# MATH 204 • Discrete Mathematics • Midterm I

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Ders Tanıtımı

Introduction

Negation of a Proposition

Compound Propositions

Truth Table 1

Truth Table 2

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Tautology

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Contradiction

Converse Inverse Contrapositive

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Logical Equivalences & De Morgan's Laws

Logical Equivalences & De Morgan's Laws 2

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Universal Quantifiers

Existential Quantifiers

Truth Value of Propositions with Quantifiers

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Nested Quantifiers

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Negation of Nested Quantifiers

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Translations

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Translation of Mathematical Statements

Translation of Statements With Multiple Variables

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Logic Puzzle

Logic Puzzle 2

Arguments

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Direct Proof

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Example 1

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Contrapositive Proof

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Proof by Contradiction

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Example 7

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Proof by Counterexample

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If and Only if Statements

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Introduction

Proof of Formulas by Induction

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Proof of Divisibility by Induction

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Proof of Inequality by Induction

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Induction Related to Fibonacci

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Strong Induction

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Definition and Notation

Subset

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Union and Intersection of Two Sets

Difference of Two Sets

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Symmetric Difference

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Set Identities

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Power Set

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Cartesian Product

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Generalized Intersections and Unions

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Definition of Function

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Number of Functions

Injective Functions

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Surjective Functions

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Bijective Function

Composition of Functions

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Inverse Function

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Image of a Set

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Proof Example For Image of a Function

Preimage of a Set

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Proof Example for Preimage of a Function

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Definition

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Countable Sets

Properties of Countable Sets

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Uncountable Sets

Definition of Sequence

Arithmetique Sequence

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Geometric Sequence

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Sum Notation

Example 1

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## 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.

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