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Sets
Definition and Notation
Subset
Example 1
Union and Intersection of Two Sets
Difference of Two Sets
Example 2
Set Identities
Example 3
Power Set
Example 4
Example 5
Cartesian Product
Example 6
Generalized Intersections and Unions
Example 7
Example 8
Relations: Part 1
Definition of Relation
Example 1
Example 2
Example 3
Reflexive Relations
Example 4
Symmetric Relations
Antisymmetric Relations
Example 5
Transitive Relations
Properties of Relations
Example 6
Example 7
Relations: Part 2
Composition of Relations
Inverse and Complementary of a Relation
Matrix Representation of a Relation 1
Matrix Representation of a Relation 2
Example 1
Reflexive Closure
Symmetric Closure
Example 2
Transitive Closure & Connectivity Relation
Equivalence Relation
Example 3
Example 4
Partially Ordered Set
Example 5
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
Divisibility and Modular Arithmetic
Definition of Divisibility
Example 1
Example 2
Example 3
Division Algorithm
Definition of Modular Arithmetic
Example 4
Properties of Modular Arithmetic
Example 5
Example 6
GCD Greatest Common Divisor
LCM Least Commun Multiple
Example 7
Cyrptography
Ceasar Cipher
Affine Cipher
Example 1
Example 2
Example 3
Example 4
Graph Theory
Introduction
Example 1
Graph Terminology
Example 2
Handshaking Theorem
Example 3
Example 4
Special Graphs
Example 5
Example 6
Bipartite Graphs
Example 7
Example 8
Complete Bipartite Graph
Complementary Graph
Example 9
Example 10
Example 11
Adjacency Matrices - Undirected Graphs
Adjacency Matrices - Directed Graphs
Example 12
Example 13
Incidence Matrices
Example 14
Sample Final Problems
Sets 1
Proofs & Sets 1
Proofs & Sets 2
Proofs & Sets 3
Proofs & Sets 4
Proofs & Sets 5
Proof & Sets 6
Proofs & Sets 7
Proofs & Sets 8
Proofs & Sets 9
Proofs & Sets 10
Relations 1
Relations 2
Relations 3
Relations 4
Relations 5
Functions 1
Functions 2
Functions 3
Functions 4
Functions 5
Functions 6
Functions 7
Sets & Functions
Selected Questions from Midterm Topics
Relations 1
Relations 2
Relations 3
Relations 4
Induction 1
Induction 2
Functions 1
Functions 2
Sets 1
Sets 2
Logic 1
Logic 2
Logic 3
Logic 4
Logic 5
Logic 6
Logic 7
Proof Techniques 1
Proof Techniques 2
Proof Techniques 3
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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