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Principle Inclusion - Exclusion
Principle Inclusion-Exclusion
Example 1
Example 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Generating Functions
Definition
Example 1
Example 2
Example 3
Example 4
Extended Binomial Theorem
Counting Problems with Generating Functions
Example 5
Example 6
Example 7
Relations Part I
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
Example 14
Composition of Relations
Example 15
Example 16
Combining Relations
Inverse and Complementary of a Relation
Example 17
Equivalence Relation
Example 22
Example 23
Example 24
Example 25
Example 26
Example 27
Example 28
Example 29
Example 30
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Relations Part II
Partially Ordered Set
Example
Example
Example
Totally Ordered Set
Example
Hasse Diagram
Example
Maximal and Minimal Elements
Greatest and Least Elements
Example
Upper and Lower Bound
Least Upper and Greatest Lower Bound
Example
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
Past Exam Questions
Generating Functions 1
Relations 1
Relations 2
Relations 3
Graphs 1
Graphs 2
Graphs 3
Graphs 4
Graphs 5
Graphs 6
Graphs 7
Graphs 8
Spring 2023 Final Problems
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Spring 2024 Final Problems
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
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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