COMP 106 • Final • Discrete Mathematics for Computer Science and Engineering
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Konular
Sets and Functions
Injective Functions
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Surjective Functions
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Bijective Function
Image of a Set
Example 1
Proof Example For Image of a Function
Preimage of a Set
Example 1
Example 2
Proof Example for Preimage of a Function
Example 1
Relations
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
Composition of Relations
Example 12
Example 13
Combining Relations
Inverse and Complementary of a Relation
Example 14
Matrix Representation of a Relation 1
Matrix Representation of a Relation 2
Example 15
Operations on Zero - One Matrices
Example 16
Reflexive Closure
Symmetric Closure
Example 17
Transitive Closure & Connectivity Relation
Matrix Representation of Transitive Closure
Example 18
Equivalence Relation
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24
Partially Ordered Set
Example 25
Example 26
Sample Final Problems I
Proofs & Sets 1
Proofs & Sets 2
Proofs & Sets 3
Proofs & Sets 4
Sets and Function 1
Relations 1
Relations 2
Relations 3
Relations 4
Relations 5
Relations 6
Relations 7
Relations 8
Relations 9
Mathematical Induction
Introduction
Proof of Formulas by Induction
Example 1
Example 2
Example 3
Example 4
Exam-like Question 1
Exam-like Question 2
Proof of Divisibility by Induction
Example 1
Example 2
Exam-like Question 1
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
Strong Induction
Sample Final Problems II
Complexity 1
Complexity 2
Complexity 3
Complexity 4
Complexity 5
Complexity 6
Algorithms 1
Algorithms 2
Algorithms 3
Algorithms 4
Algorithms 5
Induction 1
Induction 2
Induction 3
Induction 4
Strong Induction 1
Algortithm & Induction
Number Theory 1
Number Theory 2
Number Theory 3
Number Theory 4
Number Theory 5
Number Theory & Induction
Cryptography
Modeling Computation - Languages and Grammar
Language and Grammar
Phase-Structure Grammar
Grammar -> Language Example 1
Grammar -> Language Example 2
Language -> Grammar Example 1
Language -> Grammar Example 2
Modeling Computation - Finite State Machines / Turing Machine
Finite State Machines with Output
Example 1
Example 2
Finite State Machines with NO Output
Example 3
Example 4
Example 5
Turing Machine
Example 6
Example 7
Sample Final Problems III
Grammar -> Language 1
Grammar -> Language 2
Language -> Grammar 1
Language -> Grammar 2
Language -> Grammar 3
Finite State Machines with Output
Finite State Machines with NO Output 1
Finite State Machines with NO Output 2
Turing Machine
Old Exam and Quiz Questions
Induction 1
Algorithm and Complexity 1
Algorithm and Complexity 2
Complexity 1
Complexity 2
Complexity 3
Number Theory 1
Number Theory 2
Cryptography 1
Before Exam Questions (NEW)
Logic
Proof Techniques
Induction
Growth of Functions
Recursion and Induction
Recursive Algorithm and Complexity
Modular Arithmetic 1
Modular Arithmetic 2
Modeling Computation 1
Modeling Computation 2
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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