# COMP 106 • Discrete Mathematics for Computer Science and Engineering • Midterm I

Ders Tanıtımı

Introduction

Negation of a Proposition

Conjunction

Disjunction

Conditional Statements : IF

BiConditional : If and only If

Exclusive OR

Truth Table 1

Truth Table 2

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Tautology

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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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Contrapositive Proof

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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

Example 1

Example 2

Example 3

Example 4

Sum Property of Big-O Notation

Multiplication Property of Big-O Notation

Example 1

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Big-Omega Notation

Big-Theta Notation

Example 1

Example 2

Linear Search Algorithm

Binary Search Algorithm

Bubble Sort Algorithm

Introduction

Proof of Formulas by Induction

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Example 2

Example 3

Example 4

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Proof of Divisibility by Induction

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Example 2

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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

Definition of Divisibility

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Example 2

Example 3

Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

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Prime Numbers

Example 1

Example 2

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GCD Greatest Common Divisor

LCM Least Commun Multiple

Example 1

Euclidian Algorithm

Example 1

Bézout Identity

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Example 2

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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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Example 2

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Example 4

Ceasar Cipher

Affine Cipher

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Example 2

Example 3

Example 4

Transposition Cipher

RSA Algorithm

Example 1

Example 2

Example 3

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Diffie - Hellman Protocol

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Question 8

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Question 9

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Question 10

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Question 11

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Question 13

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Question 14

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Question 15

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Question 16

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Question 18

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Question 19

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Question 21

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Question 31

## 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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