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Information
| Code | CEN130 |
| Name | Discrete Mathematics |
| Term | 2024-2025 Academic Year |
| 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 Instructor |
1 2 |
Course Goal / Objective
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 |
| LO04 | Interprets problems with the pigeonhole principle |
| LO05 | Interprets simple classification problems using probability and Bayes' Theorem |
| LO06 | Represents problems with graphs |
| LO07 | Solves problems with graph algorithms |
| LO08 | Represents problems with trees |
| LO09 | Solves problems with tree algorithms |
| LO10 | Interprets language problems with Finite State Machines |
| LO11 | Interprets language problems with Context Free Grammar |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Adequate knowledge of mathematics, science and related engineering disciplines; ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Ability to identify, formulate and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. | 2 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice; ability to use information technologies effectively. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to design and conduct experiments, collect data, analyze and interpret results to investigate complex engineering problems or discipline-specific research topics. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Ability to work effectively in interdisciplinary and multidisciplinary teams; individual working skills. | 1 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Ability to communicate effectively verbally and in writing; knowledge of at least one foreign language; ability to write effective reports and understand written reports, prepare design and production reports, make effective presentations, and give and receive clear and understandable instructions. | 1 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology, and constantly renew oneself. | 1 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Knowledge of ethical principles, professional and ethical responsibility, and standards used in engineering practice. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Knowledge of the effects of engineering practices on health, environment and safety in universal and social dimensions and the problems of the age reflected in the field of engineering; awareness of the legal consequences of engineering solutions. |
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 | ||