MATH 132 • Final • Discrete 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.
Paketi Tamamla
🎓 Bilkent Üniversitesinde öğrencilerin %92'si tüm paketi alarak çalışıyor.
Konular
Recurrence Relations
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
Principle Inclusion - Exclusion
Principle Inclusion-Exclusion
Example 1
Example 2
Exam like Question 1
Generating Functions
Definition
Example 1
Example 2
Example 3
Example 4
Extended Binomial Theorem
Counting Problems with Generating Functions
Example 5
Example 6
Example 7
Relations Part I
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
Example 13
Example 14
Composition of Relations
Example 15
Example 16
Combining Relations
Inverse and Complementary of a Relation
Example 17
Matrix Representation of Relation: Part 1
Matrix Representation of Relation: Part 2
Example 18
Operations on Zero - One Matrices
Example 19
Equivalence Relation
Example 22
Example 23
Example 24
Example 25
Example 26
Example 27
Example 28
Example 29
Example 30
Exam like Question 1
Relations Part II
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
Past Exam Questions
Recurrence Relations 1
Recurrence Relations 2
Recurrence Relations 3
Recurrence Relation & Advanced Counting Techniques
Principle Inclusion Exclusion 1
Principle Inclusion Exclusion 2
Principle Inclusion Exclusion 3
Principle Inclusion Exclusion 4
Principle Inclusion Exclusion 5
Relations 1
Relations 2
Relations 3
Relations 4
Relations 5
Relations 6
Relations 7
Relations 8
Relations 9
Relations 10
Generating Functions
Generating Functions
Spring 2023 Final Problems
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Spring 2024 Final Problems
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Spring 2025 Final Problems
Relations
Relations
Relations
Relations
Counting & Derangement
Counting & Derangement
Değerlendirmeler
Ders İçeriği
Recurrence Relations
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
Principle Inclusion - Exclusion
Principle Inclusion-Exclusion
Example 1
Example 2
Exam like Question 1
Generating Functions
Definition
Example 1
Example 2
Example 3
Example 4
Extended Binomial Theorem
Counting Problems with Generating Functions
Example 5
Example 6
Example 7
Relations Part I
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
Example 13
Example 14
Composition of Relations
Example 15
Example 16
Combining Relations
Inverse and Complementary of a Relation
Example 17
Matrix Representation of Relation: Part 1
Matrix Representation of Relation: Part 2
Example 18
Operations on Zero - One Matrices
Example 19
Equivalence Relation
Example 22
Example 23
Example 24
Example 25
Example 26
Example 27
Example 28
Example 29
Example 30
Exam like Question 1
Relations Part II
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
Past Exam Questions
Recurrence Relations 1
Recurrence Relations 2
Recurrence Relations 3
Recurrence Relation & Advanced Counting Techniques
Principle Inclusion Exclusion 1
Principle Inclusion Exclusion 2
Principle Inclusion Exclusion 3
Principle Inclusion Exclusion 4
Principle Inclusion Exclusion 5
Relations 1
Relations 2
Relations 3
Relations 4
Relations 5
Relations 6
Relations 7
Relations 8
Relations 9
Relations 10
Generating Functions
Generating Functions
Spring 2023 Final Problems
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Spring 2024 Final Problems
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Spring 2025 Final Problems
Relations
Relations
Relations
Relations
Counting & Derangement
Counting & Derangement
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.