MATHEMATICS
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT2033	Discrete Mathematics	Fall	3	0	3	6

Basic information

Language of instruction:	English
Type of course:	Must Course
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :	Assist. Prof. NERMINE AHMED EL SISSI
Course Lecturer(s):	Prof. Dr. NAFİZ ARICA
Recommended Optional Program Components:	None
Course Objectives:	The main course objective is to introduce basic ideas of discrete mathematics such as formal mathematical reasoning techniques, relations, graphs and a basic introduction to number theory. The course trains students to develop their analytical and critical thinking abilities through the following important topics: mathematical reasoning, discrete structure, and algorithmic thinking. The successful students will be able to demonstrate their ability to apply these to practical problems, and to communicate their knowledge of these areas.

Learning Outcomes

The students who have succeeded in this course;
1. Use and apply basic definitions and properties of logic.
2. Construct valid proofs using different proof techniques.
3. Understand the basic principles of sets and apply operations on sets.
4. Identify functions and determine their properties.
5. Determine properties of relations, identify equivalence and partial order relations.
6. Demonstrate an understanding of the basic properties of graphs.
7. Apply given definitions and theorems to solve problems and prove statements in elementary number theory.

Course Content

Mathematical logic, induction, set theory, relations, functions, graphs, elementary number theory and its application to cryptography

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Propositional Logic Applications of Propositional Logic	Read sections 1.1 and 1.2
2)	Propositional Equivalences	Read section 1.3
3)	Predicates and Quantifiers	Read sections 1.4 and 1.5
4)	Rules of inference, introduction to proofs, proof methods and strategy	Read sections 1.6, 1.7, and 1.8
5)	Mathematical induction and strong mathematical induction and Well-Ordering principle	Read sections 5.1 and 5.2
6)	Sets and Set Operations	Read sections 2.1 and 2.2
7)	Midterm Review	Complete the review problems worksheet.
8)	Functions	Read section 2.3
9)	Divisibility and modular arithmetic, primes and greatest common divisors	Read sections 4.1 and 4.3
10)	Primes and greatest common divisors, cryptography	Read sections 4.3 and 4.6
11)	Relations and Their Properties, n-ary relations and their applications	Read sections 9.1 and 9.2
12)	Equivalence relations, partial orderings	Read sections 9.5 and 9.6
12)	Primes, Greatest Common Divisors, and Cryptography \ review.
13)	Graphs and graph models, graph terminology and special types of graphs	Read sections 10.1 and 10.2
14)	Final Exam Review	Complete the review problems worksheet

Sources

Course Notes / Textbooks:	- Discrete Mathematics and its Applications, Kenneth H. Rosen, McGraw-Hill Publishing Company.
References:	- Elements of Discrete Mathematics, C. L. Liu, McGraw-Hill Publishing Company. - Discrete and Combinatorial Mathematics, R. P. Grimaldi, Addison-Wesley Publishing Company.

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Midterms	2	% 60
Final	1	% 40
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 60
PERCENTAGE OF FINAL WORK		% 40
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	7	98
Midterms	2	2	4
Final	1	2	2
Total Workload			146

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

Program Outcomes

Level of Contribution