Industrial and Systems Engineering (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH111

Course Name:

Discrete Mathematics

Semester:

Fall

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Dr. Öğr. Üy. FUNDA ÖZDEMİR

Course Lecturer(s):

Assist. Prof. Dr. FUNDA ÖZDEMIR

Course Assistants:

Course Objective and Content

Course Objectives:

The course aims to introduce discrete mathematical structures suh as formal mathematical reasoning techniques, algorithm formulation, computation of time complexity, basic counting techniques, relations, graphs and trees. The course aims to acquire the necessary mathematical background for areas that require computation such as computer science and to apply the acquired skills to practical problems.

Course Content:

The content of the course consists of logic, proof methods, sets, functions, sequences, sums, algorithms, growth of functions, complexity of algorithms, elementary number theory, cryptography, counting, solving recurrence relations, relations, graphs and trees.

Learning Outcomes

The students who have succeeded in this course;
1) Gains the ability to express mathematical arguments and natural language sentences through the language of symbolic logic; decides whether a given argument is valid or not using logic and inference rules and makes simple mathematical proofs.
2) Describes computer programs in a formal mathematical manner by means of pseudocodes and analyzes algorithms in terms of time complexity.
3) Comprehends basic number theory concepts such as modular arithmetic, integer representations and primality, and their basic applications in cryptography.
4) Understands and applies counting principles.
5) Solves recurrence relations.
6) Knows the basic properties of relations, graphs and trees.

Course Flow Plan

Week	Subject	Related Preparation
1)	Propositional logic and applications; propositional function and quantifiers
2)	Inference rules, proof methods
3)	Sets, functions, sums and sequences
4)	Algorithms
5)	Growth of functions, complexity of algorithms
6)	Divisibility, modular arithmetic, integer representations
7)	Primes, greatest common divisor, solving congruences
8)	Midterm Exam
9)	Cryptography
10)	Mathematical induction, strong induction and well-ordering
11)	Counting
12)	Solving recurrence relations
13)	Relations
14)	Graphs and trees

Sources

Course Notes / Textbooks:	Discrete Mathematics and Its Applications, Kenneth H. Rosen, McGraw-Hill Education
References:	Discrete Mathematics, Richard Johnsonbaugh, Pearson

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5	6
Program Outcomes
1) Acquires sufficient accumulation of knowledge in natural and applied sciences, engineering and technology, and has the ability to design, and identify/formulate/solve problems related to, complex manufacturing and service systems using this knowledge.
2) Possesses the ability to select and apply appropriate methods for analysing integrated systems comprising humans, knowledge, raw materials and energy; to acquire, process and interpret data; and to reach conclusions using her/his engineering skills.
3) Has the ability to select and efficiently use engineering design principles along with appropriate analytical, computational and experimental engineering techniques in order to optimize outputs related to various systems under realistic constraints.
4) Possesses the skills to select from among and efficiently use modern technologies, equipment, software and software languages in applications related to her/his respective field.
5) Possesses the ability to produce industry-focused solutions that are able to contribute to social health, safety and welfare, while being cognizant of global, cultural, societal, economical and environmental matters.
6) Has the awareness to take decisions ethically, professionally and without overlooking her/his legal responsibilities in situations related to her/his professions.
7) Has the awareness about contemporary issues such as sustainability, entrepreneurship and innovation; and the ability to comprehend the impacts of these notions on her/his profession.
8) Has the skills to communicate and make presentations to a level that will allow her/him to effectively make an exchange of information and experience both verbally and in written and with various communities related to her/his area.
9) Is able to use a foreign language at least at B1 level, measured in terms of the European Language Portfolio criterion.
10) In cognizance of life-long learning, possesses the ability to follow and adapt to changes that may arise in her/his field and reflect them into her/his profession.
11) Has the ability to work efficiently in interdisciplinary projects, be open to collaboration and take initiative when necessary, manage risks, plan activities and develop strategies.
12) She has the ability to follow new approaches in the field of human-machine interaction and artificial intelligence and apply them to problems in her field.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Acquires sufficient accumulation of knowledge in natural and applied sciences, engineering and technology, and has the ability to design, and identify/formulate/solve problems related to, complex manufacturing and service systems using this knowledge.
2)	Possesses the ability to select and apply appropriate methods for analysing integrated systems comprising humans, knowledge, raw materials and energy; to acquire, process and interpret data; and to reach conclusions using her/his engineering skills.
3)	Has the ability to select and efficiently use engineering design principles along with appropriate analytical, computational and experimental engineering techniques in order to optimize outputs related to various systems under realistic constraints.
4)	Possesses the skills to select from among and efficiently use modern technologies, equipment, software and software languages in applications related to her/his respective field.
5)	Possesses the ability to produce industry-focused solutions that are able to contribute to social health, safety and welfare, while being cognizant of global, cultural, societal, economical and environmental matters.
6)	Has the awareness to take decisions ethically, professionally and without overlooking her/his legal responsibilities in situations related to her/his professions.
7)	Has the awareness about contemporary issues such as sustainability, entrepreneurship and innovation; and the ability to comprehend the impacts of these notions on her/his profession.
8)	Has the skills to communicate and make presentations to a level that will allow her/him to effectively make an exchange of information and experience both verbally and in written and with various communities related to her/his area.
9)	Is able to use a foreign language at least at B1 level, measured in terms of the European Language Portfolio criterion.
10)	In cognizance of life-long learning, possesses the ability to follow and adapt to changes that may arise in her/his field and reflect them into her/his profession.
11)	Has the ability to work efficiently in interdisciplinary projects, be open to collaboration and take initiative when necessary, manage risks, plan activities and develop strategies.
12)	She has the ability to follow new approaches in the field of human-machine interaction and artificial intelligence and apply them to problems in her field.

Assessment & Grading

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

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	3		39
Study Hours Out of Class	13	0	5		65
Midterms	1	13	2		15
Final	1	23	2		25
Total Workload					144