COURSE INFORMATION Course Title: DISCRETE MATHEMATICS

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
MTH 106	B	99	3	0	0	3	5

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	Dr. Shkëlqim Hajrulla shhajrulla@epoka.edu.al
Main Course Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Dr. Shkëlqim Hajrulla shhajrulla@epoka.edu.al
Second Course Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Study program: (the study for which this course is offered)	Bachelor in Software Engineering (3 years)
Classroom and Meeting Time:
Teaching Assistant(s) and Office Hours:	NA
Code of Ethics:	Code of Ethics of EPOKA University Regulation of EPOKA University "On Student Discipline"
Attendance Requirement:	N/A
Course Description:	To equip Computer Science students with the necessary mathematical background in enumeration, relations, logic and elements of graph theory. Sets and propositions: Finite and infinite sets, mathematical induction, propositions. Permutations, combinations and discrete probability. Relations and functions: binary, equivalence relations, partitions, partial ordering, functions. Graphs: weighted graphs, paths and circuits, shortest paths. Eulerian and Hamiltonian paths. Trees. Abstract algebra: groups, cosets, Lagrange's theorem, Boolean algebra.
Course Objectives:	The objective of this course is to provide the fundamental principles of discrete mathematics and its applications. Students are introduced to basics of logic and proof methods, mathematical induction, counting techniques, recurrence relations and graph theory. Students see extensive practical applications especially in the topics of inference rules, counting and graph theory.

BASIC CONCEPTS OF THE COURSE

1	Concepts on algebra, sets, relations, and functions.
2	Logic chapter Inductive arguments and various recursive relations.
3	The ways of proofs.
4	Sequences, Arithm and geom sequences
5	Mathematical induction
6	Recursive sequences
7	Combinatoric chapter. Permutations, combinations
8	Binomial Coefficients
9	Discrete probability
10	binary trees, and tree traversal algorithms.

COURSE OUTLINE

Week	Topics
1	General introduction. Propositional logic. Equivalences.
2	Congruence. LCM(Least common multiplies) and gcd(great common divisors) Predicates and quantifiers
3	Set Theory. Inference rules. Sequences, series.
4	Mathematical reasoning. Mathematical induction. Applications of mathematical induction.
5	Counting. Product and sum rules. Principle of inclusion-exclusion.
6	Pigeonhole principle.Permutations & combinations.Binomial coefficients
7	Combinations with repetition. Summary 1
8	Midterm exam.
9	Probability, discrete probability. Examples
10	Discrete Probability distribution. Graphics and Examples
11	Advanced counting techniques. Solving recurrence relations.
12	Examples with recurrence relations. Graph connectivity. Graph isomorphism.
13	Trees. Their applications. Tree traversals. Polish notation.
14	(Overview). General review. Summary 2 and summary 3.

Prerequisite(s):
Textbook(s):	“Discrete mathematics and its applications”, 7th edition, Kenneth Rosen
Additional Literature:
Laboratory Work:
Computer Usage:
Others:	No

COURSE LEARNING OUTCOMES

1	To analyze and solve problems involving logic, boolean algebra, sets, relations, and functions.
2	To be able to construct inductive arguments. To solve various recursive relations.
3	To enumerate combinatorial objects using permutations, combinations and the counting principles.
4	Analyze and solve problems involving trees, spanning trees, rooted trees, binary trees, and tree traversal algorithms.
5	Explain and solve problems involving graphs, paths, circuits, graph coloring, directed graphs, spanning trees, minimal spanning trees, shortest path algorithms

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
Bachelor in Software Engineering (3 years) Program
1	Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice.	5
2	Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations	5
3	Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects.	4
4	Engineering graduates with the practice of selecting and using appropriate technical and engineering tools in engineering problems, and ability of effective usage of information science technologies.	5
5	Ability of designing and conducting experiments, conduction data acquisition and analysis and making conclusions.	4
6	Ability of identifying the potential resources for information or knowledge regarding a given engineering issue.	3
7	The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence.	3
8	Ability for effective oral and official communication skills in foreign language.	4
9	Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology.	4
10	Engineering graduates with well-structured responsibilities in profession and ethics.	4
11	Engineering graduates who are aware of the importance of safety and healthiness in the project management, workshop environment as well as related legal issues.	2
12	Consciousness for the results and effects of engineering solutions on the society and universe, awareness for the developmental considerations with contemporary problems of humanity.	2

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	2	5
Midterm Exam(s)	1	35
Quiz	2	5
Final Exam	1	45
Other	1
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	16	3	48
Hours for off-the-classroom study (Pre-study, practice)	9	3	27
Mid-terms	1	15	15
Assignments	2	10	20
Final examination	1	15	15
Other			0
Total Work Load:			125
Total Work Load/25(h):			5
ECTS Credit of the Course:			5

CONCLUDING REMARKS BY THE COURSE LECTURER

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