Course Detail
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| DISCRETE MATHEMATICS | - | Spring Semester | 3+0 | 3 | 5 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Elective |
| Course Coordinator | Assist.Prof. Cihan Bilge KAYASANDIK |
| Name of Lecturer(s) | Assist.Prof. Cihan Bilge KAYASANDIK |
| Assistant(s) | Slides, Lecture Notes and Textbook |
| Aim | The course is aimed at equipping students with logical and mathematical thinking. The course is designed to accomplish five major themes: (i) Mathematical reasoning, (ii) combinatorial analysis, (iii) discrete structures, (iv) algorithmic thinking, (v) applications and modeling. |
| Course Content | This course contains; Fundamentals,Fundamentals of Logic ,Logic, Conditional Statements,Logic of Quantified Statements,Introduction to Number Theory, Direct Proof and Counterexample,Sequences, Mathematical Induction,Strong Induction, Recursion and Structural Induction,Introduction to Set theory,Functions,Cardinality applications to computability,Relation,Equivalence Relation and Modular Arithmetic,Basic Cryptography ,Basic Problems on Graphs and Tree representation,Applications of Graph theory. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| Determine an argument using logical notation and whether the argument is or not valid | 10, 12, 16, 9 | A, E |
| Execute proof writing and evaluation. | 10, 12, 16, 9 | A, E |
| Comprehend set fundamentals, operations, and validation of elementary set equalities. | 10, 12, 16, 9 | A, E |
| Comprehend the properties of functions, relationships between them, and introductory knowledge of graph theory and cryptology. | 10, 12, 16, 9 | A, E |
| Teaching Methods: | 10: Discussion Method, 12: Problem Solving Method, 16: Question - Answer Technique, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Fundamentals | Chapter |
| 2 | Fundamentals of Logic | Chapter 2.1 |
| 3 | Logic, Conditional Statements | Chapter 2.2, 2.3 |
| 4 | Logic of Quantified Statements | Chapter 3 |
| 5 | Introduction to Number Theory, Direct Proof and Counterexample | Chapter 4 |
| 6 | Sequences, Mathematical Induction | Chapter 5.1, 5.2 |
| 7 | Strong Induction, Recursion and Structural Induction | Chapter 5 |
| 8 | Introduction to Set theory | Chapter 6.1 |
| 8 | Functions | Chapter 7.1-7.3 |
| 9 | Cardinality applications to computability | Chapter 7.4 |
| 10 | Relation | Chapter 8.1, 8.2 |
| 11 | Equivalence Relation and Modular Arithmetic | Chapter 8.3, 8.4 |
| 12 | Basic Cryptography | Chapter 8.4 |
| 13 | Basic Problems on Graphs and Tree representation | Chapter 10.1-10.5 |
| 14 | Applications of Graph theory | Chapter 10.5, 10.7 |
| Resources |
| Discrete Mathematics and Its Applications, Kenneth H. Rosen, 7th edition, McGraw-Hill, 2012 |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||
| 2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||
| 3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | ||||||
| 4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | X | |||||
| 5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | ||||||
| 6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | ||||||
| 7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | ||||||
| 8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | X | |||||
| 9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | ||||||
| 10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||
| 11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 30 | |
| Rate of Final Exam to Success | 70 | |
| Total | 100 | |
| ECTS / Workload Table | ||||||
| Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||
| Course Hours | 14 | 3 | 42 | |||
| Guided Problem Solving | 0 | 0 | 0 | |||
| Resolution of Homework Problems and Submission as a Report | 0 | 0 | 0 | |||
| Term Project | 14 | 3 | 42 | |||
| Presentation of Project / Seminar | 0 | 0 | 0 | |||
| Quiz | 3 | 5 | 15 | |||
| Midterm Exam | 1 | 20 | 20 | |||
| General Exam | 1 | 30 | 30 | |||
| Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
| Total Workload(Hour) | 149 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(149/30) | 5 | |||||
| ECTS of the course: 30 hours of work is counted as 1 ECTS credit. | ||||||
Detail Informations of the Course
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| DISCRETE MATHEMATICS | - | Spring Semester | 3+0 | 3 | 5 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Elective |
| Course Coordinator | Assist.Prof. Cihan Bilge KAYASANDIK |
| Name of Lecturer(s) | Assist.Prof. Cihan Bilge KAYASANDIK |
| Assistant(s) | Slides, Lecture Notes and Textbook |
| Aim | The course is aimed at equipping students with logical and mathematical thinking. The course is designed to accomplish five major themes: (i) Mathematical reasoning, (ii) combinatorial analysis, (iii) discrete structures, (iv) algorithmic thinking, (v) applications and modeling. |
| Course Content | This course contains; Fundamentals,Fundamentals of Logic ,Logic, Conditional Statements,Logic of Quantified Statements,Introduction to Number Theory, Direct Proof and Counterexample,Sequences, Mathematical Induction,Strong Induction, Recursion and Structural Induction,Introduction to Set theory,Functions,Cardinality applications to computability,Relation,Equivalence Relation and Modular Arithmetic,Basic Cryptography ,Basic Problems on Graphs and Tree representation,Applications of Graph theory. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| Determine an argument using logical notation and whether the argument is or not valid | 10, 12, 16, 9 | A, E |
| Execute proof writing and evaluation. | 10, 12, 16, 9 | A, E |
| Comprehend set fundamentals, operations, and validation of elementary set equalities. | 10, 12, 16, 9 | A, E |
| Comprehend the properties of functions, relationships between them, and introductory knowledge of graph theory and cryptology. | 10, 12, 16, 9 | A, E |
| Teaching Methods: | 10: Discussion Method, 12: Problem Solving Method, 16: Question - Answer Technique, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Fundamentals | Chapter |
| 2 | Fundamentals of Logic | Chapter 2.1 |
| 3 | Logic, Conditional Statements | Chapter 2.2, 2.3 |
| 4 | Logic of Quantified Statements | Chapter 3 |
| 5 | Introduction to Number Theory, Direct Proof and Counterexample | Chapter 4 |
| 6 | Sequences, Mathematical Induction | Chapter 5.1, 5.2 |
| 7 | Strong Induction, Recursion and Structural Induction | Chapter 5 |
| 8 | Introduction to Set theory | Chapter 6.1 |
| 8 | Functions | Chapter 7.1-7.3 |
| 9 | Cardinality applications to computability | Chapter 7.4 |
| 10 | Relation | Chapter 8.1, 8.2 |
| 11 | Equivalence Relation and Modular Arithmetic | Chapter 8.3, 8.4 |
| 12 | Basic Cryptography | Chapter 8.4 |
| 13 | Basic Problems on Graphs and Tree representation | Chapter 10.1-10.5 |
| 14 | Applications of Graph theory | Chapter 10.5, 10.7 |
| Resources |
| Discrete Mathematics and Its Applications, Kenneth H. Rosen, 7th edition, McGraw-Hill, 2012 |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||
| 2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||
| 3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | ||||||
| 4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | X | |||||
| 5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | ||||||
| 6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | ||||||
| 7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | ||||||
| 8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | X | |||||
| 9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | ||||||
| 10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||
| 11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 30 | |
| Rate of Final Exam to Success | 70 | |
| Total | 100 | |