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Ücretsiz Dersi AlMATH 111 • Final • Discrete Mathematics
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Konular
Cryptography
Ceasar Cipher
Affine Cipher
Example 1
Example 2
Example 3
Example 4
Mathematical Induction
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
Sample Final Problems I
Induction for Formulas 1
Induction for Formulas 2
Induction for Formulas 3
Induction for Formulas 4
Induction for Formulas 5
Induction Proof for Divisibility 1
Induction Proof for Divisibility 2
Induction for Inequalities 1
Induction for Inequalities 2
Induction for Inequalities 3
Induction with Fibonacci 1
Induction with Fibonacci 2
Counting
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
Principle Inclusion-Exclusion
Example 1
Distributing Objects into Boxes 1
Distributing Objects into Boxes 2
Example 1
Example 2
Pigeonhole Principle
Example 1
Example 2
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
Sample Midterm Problems II
Counting 1
Counting 2
Counting 3
Counting 4
Counting 5
Counting 6
Counting 7
Counting 8
Counting 9
Counting 10
Counting 11
Counting 12
Pigeonhole Principle 1
Pigeonhole Principle 2
Pigeonhole Principle 3
Recurrence Relations 1
Recurrence Relations 2
Recurrence Relations 3
Recurrence Relations 4
Recurrence Relations 5
Relations: Part 1
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
Composition of Relations
Example 13
Example 14
Combining Relations
Inverse and Complementary of a Relation
Example 15
Matrix Representation of a Relation 1
Matrix Representation of a Relation 2
Example 16
Operations on Zero - One Matrices
Example 17
Reflexive Closure
Symmetric Closure
Example 18
Transitive Closure & Connectivity Relation
Matrix Representation of Transitive Closure
Example 19
Equivalence Relation
Example 20
Example 21
Example 22
Relations: Part 2
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
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
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
Sample Final Problems III
Relations 1
Relations 2
Relations 3
Relations 4
Relations 5
Relations 6
Relations 7
Relations 8
Relations 9
Relations 10
Graphs 1
Graphs 2
Graphs 3
Graphs 4
Graphs 5
Graphs 6
Graphs 7
Graphs 8
Graphs 9
Graphs 10
Graphs 11
Graphs 12
Graphs 13
Graphs 14
Graphs 15
Graphs 16
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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