MAT 2033 • Discrete Mathematics • Final
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
Relations
Definition of Relation
Example 1
Example 2
Example 3
Example 4
Reflexive Relations
Example 5
Example 6
Symmetric Relations
Antisymmetric Relations
Example 7
Transitive Relations
Example 8
Properties of Relations
Example 9
Example 10
Example 11
Example 12
Example 13
Composition of Relations
Example 14
Example 15
Example 16
Equivalence Relation
Example 17
Example 18
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24
Divisibility and Modular Arithmetic
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
Primes and Greatest Common Divisors
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
Solving Linear Congruences
Example 1
Example 2
Chinese Remainder Theorem
Example 1
Example 2
Example 3
Example 4
Cyrptography
Ceasar Cipher
Affine Cipher
Example 1
Example 2
Example 3
Example 4
Transposition Cipher
RSA Algorithm
Example 1
Example 2
Example 3
Exam-like Question 1
Exam-like Question 2
Diffie - Hellman Protocol
Example 1
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
Matching
Example 9
Subgraph
Example 10
Subgraph Induced
Edge Contraction
Example 11
Complementary Graph
Example 12
Example 13
Example 14
Adjacency Matrices - Undirected Graphs
Adjacency Matrices - Directed Graphs
Example 15
Example 16
Incidence Matrices
Example 17
Isomorphism of Graphs
Example 18
Example 19
Example 20
Example 21
Definition of Paths and Circuits
Connected Graphs
Euler Paths and Circuits
Example 22
Hamilton Paths and Circuits
Example 23
Example 24
Eğitmen
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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