MAT 201 • Final • Discrete Mathematics
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Eğitmen
İhsan Altundağ
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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Konular
Induction
14 konu anlatımı
Introduction
Proof of Formulas by Induction
Example 1
Example 2
Example 3
Example 4
Proof of Divisibility by Induction
Example 1
Example 2
Proof of Inequality by Induction
Example 1
Example 2
Induction Related to Fibonacci
Strong Induction
Recursion
10 konu anlatımı
Introduction
Recursively Defined Functions
Example 1
Recursively Defined Sets
Example 2
Recursively Defined Strings
Example 3
Structural Induction
Example 4
Example 5
Sample Final Problems I
10 soru
Induction for Formulas 1
Induction for Formulas 2
Induction for Formulas 3
Induction for Formulas 4
Induction Proof for Divisibility 1
Induction Proof for Divisibility 2
Induction for Inequalities
Induction with Fibonacci
Recursion and Induction
Recursive Algorithm
Counting
14 konu anlatımı
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
Binomial Coefficients and Identities
7 konu anlatımı
Binomial Theorem
Example 1
Example 2
Example 3
Pascal Identity
Combinatorial Proof
Example 4
(NEW) Pigeonhole Principle
9 konu anlatımı
Pigeonhole Principle
Example 1
Example 2
Example 3
Example 4
Example 5
Principlie Inclusion Exclusion
Example 1
Example 2
Advanced Counting Techniques
17 konu anlatımı
Generating Functions
Example 1
Example 2
Extended Binomial Theorem
Counting Problems with Generating Functions
Example 1
Example 2
Recurrence Relations
Homogenous Recurrence Relations
Example 1
Example 2
Non Homogenous Recurrence Relations
Example 3
Example 4
Creating Recurrence Relations
Example 5
Example 6
Sample Final Problems II
20 soru
Counting 1
Counting 2
Counting 3
Counting 4
Counting 5
Counting 6
Recurrence Relations 1
Recurrence Relations 2
Recurrence Relations 3
Recurrence Relations 4
Recurrence Relations 5
Recurrence Relations 6
Generating Functions 1
Generating Functions 2
Generating Functions 3
Pigeonhole Principle 1
Pigeonhole Principle 2
Pigeonhole Principle 3
Pigeonhole Principle 4
Pigeonhole Principle 5
Relations: Part 1
27 konu anlatımı
Definition of Relation
Example 1
Example 2
Example 3
Reflexive Relations
Example 4
Symmetric Relations
Antisymmetric Relations
Example 5
Transitive Relations
Example 6
Properties of Relations
Example 7
Example 8
Composition of Relations
Example 9
Example 10
Combining Relations
Inverse and Complementary of a Relation
Example 11
Matrix Representation of a Relation 1
Matrix Representation of a Relation 2
Example 12
Operations on Zero - One Matrices
Example 13
Equivalence Relation
Example 14
Relations: Part 2
14 konu anlatımı
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 Part 1
17 konu anlatımı
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
17 konu anlatımı
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
Trees
9 konu anlatımı
Introduction
Rooted Tree
Terminology for Rooted Trees
Full m-ary Trees
Some Formulas
What is a Minimum Spanning Tree?
Prim's Algorithm
MST Example 1
MST Example 2
Sample Final Problems III
19 soru
Properties of Relation
Properties of Relation
Equivalence Relation 1
Equivalence Relation 2
Equivalence Relation 3
Hasse Diagram 1
Hasse Diagram 2
Adjacency Matrices
Incidence Matrices
Bipartite Graphs & Euler Circuits
Euler Path, Induced Subgraph & Incidence Matrix
Isomorphism 1
Isomorphism 2
Isomorphism 3
Isomorphism 4
Isomorphism 5
Minimum Spanning Trees 1
Minimum Spanning Trees 2
Minimum Spanning Trees (T/F)
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