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 : Instructor MAHMOUD JAFARI SHAH BELAGHI
Course Lecturer(s): Prof. Dr. MURAT SARI
Prof. Dr. NAFİZ ARICA
Recommended Optional Program Components: None
Course Objectives: To provide the necessary background in discrete mathematical structures for students who would work which involves machine calculation. To teach basic algorithms on discrete structures.

Learning Outcomes

The students who have succeeded in this course;
1. Understand the basic principles of Logic.
2. Understand the basic principles of sets and operations in sets.
3. Understand methods of mathematical proofs, and be able to apply them in problem solving.
4. Demonstrate relations and determine their properties.
5. Demonstrate functions and determine when a function is 1-1 and "onto".
6. Understand some basic properties of number theory and mathematical cryptography.
7. Understand and use some basic properties of graphs.

Course Content

Mathematical logic, induction, set theory, relations, functions, graphs, number theory, and mathematical cryptography

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Propositional Logic
2) Propositional Equivalences
3) Predicates and Quantifiers
4) Rules of Inference
5) Proof Methods
6) Sets and Set Operations \ review.
7) Relations and Their Properties
8) Representing Relations and Closures of Relations
9) Equivalence Relations and Partial Orderings
10) Functions
11) Divisibility and Modular Arithmetic
12) Primes, Greatest Common Divisors, and Cryptography \ review.
13) Graphs and Graph Models
14) Graph Terminology and Special Types of Graphs

Sources

Course Notes / Textbooks: - Instructor's own lecture notes.
- 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.
- AND any textbook that covers given topics can be used.

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
1) To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics 5
2) To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods, 5
3) To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials, 5
4) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, 4
5) To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way, 4
6) To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level, 4
7) To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement, 4
8) To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, 4
9) By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere, 5
10) To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning, 4
11) To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school, 3
12) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. 4