Course Title : Discrete Mathematics
Code		Course Type	Regular Semester	Lecture (hours/week)	Seminar (hours/week)	Lab (hours/week)	Credits	ECTS
CMP 130-1		B	2	3	1	0	3.50	5
Lecturer and Office Hours
Teaching Assistant and Office Hours
Language				Albanian
Course Level
Description
Objectives
Course Outline
Week	Topics
1	Elements of mathematical logics: Propositional logics and connectives. Propositional Equivalences. Applications of propositional logics.
2	Predicates and quantifiers. Rules of Interference. Proof methods and strategy.
3	Sets. Sequences and recurrence relations.
4	Number Theory: Divisibility and modular arithmetic. Prime numbers, greatest common divisor and least common multiple.The Euclidian Algorithm and Bezout identity.
5	Solving congruences. Applications of congruences.
6	Mathematical induction, strong induction and well-ordering.
7	Recursive definitions and structural induction. Recursive algorithms.
8	Midterm exam
9	Counting, the basic of counting. The Pigeonhole principle. Permutations and combinations. Binomial coefficients and identities.
10	Advanced counting techniques. Applications of recurrence relations. Solving linear recurrence relations.
11	Relations and their properties. Representing relations. Equivalence relations, partial orderings.
12	Introduction to graph theory. Graphs models. Special types of graphs
13	Representing graphs and graphs isomorphism. Connectivity. Euler and Hamilton paths.
14	Shortest path problems. Planar graphs and graph coloring.
15	Trees and their applications.
16	Final Exam
Prerequisites
Textbook
Other References
Laboratory Work
Computer Usage
Other
Learning Outcomes and Competences
1	Theoretical and practical training, sufficient for a successful and skillful profession of basic scientific knowledge in student practice.
2	Skills and professional training in description, formulation, modeling and problem analysis, with consideration for appropriate analytical solutions in all necessary situations.
3	Required techincal, academic and practical knowledge and confidence design and evaluation of mechanical systems with consideration for productivity, feasibility, and social and environmental aspects.
4	Ability to design and run experiments, gather data, analyze and draw conclusions
Course Evaluation Methods
In-term studies						Quantity	Percentage
Midterms						1	40
Quizzes						0	0
Projects						1	10
Term Projects						0	0
Laboratory						0	0
Attendance						1	10
Contribution of in-term studies to overall grade							60
Contribution of final examination to overall grade							40
Total							100
ECTS (Allocated Based on Student) Workload
Activities					Quantity	Duration (hours)	Total Workload (hours)
Course Duration (Including the exam week : 16 x Total course hours)					16	4	64
Hours for off-the-classroom study (Pre-study, practice)					14	3	42
Assignments					1	0	0
Midterms					1	9	9
Final examination					1	10	10
Other					0	0	0
Total Work Load							125
Total Work Load / 25 (hours)							5
ECTS							5

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