MATH 108 • Discrete and Combinatorial Mathematics • Final
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Konular
Counting: Part 1
Basic Principles of Counting
Counting Examples
Permutations
Permutations Example
Groups and Circular Permutation Example
Identical Objects Example 1
Identical Objects Example 2
Identical Objects Example 3
Combination
n choose r
Committee Example 1
Committee Example 2
Ball Example 1
Ball Example 2
Counting: Part 2
Principle Inclusion-Exclusion
Example 1
Example 2
Distributing Objects into Boxes 1
Distributing Objects into Boxes 2
Example 1
Example 2
Example 3
Example 4
Example 5
Exam Like Question 1
Exam Like Question 2
Exam Like Question 3
Pigeonhole Principle
Example 1
Example 2
Example 3
Example 4
Example 5
Sample Final Problems I
Counting Standard Models 1
Counting Standard Models 2
Counting Standard Models 3
Counting Standard Models 4
Counting Standard Models 5
Counting Standard Models 6
Counting Standard Models 7
Inclusion-Exclusion Principle 1
Inclusion-Exclusion Principle 2
Inclusion-Exclusion Principle & Distributing Objects 1
Distributing Objects into Boxes 1
Distributing Objects into Boxes 2
Distributing Objects into Boxes 3
Distributing Objects into Boxes 4
Distributing Objects into Boxes 5
Distributing Objects into Boxes 6
Pigeonhole Principle 1
Pigeonhole Principle 2
Pigeonhole Principle 3
Advanced Counting: 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
Advanced Counting: 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
Sample Final Problems II
Recurrence Relations 1
Recurrence Relations 2
Recurrence Relations 3
Recurrence Relations 4
Recurrence Relations 5
Recurrence Relations 6
Recurrence Relations 7
Recurrence Relations 8
Generating Functions 1
Generating Functions 2
Generating Functions 3
Discrete Probability
Axioms of Probability 1
Axioms of Probability 2
Axioms of Probability 3
Axioms of Probability 4
Intuition of Conditional Probability
Conditional Probability 1
Conditional Probability 2
Example 1
Example 2
Total Probability Rule
Discrete Random Variables
Expected Value
Variance
Expected Value and Variance Arithmetic
Sample Final Problems III
Discrete Probability 1
Discrete Probability 2
Discrete Probability 3
Discrete Probability 4
Discrete Probability 5
Discrete Probability 6
Discrete Probability 7
Discrete Random Variables 1
Discrete Random Variables 2
Discrete Random Variables 3
Discrete Random Variables 4
Graph Theory Part 1
Introduction
Graph Terminology
Handshaking Theorem
Example 1
Special Graphs
Example 2
Bipartite Graphs
Example 3
Example 4
Complete Bipartite Graph
Matching
Subgraph
Example 5
Subgraph Induced
Edge Contraction
Example 6
Complementary Graph
Graph Theory Part 2
Adjacency Matrices - Undirected Graphs
Adjacency Matrices - Directed Graphs
Example 1
Example 2
Incidence Matrices
Example 3
Isomorphism of Graphs
Example 4
Example 5
Example 6
Example 7
Definition of Paths and Circuits
Connected Graphs
Euler Paths and Circuits
Example 8
Hamilton Paths and Circuits
Example 9
Example 10
Planar Graph
Planar Graph - Euler Formula
Example 11
Corollaries about Planar Graph
Example 12
Sample Final Problems IV
Adjacency Matrices
Incidence Matrices
Bipartite Graphs & Euler Circuits
Bipartite Graphs, Euler Circuit & Planar Graphs
Euler Path, Induced Subgraph & Incidence Matrix
Chromatic Number 1
Chromatic Number 2
Isomorphism 1
Isomorphism 2
Isomorphism 3
Isomorphism 4
Isomorphism 5
Eğitmen
İhsan AltundağEğitmen
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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