MATH 108 • Final • Discrete and Combinatorial Mathematics
Bu ders ile hem bir sürü soru çözmüş, hem kendini denemiş, hem de konuların püf noktalarını öğrenmiş olacaksın.
Kolayca yüksek notlar alabilmen için özenle hazırlanmış video derslerlerimizi izle. Çıkma ihtimali yüksek ve çıkmış soruların soru çözümleriyle sınava en iyi şekilde hazırlan. Hızını sen ayarla. İstediğin yerde hızlandırır, dersleri istediğin kadar tekrar et.
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.
Unicourse Garantisi
Bu dersi alma kararını senin için kolaylaştıralım. Eğer memnun kalmazsan 30 gün içinde bize ulaş, 3'ten fazla içerik tamamlamadıysan iade alabilirsin. Koşullar
Paketi Tamamla
🎓 MEF Üniversitesi öğrencilerinin %92'si tüm paketi alarak çalışıyor.
Konular
Number Theory
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
GCD Greatest Common Divisor
LCM Least Commun Multiple
Euclidian Algorithm
Example 1
Bézout Identity
Example 1
Example 2
Example 3
Inverse of a Number in Modular Arithmetic
Fermat's Little Theorem
Solving Linear Congruences
Example 1
Example 2
Chinese Remainder Theorem
Example 1
Example 2
Example 3
Example 4
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
Recursion
Introduction
Recursively Defined Functions
Example 1
Recursively Defined Sets
Example 2
Recursively Defined Strings
Example 3
Structural Induction
Example 4
Example 5
Sample Final Problems I
Number Theory 1
Number Theory 2
Number Theory 3
Number Theory 4
Number Theory 5
Number Theory 6
Number Theory 7
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
Recursion and Induction
Recursive Algorithm
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
Discrete Probability: Part 1
Sample Space and Events
Probability
Axioms of Probability
Some Rules
Coin Example
Dice Example
Card Example 1
Card Example 2
Ball Example
Set Example
Birthday Example
Discrete Probability: Part 2
Conditioning Events
Total Probability Rule
Example 1
Example 2
Example 3
Bayes' Rule
Bayes' Rule Example 1
Bayes' Rule Example 2
Independence
Independence Example 1
Independence Example 2
Sample Final Problems I
Counting 1
Counting 2
Counting 3
Counting 4
Counting 5
Counting 6
Discrete Probability 1
Discrete Probability 2
Discrete Probability 3
Discrete Probability 4
Discrete Probability 5
Conditional Probability and Independence 1
Conditional Probability and Independence 2
Bayes' Rule 1
Bayes' Rule 2
Discrete Random Variables 1
Discrete Random Variables 2
Advanced Counting Techniques
Principle Inclusion-Exclusion
Example
Distributing Objects into Boxes 1
Distributing Objects into Boxes 2
Example 1
Example 2
Example 3
Pigeonhole Principle
Example 1
Example 2
Example 3
Generating Functions
Example 1
Example 2
Extended Binomial Theorem
Counting Problems with Generating Functions
Example 1
Example 2
Recurrence Relations
Homogenous Recurrence Relations
Example 1
Example 2
Non Homogenous Recurrence Relations
Example 3
Example 4
Creating Recurrence Relations
Example 5
Example 6
Relations
Definition of Relation
Example 1
Example 2
Reflexive Relations
Example 3
Example 4
Symmetric Relations
Antisymmetric Relations
Example 5
Transitive Relations
Example 6
Properties of Relations
Example 7
Example 8
Composition of Relations
Equivalence Relation
Example 9
Sample Final Problems II
Principle Inclusion Exclusion 1
Principle Inclusion Exclusion 2
Distributing Objects into Boxes 1
Distributing Objects into Boxes 2
Pigeonhole Principle 1
Pigeonhole Principle 2
Pigeonhole Principle 3
Pigeonhole Principle 4
Recurrence Relations 1
Recurrence Relations 2
Recurrence Relations 3
Recurrence Relations 4
Recurrence Relations 5
Recurrence Relations 6
Generating Functions 1
Generating Functions 2
Generating Functions 3
Properties of Relation
Properties of Relation
Equivalence Relation 1
Equivalence Relation 2
Equivalence Relation 3
Graph Theory Part 1
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
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
Introduction
Rooted Tree
Terminology for Rooted Trees
Full m-ary Trees
Some Formulas
Sample Final Problems III
Adjacency Matrices
Incidence Matrices
Bipartite Graphs & Euler Circuits
Euler Path, Induced Subgraph & Incidence Matrix
Isomorphism 1
Isomorphism 2
Isomorphism 3
Isomorphism 4
Isomorphism 5
Değerlendirmeler
Henüz hiç değerlendirme yok.
Sıkça Sorulan Sorular
Örneğin, Koç Üniversitesi - MATH 101 (Calculus) veya başka bir okulun benzer dersi olsun, paketlerimiz tam da o derse göre tasarlanır. Böylece nokta atışı çalışır, zaman kazanırsın.
Sınava özel videolar —konu anlatımları, çıkmış sorular ve çözümleri, özet notlar—içerir. Sınavda sıkça çıkan soruları hedefler. Eğitmenlerimiz, üniversitenin akademik takvimini takip ederek paketleri sürekli günceller. Böylece, gereksiz detaylarla vakit kaybetmeden başarını artırmaya odaklanabilirsin.
Ders İçeriği
Number Theory
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
GCD Greatest Common Divisor
LCM Least Commun Multiple
Euclidian Algorithm
Example 1
Bézout Identity
Example 1
Example 2
Example 3
Inverse of a Number in Modular Arithmetic
Fermat's Little Theorem
Solving Linear Congruences
Example 1
Example 2
Chinese Remainder Theorem
Example 1
Example 2
Example 3
Example 4
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
Recursion
Introduction
Recursively Defined Functions
Example 1
Recursively Defined Sets
Example 2
Recursively Defined Strings
Example 3
Structural Induction
Example 4
Example 5
Sample Final Problems I
Number Theory 1
Number Theory 2
Number Theory 3
Number Theory 4
Number Theory 5
Number Theory 6
Number Theory 7
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
Recursion and Induction
Recursive Algorithm
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
Discrete Probability: Part 1
Sample Space and Events
Probability
Axioms of Probability
Some Rules
Coin Example
Dice Example
Card Example 1
Card Example 2
Ball Example
Set Example
Birthday Example
Discrete Probability: Part 2
Conditioning Events
Total Probability Rule
Example 1
Example 2
Example 3
Bayes' Rule
Bayes' Rule Example 1
Bayes' Rule Example 2
Independence
Independence Example 1
Independence Example 2
Sample Final Problems I
Counting 1
Counting 2
Counting 3
Counting 4
Counting 5
Counting 6
Discrete Probability 1
Discrete Probability 2
Discrete Probability 3
Discrete Probability 4
Discrete Probability 5
Conditional Probability and Independence 1
Conditional Probability and Independence 2
Bayes' Rule 1
Bayes' Rule 2
Discrete Random Variables 1
Discrete Random Variables 2
Advanced Counting Techniques
Principle Inclusion-Exclusion
Example
Distributing Objects into Boxes 1
Distributing Objects into Boxes 2
Example 1
Example 2
Example 3
Pigeonhole Principle
Example 1
Example 2
Example 3
Generating Functions
Example 1
Example 2
Extended Binomial Theorem
Counting Problems with Generating Functions
Example 1
Example 2
Recurrence Relations
Homogenous Recurrence Relations
Example 1
Example 2
Non Homogenous Recurrence Relations
Example 3
Example 4
Creating Recurrence Relations
Example 5
Example 6
Relations
Definition of Relation
Example 1
Example 2
Reflexive Relations
Example 3
Example 4
Symmetric Relations
Antisymmetric Relations
Example 5
Transitive Relations
Example 6
Properties of Relations
Example 7
Example 8
Composition of Relations
Equivalence Relation
Example 9
Sample Final Problems II
Principle Inclusion Exclusion 1
Principle Inclusion Exclusion 2
Distributing Objects into Boxes 1
Distributing Objects into Boxes 2
Pigeonhole Principle 1
Pigeonhole Principle 2
Pigeonhole Principle 3
Pigeonhole Principle 4
Recurrence Relations 1
Recurrence Relations 2
Recurrence Relations 3
Recurrence Relations 4
Recurrence Relations 5
Recurrence Relations 6
Generating Functions 1
Generating Functions 2
Generating Functions 3
Properties of Relation
Properties of Relation
Equivalence Relation 1
Equivalence Relation 2
Equivalence Relation 3
Graph Theory Part 1
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
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
Introduction
Rooted Tree
Terminology for Rooted Trees
Full m-ary Trees
Some Formulas
Sample Final Problems III
Adjacency Matrices
Incidence Matrices
Bipartite Graphs & Euler Circuits
Euler Path, Induced Subgraph & Incidence Matrix
Isomorphism 1
Isomorphism 2
Isomorphism 3
Isomorphism 4
Isomorphism 5
Unicourse Garantisi kapsamında