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Information
| Code | CEN130 |
| Name | Discrete Mathematics |
| Semester | 2. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. UMUT ORHAN |
Course Goal
In this course, the mathematical foundations related to computer sciences like formal logic, set theory, mathematical induction, methods of counting, discrete probability, elementary graph theory are discussed.
Course Content
Logic, Sets, Function, Algorithm Complexity, Modular Arithmetic, Sequences and Strings, Recurrence Relations, Combinatorics, Probability and Bayes Theorem, Graph Theory, Trees, Finite-State Machine and Automata, Context Free Language and Grammar
Course Precondition
none
Resources
Notes on Discrete Mathematics, M. A. Lerma, Northwestern University
Notes
Discrete Mathematical Structures: Theory and Applications, D.S. Malik and M.K. Sen, Thomson.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Solves a problem using rules of logical inference |
| LO02 | Interprets partially ordered sets using Hasse diagram |
| LO03 | Encrypts a message with RSA method using modular arithmetic |
| LO04 | Interprets complexity in problems solved by combinatorial trials |
| LO05 | Interprets problems with the pigeonhole principle |
| LO06 | Interprets simple classification problems using probability and Bayes' Theorem |
| LO07 | Solves problems by representing them with graphs |
| LO08 | Solves tree data structure by applying it to problems |
| LO09 | Interprets language problems with Finite State Machines and Context Free Grammar |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has capability in the fields of mathematics, science and computer that form the foundations of engineering | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Identifies, formulates, and solves engineering problems, selects and applies appropriate analytical methods and modeling techniques, | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Analyzes a system, its component, or process and designs under realistic constraints to meet the desired requirements,gains the ability to apply the methods of modern design accordingly. | 2 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Ability to use modern techniques and tools necessary for engineering practice and information technologies effectively. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to design and to conduct experiments, to collect data, to analyze and to interpret results | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Has ability to work effectively as an individual and in multi-disciplinary teams, take sresponsibility and builds self-confidence | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Can access information,gains the ability to do resource research and uses information resources | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Awareness of the requirement of lifelong learning, to follow developments in science and technology and continuous self-renewal ability | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Ability to communicate effectively orally and in writing, and to read and understand technical publications in at least one foreign language | |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Professional and ethical responsibility, | |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Awareness about project management, workplace practices, employee health, environmental and occupational safety, and the legal implications of engineering applications, | |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | Becomes aware of universal and social effects of engineering solutions and applications, entrepreneurship and innovation, and knowledge of contemporary issues |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Logic and Proofs, Propositions | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 2 | Sets, Function-Relation | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 3 | Algorithm Complexity, Modular Arithmetic, RSA | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 4 | Sequences, Strings, Induction, Recurrence Relations | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 5 | Combinatorics, The Pigeonhole Principle, Probability and Bayes Theorem | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 6 | Introduction to Graph Theory, Representations of Graphs | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 7 | Paths and Circuits in Graphs | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Midterm exam | Study to lecture notes and apllications | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Graph Algorithms | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 10 | Trees, Binary Trees | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 11 | Decision Trees, Game Trees | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 12 | Spanning Tree Algorithms | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 13 | Finite-State Machine and Automata | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 14 | Context Free Language an Grammar | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 15 | Review for Final exam | Reading related chapter in lecture notes | Öğretim Yöntemleri: Anlatım |
| 16 | Final Exam | Study to lecture notes and apllications | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Final Exam | Study to lecture notes and apllications | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||