Faculty: Faculty of Engineering

Department(s): IT

Course: Discrete Computational Structures

Weekly hours: Theory: 2 Exercises: 3

ECTS Credits: 6

Semester: Spring

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 aim of this course is to learn a set of mathematical facts and to

apply them; and more importantly to teach the students how to think logically and mathematically. To achieve these goals, this course stresses mathematical reasoning and the different ways problems are solved.

**Learning Outcomes:**

After completing this course, students will be able to:

- Understand mathematical reasoning in order to read, comprehend, and construct mathematical arguments.
- Work with discrete structures, which are the abstract mathematical structures used to represent discrete objects and relationships between these objects.
- Construct algorithms and to implement them in a computer program.
- Learn about the applications of discrete mathematics in different areas of studies.

Skill outcomes | Necessary ( + ) Not Necessary ( –) |
---|---|

Written communication skills | + |

Oral communication skills | + |

Computer skills | + |

Working in laboratory | - |

Working team | + |

Preparing projects | + |

Knowledge of foreign language | + |

Scientific and professional literature analysis | + |

Problem solving skills | + |

Management skills | + |

Presentation skills | + |

**Course Textbooks:**

- Discrete Mathematics and Its Applications by Kenneth Rosen, Sixth Edition, McGraw Hill Higher Education, 2007.
- 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.

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

Teaching ex cathedra (teacher as the figure of authority, standing in front of the class and lecturing) | 80 |

Interactive teaching (ask questions in class, assign and check homework, or hold class or group discussions) | 10 |

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 | 5 |

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

Students Team work | 5 |

**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 10CPs - midterm + 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. 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 | Introduction Proofs. |

5 | Basic Structures: Functions. |

6 | Basic Structures: Sequences and Sums. |

7 | Mid term review - discussion - 2 CPs of activity. |

- | Mid Term Exam Week |

8 | Induction and Recursion: Mathematical induction and strong induction. |

9 | Induction and Recursion: Recursive definitions and structural induction. |

10 | Recursive algorithms. |

11 | Relations and their properties. |

12 | Representing relations and equivalence relations. |

13 | Graphs and Graph models. |

14 | Final exam review - discussion - 3 CPs of activity. |

- | Final exam week. |

**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: | 42 |

Student Mentoring for 14 weeks: | - |

Consultation for 14 weeks: | 4 |

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. | 50 |

Homework and work practice for 14 weeks: | 26 |

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