MATH 204Discrete MathematicsMidterm I

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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Example 2

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Example 3

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Example 4

Example 5

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Contrapositive Proof

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Example 5

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Proof by Contradiction

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Example 6

Example 7

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Proof by Counterexample

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Existence Proof

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Existence and Uniqueness Proof

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If and Only if Statements

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Big-O Notation

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Sum Property of Big-O Notation

Multiplication Property of Big-O Notation

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Big-Omega Notation

Big-Theta Notation

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Linear Search Algorithm

Binary Search Algorithm

Bubble Sort Algorithm

Definition of Divisibility

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Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

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Prime Numbers

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GCD Greatest Common Divisor

LCM Least Commun Multiple

Example 1

Euclidian Algorithm

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Bézout Identity

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Inverse of a Number in Modular Arithmetic

Primitive Root

Discrete Logarithm

Fermat's Little Theorem

Solving Linear Congruences

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Chinese Remainder Theorem

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Example 4

Ceasar Cipher

Affine Cipher

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Transposition Cipher

RSA Algorithm

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Example 3

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Diffie - Hellman Protocol

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Introduction

Proof of Formulas by Induction

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Example 4

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Proof of Divisibility by Induction

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Proof of Inequality by Induction

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Example 3

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Induction Related to Fibonacci

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Strong Induction

Example 1

Eğitmen

İhsan Altundağİhsan 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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