Discrete Computational Structures

Faculty: Faculty of Engineering
Department(s): IT
Course: Discrete Computational Structures
Weekly hours: Theory: 2 Exercises: 3
ECTS Credits: 6
Semester: Spring


Lecture schedule -

Monday (Lecture - Avtocomanda, Classroom 405) : 08:15 - 10:00
Monday (Exercises - Avtocomanda, Classroom 405) : 10:15 - 13:00


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:

  1. Understand mathematical reasoning in order to read, comprehend, and construct mathematical arguments.
  2. Work with discrete structures, which are the abstract mathematical structures used to represent discrete objects and relationships between these objects.
  3. Construct algorithms and to implement them in a computer program.
  4. 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:

  1. Discrete Mathematics and Its Applications by Kenneth Rosen, Sixth Edition, McGraw Hill Higher Education, 2007.
  2. The essence of computing and essence of discrete mathematics by Neville Dean, Prentice Hall, 1997.
  3. 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 10 weeks out of 14 weeks of lectures, exercises, and other activities (72%).
  • 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 (5 weeks) and for non-overlapping courses is 57% (8 weeks);
  • The attendance rule for course from upper semester is 57% (8 weeks).
  • Students are not obliged to attend the course if the course is double repeated. However, they need to register and to pay repeated 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 (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 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: -
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