Faculty: Faculty of Engineering

Department(s): CE

Course: Discrete Mathematics

Weekly hours: Theory: 2 Exercises: 1

ECTS Credits: 6

Semester: Fall

Lecture schedule:

Lecturer: Dr. Hiqmet Kamberaj

Room Number: 409

Phone Number of the lecturer: +389 (0)23174010 (ext. 123)

E-mail address of the lecturer: km.ude.ubi|jarebmakh#km.ude.ubi|jarebmakh

**Course objectives**

The main purpose of the course is to help the students grow in mathematical maturity, and in particular towards an understanding of the basic concepts of discrete mathematics. We will present the underlying foundations of discrete mathematics to develop the ability of the students to think in a more mathematical way, to show how these mathematical concepts can be applied and to encourage the students to apply these skills and knowledge. Final message taken home would be that mathematics exists to make our life easier and one could benefit greatly from its application in the area such as informatics where in particular the discrete mathematics is needed.

**Course Textbook:**

**Main Material (Prepared based on the provided additional materials):**

- H. Kamberaj, Lecture notes on Discrete Mathematics, International Balkan University, 2015.

**Additional Materials:**

- The essence of computing and essence of discrete mathematics by Neville Dean, Prentice Hall, 1997.
- 2000 Solved problems in discrete mathematics by Seymour Libschutz and Mark Lars Lipson, McGraw Hill, 1992.
- Discrete Mathematics and Its Applications by Kenneth Rosen, Sixth Edition, McGraw Hill Higher Education, 2007.

**Attendance:**

- Students are obliged to attend at least 72 % out of 12 weeks of lectures, exercises, and other activities.
- The teaching staff should monitor and submit Course Attendance Report to the Student Affairs Office at the end of 14th week of each semester.
- The attendance rule for failed overlapping courses is 36 % out of 12 weeks of lectures, exercises, and other activities.
- The attendance rule for course from upper semester is 57% out of 12 weeks of lectures, exercises, and other activities.
- Students are not obliged to attend the course if the course is double repeated. However, they need to register the course.

**Exams (Mid-Term Exam, Final Exam, Make-up Exam):**

There are two exams, the Mid-Term and Final Exam, at the middle and at the end of the semester, respectively. The students, who do not earn minimum 50 credit points from the Mid-Term, Final Exam including Homework Assignments, have to take the Make-Up Exam, which counts only for Final Exam credit points. The terms of the exams are defined by the Academic Calendar announced on the University web site.

**Passing Score:**

The maximum number of credit points is collected during the semester, as follows: Mid-term Exam = 40 Credit Points (minimum requirement is 25 % (midterm exam + activity) to enter Final Exam), Final Exam (minimum requirement is 25 % to pass) = 40 Credit Points. Homeworks, quizzes, specific assignments and term papers = 20 Credit Points (minimum requirement is 5 credit points to enter Final Exam). Total=100.

**Weekly Study Plan**

Weeks | Topics |
---|---|

1 | Introduction to the philosophy of this course. Propositional logic. |

2 | Propositional Equivalences. Predicates and Quantifiers. |

3 | Nested quantifiers. Rules of Inference. |

4 | Sets. |

5 | Functions. |

6 | Sequences and Sums. |

7 | Mid term Discussion. |

- | Mid Term Exam Week |

8 | Number Theory and matrices. |

9 | Mathematical Induction. |

10 | Recursive structures and algorithms. |

11 | Relations. |

12 | Equivalence Relations and Equivalence classes. |

13 | Graphs. |

14 | Final exam Discussion. |

- | Final exam week. |

**Teaching methods:**

Teaching methods | Ideal % |
---|---|

Teaching ex cathedra (teacher as the figure of authority, standing in front of the class and lecturing) | 70 |

Interactive teaching (ask questions in class, assign and check homework, or hold class or group discussions) | 20 |

Mentor teaching (consultant-teacher who has a supervisory responsibility and supervising the students) | - |

Laboratory work | - |

Seminar work | - |

Field Work (enables students to examine the theories and the practical experiences of a particular discipline interact) | - |

Semester project | - |

Case Study (An in-depth exploration of a particular context) | 5 |

Students Team work | 5 |

**Student workload:**

For calculating the Total Student Work Load we multiply the course ECTS credits with standard figure 30. (ECTS Credit: 6) x 30 = 180 hours.

Activities | Hours |
---|---|

Lecture hours for 14 weeks: | 28 |

Laboratory and class exercises for 14 weeks: | 14 |

Student Mentoring for 14 weeks: | - |

Consultation for 14 weeks: | 5 |

Exam preparations and exam hours (Midterm, final, Makeups): | 30 |

Individual reading work for 14 weeks (Reading assignments/expectations for reading and comprehension is 5 pages per hour. Example: If a book 300 pages, total Individual reading work for 14 weeks 300:5 = 60 hours. | 40 |

Homework and work practice for 14 weeks: | 63 |

Preparation of diploma work, for 14 weeks: | - |