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Logic Part 1 : Basics
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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Logic Part 2 : Quantifiers
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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Proof Techniques Part 1
Direct Proof
Example 1
Example 2
Example 3
Example 4
Example 5
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Contrapositive Proof
Example 1
Example 2
Example 3
Example 4
Example 5
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Proof by Contradiction
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
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Proof Techniques Part 2
Proof by Counterexample
Example 1
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If and Only if Statements
Example 1
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Example 3
Example 4
Example 5
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Induction
Introduction
Proof of Formulas by Induction
Example 1
Example 2
Example 3
Example 4
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Proof of Divisibility by Induction
Example 1
Example 2
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Proof of Inequality by Induction
Example 1
Example 2
Example 3
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Induction Related to Fibonacci
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Strong Induction
Example 1
Sets
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
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
Cardinality
Definition
Example 1
Countable Sets
Properties of Countable Sets
Example 1
Uncountable Sets
Sequences and Sums
Definition of Sequence
Arithmetique Sequence
Example 1
Geometric Sequence
Example 1
Sum Notation
Example 1
Sample Exam Problems
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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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