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
WeekTopics
1Elements of mathematical logics: Propositional logics and connectives. Propositional Equivalences. Applications of propositional logics.
2Predicates and quantifiers. Rules of Interference. Proof methods and strategy.
3Sets. Sequences and recurrence relations.
4Number Theory: Divisibility and modular arithmetic. Prime numbers, greatest common divisor and least common multiple.The Euclidian Algorithm and Bezout identity.
5Solving congruences. Applications of congruences.
6Mathematical induction, strong induction and well-ordering.
7Recursive definitions and structural induction. Recursive algorithms.
8Midterm exam
9Counting, the basic of counting. The Pigeonhole principle. Permutations and combinations. Binomial coefficients and identities.
10Advanced counting techniques. Applications of recurrence relations. Solving linear recurrence relations.
11Relations and their properties. Representing relations. Equivalence relations, partial orderings.
12Introduction to graph theory. Graphs models. Special types of graphs
13Representing graphs and graphs isomorphism. Connectivity. Euler and Hamilton paths.
14Shortest path problems. Planar graphs and graph coloring.
15Trees and their applications.
16Final Exam
Prerequisites
Textbook
Other References
Laboratory Work
Computer Usage
Other
Learning Outcomes and Competences
1Theoretical and practical training, sufficient for a successful and skillful profession of basic scientific knowledge in student practice.
2Skills and professional training in description, formulation, modeling and problem analysis, with consideration for appropriate analytical solutions in all necessary situations.
3Required techincal, academic and practical knowledge and confidence design and evaluation of mechanical systems with consideration for productivity, feasibility, and social and environmental aspects.
4Ability to design and run experiments, gather data, analyze and draw conclusions
Course Evaluation Methods
In-term studies Quantity Percentage
Midterms140
Quizzes00
Projects110
Term Projects00
Laboratory00
Attendance110
Contribution of in-term studies to overall grade60
Contribution of final examination to overall grade40
Total100
ECTS (Allocated Based on Student) Workload
Activities Quantity Duration
(hours)
Total Workload
(hours)
Course Duration (Including the exam week : 16 x Total course hours) 16464
Hours for off-the-classroom study (Pre-study, practice) 14342
Assignments 100
Midterms 199
Final examination 11010
Other 000
Total Work Load 125
Total Work Load / 25 (hours) 5
ECTS 5

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