| School/Faculty/Institute | Faculty of Engineering | ||||
| Course Code | MATH 108 | ||||
| Course Title in English | Discrete and Combinatorial Mathematics | ||||
| Course Title in Turkish | Ayrık ve Kombinatorik Matematik | ||||
| Language of Instruction | EN | ||||
| Type of Course | Flipped Classroom | ||||
| Level of Course | Introductory | ||||
| Semester | Spring | ||||
| Contact Hours per Week |
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| Estimated Student Workload | 130 hours per semester | ||||
| Number of Credits | 5 ECTS | ||||
| Grading Mode | Standard Letter Grade | ||||
| Pre-requisites | None | ||||
| Expected Prior Knowledge | None | ||||
| Co-requisites | None | ||||
| Registration Restrictions | Only Undergraduate Students | ||||
| Overall Educational Objective | To learn and understand the foundations of mathematics of computer science, develop analytical and critical thinking abilities and deduce mathematical and logical proofs. | ||||
| Course Description | Topics to be covered include set theory, mathematical induction, relations and functions, basic counting and probability, recursion and recurrence relations, graph theory and trees and related algorithms, algorithm complexity, and modular arithmetic. | ||||
| Course Description in Turkish | Dersin konuları, kümeler kuramı, tümevarım, bağıntı ve fonksiyonlar, temel olasılık ve sayma kuramı, özyineleme ve özyinelemeli bağıntılar, çizge ve ağaç yapıları ve ilgili algoritmalar, algoritma analizi ve modüler aritmetik içermektedir. |
Course Learning Outcomes and CompetencesUpon successful completion of the course, the learner is expected to be able to:1) apply the basics of mathematical thinking, logic, sets, functions/relations, mathematical proofs and present simple proofs in a precise and formally correct way; 2) comprehend the basic concept of an algorithm and apply appropriate algorithms to solve problems in combinatorial mathematics; 3) demonstrate an understanding of the principle of recursion and recurrence relations and apply it to mathematical and algorithmic problems; 4) comprehend graph theory, trees and related algorithms; 5) apply counting and probability. |
| Program Learning Outcomes/Course Learning Outcomes | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| 1) Thorough knowledge of the major concepts, theoretical perspectives, empirical findings, and historical trends in psychology. | |||||
| 2) Understanding of and ability to apply essential research methods in psychology, including research design, data analysis, and data interpretation. | |||||
| 3) Competence to use critical and creative thinking, skeptical inquiry and a scientific approach to solving problems related to behavior and mental processes. | |||||
| 4) Understanding and ability to apply psychological principles, skills and values in personal, social, and organizational contexts. | |||||
| 5) Ability to weigh evidence, to tolerate ambiguity, and to reflect other values that underpin psychology as a discipline. | |||||
| 6) Internalization and dissemination of professional ethical standards. | |||||
| 7) Demonstration of competence in information technologies, and the ability to use computer and other technologies for purposes related to the pursuit of knowledge in psychology and the broader social sciences. | |||||
| 8) Skills to communicate the knowledge of psychological science effectively, in a variety of formats, in both Turkish and in English (in English, at least CEFR B2 level). | |||||
| 9) Recognition, understanding, and respect for the complexity of sociocultural and international diversity. | |||||
| 10) Recognition for the need for, and the skills to pursue, lifelong learning, inquiry, and self-improvement. | |||||
| 11) Ability to formulate critical hypotheses based on psychological theory and literature, and design studies to test those hypotheses. | |||||
| 12) Ability to acquire knowledge independently, and to plan one’s own learning. | |||||
| 13) Demonstration of advanced competence in the clarity and composition of written work and presentations. |
| N None | S Supportive | H Highly Related |
| Program Outcomes and Competences | Level | Assessed by | |
| 1) | Thorough knowledge of the major concepts, theoretical perspectives, empirical findings, and historical trends in psychology. | N | |
| 2) | Understanding of and ability to apply essential research methods in psychology, including research design, data analysis, and data interpretation. | N | |
| 3) | Competence to use critical and creative thinking, skeptical inquiry and a scientific approach to solving problems related to behavior and mental processes. | H | Exam,HW,Participation |
| 4) | Understanding and ability to apply psychological principles, skills and values in personal, social, and organizational contexts. | N | |
| 5) | Ability to weigh evidence, to tolerate ambiguity, and to reflect other values that underpin psychology as a discipline. | N | |
| 6) | Internalization and dissemination of professional ethical standards. | N | |
| 7) | Demonstration of competence in information technologies, and the ability to use computer and other technologies for purposes related to the pursuit of knowledge in psychology and the broader social sciences. | N | |
| 8) | Skills to communicate the knowledge of psychological science effectively, in a variety of formats, in both Turkish and in English (in English, at least CEFR B2 level). | N | |
| 9) | Recognition, understanding, and respect for the complexity of sociocultural and international diversity. | S | Participation |
| 10) | Recognition for the need for, and the skills to pursue, lifelong learning, inquiry, and self-improvement. | S | HW,Participation |
| 11) | Ability to formulate critical hypotheses based on psychological theory and literature, and design studies to test those hypotheses. | N | |
| 12) | Ability to acquire knowledge independently, and to plan one’s own learning. | S | Exam,HW |
| 13) | Demonstration of advanced competence in the clarity and composition of written work and presentations. | H | Exam,HW |
| Prepared by and Date | ŞENİZ DEMİR , November 2023 |
| Course Coordinator | ŞENİZ DEMİR |
| Semester | Spring |
| Name of Instructor | Öğr. Gör. CEM ERÖNCEL |
| Week | Subject |
| 1) | Foundations: Logic |
| 2) | Foundations: Quantifiers, Arguments |
| 3) | Introduction to proofs |
| 4) | Relations and Functions |
| 5) | Sequences and Summations |
| 6) | Algorithms: Basics |
| 7) | Algorithm Analysis |
| 8) | Number Theory: Modular Arithmetic, Prime Numbers |
| 9) | Number Theory: Fundamental Algorithms |
| 10) | Counting and Probability |
| 11) | Advanced Counting |
| 12) | Recursion and Induction |
| 13) | Recurrence Relations |
| 14) | Graph Theory and Trees |
| 15) | Final Exam/Project/Presentation |
| 16) | Final Exam/Project/Presentation |
| Required/Recommended Readings | Discrete Mathematics and Its Applications, Kenneth Rosen, 7th Edition, 2011 Supplementary Textbook: Discrete and Combinatorial Mathematics, R. P. Grimaldi, Addison-Wesley, 2004 | ||||||||||||
| Teaching Methods | Lecturing. Independent study for students | ||||||||||||
| Homework and Projects | Pre-class Practices, In-class Practices | ||||||||||||
| Laboratory Work | None | ||||||||||||
| Computer Use | Required | ||||||||||||
| Other Activities | Not required. | ||||||||||||
| Assessment Methods |
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| Course Administration |
demirse@mef.edu.tr 536 Assoc. Prof. Şeniz Demir Instructor’s office: 5th floor, Exams: Closed book and closed notes. Rules for attendance: YÖK regulations. Missing a midterm: You are expected to be present without exception and to plan any travel around these dates accordingly. Medical emergencies are of course excluded if accompanied by a doctor’s note. A note indicating that you were seen at the health center on the day of the midterm/quiz is not a sufficient documentation of medically excused absence from the midterm/quiz. The note must say that you were medically unable to take the midterm/quiz. Provided that proper documents of excuse are presented, a make-up for the missing midterm/quiz will be given. If you fail to take the midterm/quiz on the assigned day and do not have a valid excuse, you will be given zero (0) on the midterm/quiz. Employment interviews, employer events, weddings, vacations, etc. are not excused absences. Eligibility to take the final exam: No final exam. Missing a final: No final exam. A reminder of proper classroom behavior, code of student conduct: YÖK Regulations Statement on plagiarism: YÖK Regulations |
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| Activity | No/Weeks | Hours | Calculation | ||||
| No/Weeks per Semester | Preparing for the Activity | Spent in the Activity Itself | Completing the Activity Requirements | ||||
| Course Hours | 14 | 1 | 3 | 1 | 70 | ||
| Quiz(zes) | 8 | 1 | 1 | 16 | |||
| Midterm(s) | 2 | 20 | 2 | 44 | |||
| Total Workload | 130 | ||||||
| Total Workload/25 | 5.2 | ||||||
| ECTS | 5 | ||||||