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Propositional Logic
Introduction
Negation of a Proposition
Compound Propositions
Truth Table 1
Truth Table 2
Tautology
Contradiction
Converse Inverse Contrapositive
Practice Problem 1
Practice Problem 2
Practice Problem 3
Logical Equivalences 1
Logical Equivalences 2
De Morgans' Law
Example 1
Example 2
Example 3
Example 4
Quantifiers and Translations
Universal Quantifiers
Existential Quantifiers
Truth Value of Propositions with Quantifiers
Example 1
Example 2
Nested Quantifiers
Example 3
Example 4
Negation of Nested Quantifiers
Example 5
Translations
Example 6
Example 7
Exam-like Question 1
Translation of Statements With Multiple Variables
Sample Midterm Problems I
Logic Basics 1
Logic Basics 2
Logic Basics 3
Logic Basics 4
Logic - Quantifiers 1
Logic - Quantifiers 2
Logic - Quantifiers 3
Logic - Quantifiers 4
Logic - Quantifiers 5
Logic - Translation 1
Logic - Translation 2
Logic - Translation 3
Logic - Translation 4
Logic - Translation 5
Proof Techniques Part 1
Direct Proof
Example 1
Example 2
Example 3
Example 4
Proof by Contrapositive
Example 1
Example 2
Example 3
Proof by Contradiction
Example 1
Example 2
Proof Techniques Part 2
Proof by Counterexample
Example 1
Proof By Cases
Example 1
Example 2
Example 3
Proofs of Equivalence
Example 1
Example 2
Sample Midterm Problems II
Direct Proof 1
Direct Proof 2
Proof by Contrapositive 1
Proof by Contrapositive 2
Proof by Contradiction 1
Proof by Contradiction 2
Proof by Contradiction 3
Proof by Contradiction 4
Proof by Contradiction 5
Proof by Cases 1
Proofs of Equivalence 1
Proofs of Equivalence 2
Sets
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
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
Sequences and Summation
Definition of Sequence
Arithmetique Sequence
Example 1
Geometric Sequence
Example 1
Sum Notation
Example 1
Sample Midterm Problems III
Proofs & Sets 1
Proofs & Sets 2
Proofs & Sets 3
Proofs & Sets 4
Proofs & Sets 5
Proofs & Sets 6
Proofs & Sets 7
Functions 1
Functions 2
Functions 3
Functions 4
Sets, Function, Summation 1
Sets, Function, Summation 2
Sets, Function
Algorithms and Growth of Functions
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
Example 2
Big-Omega Notation
Big-Theta Notation
Example 1
Example 2
Linear Search Algorithm
Binary Search Algorithm
Bubble Sort Algorithm
Number Theory
Definition of Divisibility
Example 1
Example 2
Example 3
Division Algorithm
Definition of Modular Arithmetic
Example 1
Properties of Modular Arithmetic
Example 1
Example 2
Prime Numbers
Example 1
Example 2
Example 3
GCD Greatest Common Divisor
LCM Least Commun Multiple
Example 1
Euclidian Algorithm
Example 1
Bézout Identity
Example 1
Example 2
Example 3
Inverse of a Number in Modular Arithmetic
Primitive Root
Discrete Logarithm
Fermat's Little Theorem
Sample Midterm Problems IV
Growth of Functions 1
Growth of Functions 2
Growth of Functions 3
Growth of Functions 4
Growth of Functions 5
Growth of Functions 6
Number Theory 1
Number Theory 2
Number Theory 3
Number Theory 4
Induction
Introduction
Proof of Formulas by Induction
Example 1
Example 2
Example 3
Example 4
Proof of Divisibility by Induction
Example 1
Example 2
Proof of Inequality by Induction
Example 1
Example 2
Induction Related to Fibonacci
Strong Induction
Sample Midterm Problems V
Induction for Formulas 1
Induction for Formulas 2
Induction for Formulas 3
Induction for Formulas 4
Induction for Formulas 5
Induction Proof for Divisibility 1
Induction Proof for Divisibility 2
Direct Proof & Induction 1
Direct Proof & Induction 2
Induction for Inequalities 1
Induction for Inequalities 2
Induction for Inequalities 3
Induction with Fibonacci 1
Induction with Fibonacci 2
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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