
Course Title : Discrete Mathematics | ||||||||
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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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