Faculty: Faculty of Engineering

Department(s): CE

Number of Students:

Course: Discrete Mathematics

Weekly hours: Theory: 2 Exercises: 1

ECTS Credits: 6

Semester: Fall

Lecture schedule:

Wednesday: From 8:15 AM - 10:25 AM

Classroom: B306 (Computer Lab)

Lecturer: Dr. Hiqmet Kamberaj

Room Number:

Phone Number of the lecturer:

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 in 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 Lipschutz 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 60 % out of 12 weeks of lectures, exercises, and other activities.
- 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 the 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 four exams, the Mid-Term (weeks 1-6, 40 CPs Maximum), Final Exam (weeks 7-12, 40 CPs Maximum), Make-up exam (weeks 1-12, 80 CPs Maximum), and Penalty Session Exam (Weeks 1-12, 100 CPs Maximum). For the Midterm and Final Exams there is a criterion of at least 10 CPs to pass the exam. 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 10CPs to enter Final Exam), Final Exam (minimum requirement is 10 CPs to pass the exam) = 40 Credit Points. Homeworks, quizzes, specific assignments and term papers = 20 Credit Points. Total=100.

**Study Plan** —- International Balkan University - Academic Calendar

Weeks | ~ Lecture | ~ Topics |
---|---|---|

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

2 | 2 | Propositional Equivalences. Predicates and Quantifiers. |

3 | 3 | Nested quantifiers. Introduction Proofs and Rules of Inference (Part I). |

4 | 4 | Introduction Proofs (Part II). Sets. |

5 | 5 | Basic Structures: Functions. |

6 | 6 | Midterm review - discussion. |

7 | - | Mid Term Exam Week |

8 | 7 | Basic Structures: Sequences and Sums. |

9 | 8 | Induction and Recursion: Mathematical induction and strong induction; structural induction. |

10 | 9 | Recursive algorithms. |

11 | 10 | Relations and their properties. Representing relations and equivalence relations. |

12 | 11 | Graphs and Graph models. |

13 | - | Winter break. |

14 | 12 | Final exam review - discussion. |

15 | - | Final exam week. |

16 | - | Make up 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 12 weeks: | 24 |

Laboratory and class exercises for 12 weeks: | 12 |

Student Mentoring for 12 weeks: | - |

Consultation for 12 weeks: | 12 |

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

Individual reading work for 12 weeks (Reading assignments/expectations for reading and comprehension is 5 pages per hour. Example: If a book 300 pages, total Individual reading work for 12 weeks 300:5 = 60 hours. | 40 |

Homework and work practice for 12 weeks: | 62 |

Preparation of diploma work, for 12 weeks: | - |