

Distributing Objects into Boxes 2

Example 1

Example 2

Example 3

Example 4

Example 5

Exam Like Question 1

Exam Like Question 2

Exam Like Question 3

Counting: The Pigeonhole Principle

Ücretsiz İçerikler

Pigeonhole Principle

Ücretsiz

Example 1

Example 2

Example 3

Example 4

Example 5

Advanced Counting: 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

Sample Exam Problems III

Inclusion-Exclusion Principle 1

Inclusion-Exclusion Principle 2

Inclusion-Exclusion Principle & Distributing Objects 1

Distributing Objects into Boxes 1 (Spring 2023)

Distributing Objects into Boxes 2

Distributing Objects into Boxes 3

Distributing Objects into Boxes 4

Distributing Objects into Boxes 5

Distributing Objects into Boxes 6 (Spring 2023 - Make up)

Pigeonhole Principle 1

Pigeonhole Principle 2 (Spring 2023)

Pigeonhole Principle 3

Recurrence Relations 1 (Fall 2022)

Recurrence Relations 2 (Fall 2022)

Recurrence Relations 3 (Fall 2022)

Recurrence Relations 4

Recurrence Relations 5 (Spring 2023)

Recurrence Relations 6 (Fall 2022)

Recurrence Relations 7 (Fall 2022)

Recurrence Relations 8 (Spring 2023)

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Çıkmış sorular
Soruları eğitmenlerimize sorma
Topluluktaki sorulara erişim
İstediğin yerden, dilediğin kadar
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