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Propositional Logic
Introduction
Negation of a Proposition
Conjunction
Disjunction
Conditional Statement
BiConditional Statement
Exclusive OR
Truth Table
Example 1
Example 2
Example 3
Example 4
Example 5
Tautology
Example 1
Contradiction
Converse Inverse Contrapositive
Example
Exam-like Question
Logical Equivalences
Logical Equivalences
De Morgan Example
Example
Example
Example
Example
Example
Exam-like Question
Exam-like Question
Exam-like Question
Logic Part 2 : Quantifiers
Universal Quantifiers
Existential Quantifiers
Truth Value of Propositions with Quantifiers
Example
Example
Example
Example
Example
Example
Nested Quantifiers
Example
Example
Example
Example
Example
Example
Negation of Nested Quantifiers
Example
Example
Translations
Example
Example
Example
Example
Example
Translation of Mathematical Statements
Translation of Statements With Multiple Variables
Example
Example
Example
Example
Example
Example
Example
Example
Logic Puzzle
Logic Puzzle
Arguments
Example
Proof Techniques
Direct Proof
Example 1
Example 2
Example 3
Example 4
Example 5
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Proof By Cases
Example 1
Example 2
Example 3
Example 4
Example 5
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Existence Proof
Example 1
Example 2
Existence and Uniqueness Proof
Example 1
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Contrapositive Proof
Example 1
Example 2
Example 3
Example 4
Example 5
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Proof by Counterexample
Example 1
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Proof by Contradiction
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
If and Only if Statements
Example 1
Example 2
Example 3
Example 4
Example 5
Exam-like Question 1
Exam-like Question 2
Induction
Introduction
Proof of Formulas by Induction
Example 1
Example 2
Example 3
Example 4
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Proof of Divisibility by Induction
Example 1
Example 2
Exam-like Question 1
Exam-like Question 2
Proof of Inequality by Induction
Example 1
Example 2
Example 3
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Induction Related to Fibonacci
Exam-like Question 1
Strong Induction
Example 1
Sets Theory
Definition and Notation
Subset
Example 1
Union and Intersection of Two Sets
Difference of Two Sets
Example 1
Symmetric Difference
Example 1
Set Identities
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Power Set
Example 1
Example 2
Cartesian Product
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Generalized Intersections and Unions
Example 1
Example 2
Example 3
Functions Theory
Definition of Function
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Number of Functions
Injective Functions
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Surjective Functions
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Bijective Function
Composition of Functions
Example 1
Example 2
Example 3
Example 4
Example 5
Inverse Function
Example 1
Example 2
Example 3
Example 4
Example 5
Image of a Set
Example 1
Proof Example For Image of a Function
Preimage of a Set
Example 1
Example 2
Example 3
Proof Example for Preimage of a Function
Example 1
Counting Part 1
Introduction to Counting
Exam like Question 6
Exam like Question 7
Combination & Permutation: Intuition
Exam like Question 8
Exam like Question 9
Combination
Exam like Question 10
Exam like Question 11
Exam like Question 12
Exam like Question 13
Permutation 1
Permutation 2
Exam like Question 14
Exam like Question 15
Exam like Question 16
Counting Part 2
Binomial Theorem
Example 1
Example 3
Example 2
Pascal Identity
Vandermonde's Identity
Example 1
Combinatorial Proof
Example 1
Principle Inclusion-Exclusion
Example 1
Example 2
Distributing Objects into Boxes
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Pigeonhole Principle
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
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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