CE 215 • Final • Discrete Mathematics for Computer Science
“Anlaşılır ve verimli”
Serkan Atak
Bilgisayar Mühendisliği
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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.
Konular
Induction
14 konu anlatımı · 8 soru
Introduction
Proof of Formulas by Induction
Example 1
Example 2
Exam-like Question 1
Exam-like Question 2
Proof of Divisibility by Induction
Example 1
Example 2
Exam-like Question 1
Exam-like Question 2
Proof of Inequality by Induction
Example 1
Example 2
Example 3
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Induction Related to Fibonacci
Exam-like Question 1
Strong Induction
Example 1
Counting: Part 1
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
Counting: Part 2
19 konu anlatımı
Binomial Theorem
Example 1
Example 3
Example 2
Pascal Identity
Vandermonde's Identity
Example 1
Combinatorial Proof
Example 1
Principle Inclusion-Exclusion
Example 1
Example 2
Pigeonhole Principle
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Sample Midterm Problems I
24 soru
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 with Fibonacci 1
Counting 1
Counting 2
Counting 3
Counting 4
Counting 5
Counting 6
Counting 7
Counting & Binomial Coefficients 1
Principle Inclusion - Exclusion 1
Pigeonhole Principle 1
Pigeonhole Principle 2
Pigeonhole Principle 3
Pigeonhole Principle 4
Pigeonhole Principle 5
Advanced Counting: Recurrence Relations
13 konu anlatımı
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
10 konu anlatımı
Definition
Example 1
Example 2
Example 3
Example 4
Extended Binomial Theorem
Counting Problems with Generating Functions
Example 5
Example 6
Example 7
Relations
47 konu anlatımı
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
Equivalence Relation
Example 18
Example 19
Example 20
Partially Ordered Set
Example 21
Example 22
Example 23
Totally Ordered Set
Example 24
Hasse Diagram
Example 25
Maximal and Minimal Elements
Greatest and Least Elements
Example 26
Upper and Lower Bound
Least Upper and Greatest Lower Bound
Example 27
Sample Final Problems II
25 soru
Recurrence Relations 1
Recurrence Relations 2
Recurrence Relations 3
Recurrence Relations 4
Recurrence Relations 5
Recurrence Relations 6 (Hard)
Generating Functions 1
Generating Functions 2
Generating Functions 3
Generating Functions 4
Generating Functions 5
Generating Functions 6
Generating Functions 7
Generating Functions 8
Relations 1
Relations 2
Relations 3
Relations 4
Relations 5
Relations 6
Relations 7
Relations 8
Relations 9
Relations 10
Relations 11
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 II
23 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
Example 10
Planar Graph
Planar Graph - Euler Formula
Example 11
Corollaries about Planar Graph
Example 12
(NEW) Trees
5 konu anlatımı
Introduction
Rooted Tree
Terminology for Rooted Trees
Full m-ary Trees
Some Formulas
Sample Final Problems III
21 soru
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
Trees 1
Trees 2
Trees 3
Trees 4
Trees 5
Handshaking Theorem 1
Handshaking Theorem 2
Handshaking Theorem 3
True/False Problems
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