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.
Geçme Garantisi
Derslerimize güveniyoruz. Olur da sınavlarına bizimle hazırlandığın halde dersten kalırsan, iade alabilirsin. Koşullar
Konular
Counting: The Basics of Counting
11 konu anlatımı
Basic Principles of Counting
Counting Examples
Permutations
Permutations Example
Groups and Circular Permutation Example
Identical Objects Example 1
Identical Objects Example 2
Combination
n choose r
Committee Example
Ball Example
Binomial Coefficients and Identities
6 konu anlatımı
Binomial Theorem
Example 1
Example 2
Pascal Identity
Combinatorial Proof
Example 3
Pigeonhole Principle & Principle Inclusion - Exclusion
9 konu anlatımı
Pigeonhole Principle
Example 1
Example 2
Example 3
Example 4
Example 5
Principlie Inclusion Exclusion
Example 1
Example 2
Generalized Permutations and Combinations
4 konu anlatımı
Distributing Objects into Boxes 1
Distributing Objects into Boxes 2
Example 1
Example 2
🦄🦄 PAST EXAM PROBLEMS: PART 1 🦄🦄
26 soru
Counting Standard Models
Counting Standard Models
Counting Standard Models
Counting Standard Models
Counting Standard Models
Counting Standard Models
Counting Standard Models
Counting Standard Models & Binomial Coefficients
Binomial Coefficient
Binomial Identities
Binomial Identities - Combinatorial Proof
Pigeonhole Principle
Pigeonhole Principle
Pigeonhole Principle
Pigeonhole Principle
Pigeonhole Principle
Pigeonhole Principle
Principle Inclusion - Exclusion
Principle Inclusion - Exclusion
Counting & Principle Inclusion - Exclusion
Generalized Permutations and Combinations
Generalized Permutations and Combinations
Generalized Permutations and Combinations
Generalized Permutations and Combinations
Generalized Permutations and Combinations
Generalized Permutations and Combinations
Advanced Counting Techniques: Recurrence Relations
10 konu anlatımı
Recurrence Relations
Homogenous Recurrence Relations
Example 1
Example 2
Non Homogenous Recurrence Relations
Example 3
Example 4
Creating Recurrence Relations
Example 5
Example 6
Advanced Counting Techniques: Generating Functions
7 konu anlatımı
Generating Functions
Example 1
Example 2
Extended Binomial Theorem
Counting Problems with Generating Functions
Example 1
Example 2
🦄🦄 PAST EXAM PROBLEMS: PART 2 🦄🦄
19 soru
Recurrence Relations
Recurrence Relations
Recurrence Relations
Recurrence Relations
Recurrence Relations
Recurrence Relations
Recurrence Relations
Recurrence Relations
Recurrence Relations
Generating Functions
Generating Functions
Generating Functions
Generating Functions
Generating Functions
Generating Functions
Generating Functions
Generating Functions
Generating Functions
Generating Functions
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
🦄🦄 PAST EXAM PROBLEMS: PART 3 🦄🦄
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)
Değerlendirmeler
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