COMP 106 (Spring 24) • Discrete Mathematics for Computer Science and Engineering • Final
Recurrence Relations
Introduction
Homogenous Recurrence Relations
Example 1
Example 2
Example 3
Example 4
Non Homogenous Recurrence Relations
Example5
Example 6
Creating Recurrence Relations
Example 7
Example 8
Example 9
Generating Functions
Definition
Example 1
Example 2
Example 3
Example 4
Example 5
Extended Binomial Theorem
Counting Problems with Generating Functions
Example 6
Example 7
Example 8
Example 9
Example 10
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
Composition of Relations
Example 12
Example 13
Combining Relations
Inverse and Complementary of a Relation
Example 14
Matrix Representation of a Relation 1
Matrix Representation of a Relation 2
Example 15
Operations on Zero - One Matrices
Example 16
Reflexive Closure
Symmetric Closure
Example 17
Transitive Closure & Connectivity Relation
Matrix Representation of Transitive Closure
Example 18
Equivalence Relation
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24
Partially Ordered Set
Example 25
Example 26
Sample Final Problems I
Recurrence Relations 1
Recurrence Relations 2
Recurrence Relations 3
Recurrence Relations 4
Generating Functions 1
Generating Functions 2
Generating Functions 3
Generating Functions 4
Relations 1
Relations 2
Relations 3
Relations 4
Relations 6
Relations 7
Relations 8
Relations 9
Relations 10
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
Planar Graph
Planar Graph - Euler Formula
Example 25
Corollaries about Planar Graph
Example 26
Kuratowski's Theorem
Example 27
Example 28
Example 29
Modeling Computation - Languages and Grammar
Language and Grammar
Phase-Structure Grammar
Grammar -> Language Example 1
Grammar -> Language Example 2
Grammar -> Language Exam Like Question 1
Grammar -> Language Exam Like Question 2
Language -> Grammar Example 1
Language -> Grammar Example 2
Language -> Grammar Exam Like Question 1
Language -> Grammar Exam Like Question 2
Language -> Grammar Exam Like Question 3
Modeling Computation - Finite State Machines / Turing Machine
Finite State Machines with Output
Example 1
Example 2
Exam Like Question 1
Finite State Machines with NO Output
Example 3
Example 4
Example 5
Exam Like Question 2
Exam Like Question 3
Turing Machine
Example 6
Example 7
Exam Like Question 4
Sample Final Problems II
Graphs 1
Graphs 2
Graphs 3
Graphs 4
Graphs 5
Graphs 6
Graphs 7
Graphs 8
Graphs 9
Graphs 10
Graphs 11
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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