Dersin Adı Dersin Seviyesi Dersin Kodu Dersin Tipi Dersin Dönemi Yerel Kredi AKTS Kredisi Ders Bilgileri
DISCRETE STRUCTURES Birinci Düzey YZ 104 Zorunlu 2 3.00 3.00 Yazdır
   
Dersin Tanımı
Ön Koşul Dersleri
Eğitimin Dili English
Koordinatör DR. ÖĞR. ÜYESİ FATİH SARIKOÇ
Dersi Veren Öğretim Eleman(lar)ı Assist. Prof. Dr. Fatih SARIKOÇ
Yardımcı Öğretim Eleman(lar)ı
Dersin Veriliş Şekli Formal education
Dersin Amacı The aim of a discrete structures course is to equip students with the fundamental concepts and techniques of discrete mathematics, essential for computer science and mathematics. It focuses on developing logical reasoning and problem-solving skills through topics like predicate logic, sets, relations, functions, combinatorics, and algorithms. The course enables students to apply mathematical tools to solve real-world problems, such as modeling and algorithm analysis, and prepares them for advanced studies in areas like algorithms, data structures, and theory of computation.
Dersin Tanımı Discrete structure is a branch of mathematics that teaches basic data structures and methodologies for computer science.

Dersin İçeriği
1 Propositional Logic, Logical operators, Conditional and bi-conditional statements, De Morgan rules, negation of implication statements Converse, inverse and contrapositive implications, Deriving truth tables by use of logical operators.
2 Predicate Logic, Definitions of tautology and contradiction, Translating spoken language sentences into combined propositions Logical algebra rules and their use to simplify combined propositions, Proving logical equivalences by truth tables and logical algebra.
3 Propositional Logic and Predicate Logic Applications, Definition of propositional functions, Valid and non-valid propositional functions, Universal and Existential quantifiers, Nested quantifiers.
4 Proofs, Rules of Inference, definitions of arguments, premises, axioms, postulates, hypotheses, conclusion, logical rules of inference, theorem. Modus Ponens, Modus Tollens, Addition, Simplification, Conjunction, Hypothetical syllogism, Disjunctive syllogism, Resolution.
5 Sets, Set Operations, Functions.
6 Sequences.
7 Mathematical Induction.
8 Algorithms .
9 Growth of Functions, Complexity of Algorithms
10 Counting (Basics of Counting, Permutation and Combination)
11 Applications of Number Theory
12 Probability Theory
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Dersin Öğrenme Çıktıları
1 Ability to understand and apply propositional logic, predicate logic operations, prove logical equivalences by truth tables, and logical algebra.
2 Ability to learn and use proofs, rules of Inference, definitions of arguments, premises, axiom, postulate, hypothesis, conclusion, logical rule of inference, theorem.
3 Ability to learn and apply modus ponens, modus tollens, addition, simplification, conjunction, hypothetical syllogism, disjunctive syllogism, resolution rules.
4 Ability to understand and apply set and function operations, mathematical Induction.
5 Ability to learn and use the growth of functions, the complexity of algorithms.
6 Ability to understand and apply counting-related methods (counting, permutation, and combination).
7 Ability to understand and apply applications of number theory and encryption algorithms.
8 Ability to understand and apply Probability concepts and Bayes Theorem.
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*Dersin Program Yeterliliklerine Katkı Seviyesi
1 Applies engineering knowledge related to mathematics, science, basic engineering, and computer-based calculations to solve engineering problems.
2 Gains the ability to develop engineering solutions using discipline-specific knowledge and methods.
3 Defines complex engineering problems and formulates them using fundamental science and engineering knowledge.
4 Defines and analyzes solutions to problems, taking into account the UN Sustainable Development Goals.
5 Designs creative solutions to complex engineering problems.
6 Gains the ability to design complex systems, processes, devices, or products by considering realistic constraints in the engineering problem-solving process.
7 For the analysis and solution of complex engineering problems, selects and effectively applies appropriate methods, techniques, resources, and modern engineering and computing tools, including estimation and modeling.
8 Aware of the limitations of the methods, techniques, and IT tools used, it produces and implements appropriate solutions.
9 Conducts literature research to examine complex engineering problems and collects data within the scope of these studies.
10 Using research methods, the student designs and conducts experimental or applied studies, analyze and evaluate the results.
11 Within the scope of the UN Sustainable Development Goals, the student is knowledgeable about the impacts of engineering solutions on society, health and safety, the economy, sustainability, and the environment, and analyze these impacts.
12 Gains awareness of the legal consequences of engineering solutions.
13 The student acts in accordance with professional principles and legal regulations in engineering practice and acquires knowledge about ethical responsibilities.
14 Gains awareness about non-discrimination, impartiality, and inclusiveness of diversity.
15 Gains the ability to work effectively as an individual, team member, or team leader in intra-disciplinary or multi-disciplinary team projects.
16 Gains the ability to communicate effectively in technical matters, both verbally and in writing by taking into account the differences in the target audience''s education, language, and profession.
17 Gains the ability to apply project management principles, perform time and resource planning, and conduct economic feasibility analysis.
18 Gains awareness about entrepreneurship and innovation.
19 Gains the ability to adapt to new and emerging technologies and to evaluate technological changes with a questioning and critical perspective.
20 Gains the ability to independently and continuously learn new knowledge and skills.
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Yıldızların sayısı 1’den (en az) 5’e (en fazla) kadar katkı seviyesini ifade eder

Planlanan Öğretim Faaliyetleri, Öğretme Metodları ve AKTS İş Yükü
  Sayısı Süresi (saat) Sayı*Süre (saat)
Yüz yüze eğitim 14 3 42
Sınıf dışı ders çalışma süresi (ön çalışma, pekiştirme) 14 1 14
Ödevler 6 1 6
Sunum / Seminer hazırlama 0 0 0
Kısa sınavlar 0 0 0
Ara sınavlara hazırlık 1 4 4
Ara sınavlar 1 1 1
Proje (Yarıyıl ödevi) 14 1 14
Laboratuvar 0 0 0
Arazi çalışması 0 0 0
Yarıyıl sonu sınavına hazırlık 1 5 5
Yarıyıl sonu sınavı 1 1 1
Araştırma 0 0 0
Toplam iş yükü     87
AKTS     3.00

Değerlendirme yöntemleri ve kriterler
Yarıyıl içi değerlendirme Sayısı Katkı Yüzdesi
Ara sınav 2 100
Kısa sınav 0 0
Ödev 0 0
Yarıyıl içi toplam   100
Yarıyıl içi değerlendirmelerin başarıya katkı oranı   40
Yarıyıl sonu sınavının başarıya katkı oranı   60
Genel toplam   100

Önerilen Veya Zorunlu Okuma Materyalleri
Ders kitabı Kenneth H.Rosen, Discrete Mathematics and Its Applications, Mc.Graw Hill,1999.
Yardımcı Kaynaklar Kimberly Brehm, Discrete Math Youtube Videos https://www.youtube.com/watch?v=A3Ffwsnad0k&list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz

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