Faculty: Faculty of Engineering

Department(s): CE

Course: Discrete Computational Structures

Weekly hours: Theory: 2 Exercises: 1

ECTS Credits: 5

Semester: Fall

Lecture schedule - Wednesday: 8:15 AM - 10:25 AM

Classroom - B-306 (Computer Lab)

Lecturer: Prof. Dr. Hiqmet Kamberaj

Room Number: rectorate building

Phone Number of the lecturer: 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) | 60 |

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) | 10 |

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 60% (based upon the new IBU regulations) 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 12th 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 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.

**Weekly Study Plan**

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. |

**Student workload:**

For calculating the Total Student Work Load we multiply the course ECTS credits with standard figure 30. (ECTS Credit: 5) x 30 = 150 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: | 24 |

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: | 20 |

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