MATH 2103 • Tüm Sınavlar • 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 & Permutations & Combinations
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
Pigeonhole Principle & Principle Inclusion-Exclusion
11 konu anlatımı
Pigeonhole Principle
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Principle Inclusion-Exclusion
Example 1
Example 2
Sample Midterm Problems I
12 soru
Counting
Counting
Counting
Counting
Counting
Counting
Counting
Pigeonhole Principle 1
Pigeonhole Principle 2
Pigeonhole Principle 3
Pigeonhole Principle 4
Pigeonhole Principle 5
Propositional Logic
8 konu anlatımı · 3 soru
Introduction
Negation of a Proposition
Compound Propositions
Truth Table 1
Truth Table 2
Tautology
Contradiction
Converse Inverse Contrapositive
Practice Problem 1
Practice Problem 2
Practice Problem 3
Logical Equivalences
7 konu anlatımı
Logical Equivalences 1
Logical Equivalences 2
De Morgans' Law
Example 1
Example 2
Example 3
Example 4
Quantifiers and Translations
14 konu anlatımı
Universal Quantifiers
Existential Quantifiers
Truth Value of Propositions with Quantifiers
Example 1
Example 2
Nested Quantifiers
Example 3
Example 4
Negation of Nested Quantifiers
Example 5
Translations
Example 6
Example 7
Translation of Statements With Multiple Variables
Rules of Inferences
7 konu anlatımı
Valid Argument
Rules of Inferences
Example 1
Example 2
Example 3
Using Rules of Inferences to Build Arguments
Example 4
Sample Midterm Problems II
19 soru
Truth Table & Tautology
Logical Equivalences
Logical Equivalences
Logical Equivalences
Logical Equivalences
Tautology
Quantifiers 1
Quantifiers 2
Quantifiers
Quantifiers
Quantifiers 3
Nested Quantifiers 1
Nested Quantifiers 2
Translations
Translations
Translations
Rules of Inferences 1
Rules of Inferences 2
Rules of Inferences 3
Sample Midterm Problems I
13 soru
Quantifiers 1
Quantifiers 2
Quantifiers 3
Quantifiers 4
Quantifiers 5
Quantifiers 6
Quantifiers 7
Translations
Translations
Translations
Rules of Inferences 1
Rules of Inferences 2
Rules of Inferences 3
Proof Techniques
17 konu anlatımı
Direct Proof
Example 1
Example 2
Example 3
Example 4
Proof by Contrapositive
Example 1
Example 2
Example 3
Proof by Contradiction
Example 1
Example 2
Proof By Cases
Example 1
Proofs of Equivalence
Example 1
Example 2
Mathematical 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
Recursive Definition and Structural Induction
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 Midterm Problems II
22 soru
Direct Proof 1
Direct Proof 2
Direct Proof 3
Direct Proof 4
Proof by Contrapositive
Proof by Contrapositive
Proof by Contrapositive
Proof by Contrapositive
Proof by Contradiction
Proof by Contradiction
Proof by Contradiction
Proof by Cases
Proof by Cases
Proofs of Equivalence
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
Sets
14 konu anlatımı
Definition and Notation
Subset
Example 1
Union and Intersection of Two Sets
Difference of Two Sets
Set Identities
Example 2
Power Set
Example 3
Cartesian Product
Example 4
Example 5
Proof Example 1
Proof Example 2
Functions & Sequences & Summation
23 konu anlatımı
Definition of Function
Example 1
Number of Functions
Injective Functions
Example 2
Example 3
Example 4
Number of Injective Functions
Surjective Functions
Example 5
Example 6
Example 7
Bijective Function
Inverse Function
Example 8
Example 9
Definition of Sequence
Arithmetique Sequence
Example 1
Geometric Sequence
Example 1
Sum Notation
Example 1
Cardinality
6 konu anlatımı
Definition
Example 1
Countable Sets
Properties of Countable Sets
Example 1
Uncountable Sets
Sample Midterm Problems III
20 soru
Sets
Sets
Sets
Sets & Cardinality
Functions
Functions
Functions & Sets
Functions & Sets & Summation
Function & Summation & Cardinality
Function & Summation
Cardinality 1
Cardinality 2
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
Number Theory
24 konu anlatımı
Definition of Divisibility
Example 1
Example 2
Example 3
Division Algorithm
Definition of Modular Arithmetic
Example 1
Properties of Modular Arithmetic
Example 1
Example 2
Prime Numbers
Example 1
Example 2
Example 3
GCD Greatest Common Divisor
LCM Least Commun Multiple
Example 1
Euclidian Algorithm
Example 1
Bézout Identity
Example 1
Example 2
Example 3
Fermat' Little Theorem
Cryptography
11 konu anlatımı
Ceasar Cipher
Affine Cipher
Example 1
Example 2
Example 3
Example 4
Transposition Cipher
RSA Algorithm
Example 1
Example 2
Example 3
Sample Final Problems I
6 soru
Number Theory 1
Number Theory 2
Number Theory 3
Number Theory 4
Cryptography 1
Cryptography 2
Relations
32 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
Graph Theory: Part 1
25 konu anlatımı
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
11 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
Trees
5 konu anlatımı
Introduction
Rooted Tree
Terminology for Rooted Trees
Full m-ary Trees
Some Formulas
Sample Exam Problems III
16 soru
Properties of Relation 1
Properties of Relation 2
Properties of Relation 3
Combining Relations
Equivalence Relation 1
Equivalence Relation 2
Equivalence Relation 3
Equivalence Relation 4
Equivalence Relation 5
Equivalence Relation - Proof
Graph Theory 1
Graph Theory 2
Graph Theory 3
Graph Theory 4
Graph Theory 5
Graph Theory 6