MATH 524 | Course Introduction and Application Information - Applied Mathematics and Statistics – With Thesis

Course Name

Discrete Mathematics

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 524	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Second Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	Lecture / Presentation
National Occupation Classification	-
Course Coordinator	Doç. Dr. Cemal Murat ÖZKUT
Course Lecturer(s)	Doç. Dr. Cemal Murat ÖZKUT
Assistant(s)	Arş.Gör. Merve KAHRAMAN ARİMAN

Course Objectives	This course aims to introduce advanced concepts in discrete and combinatorial mathematics, equipping students with rigorous mathematical reasoning and problem-solving techniques. Emphasis is placed on counting principles, recurrence relations, and graph theory, fostering algorithmic thinking essential for theoretical and applied problem-solving. The course also prepares students to analyze and model complex real-world systems through discrete structures.
Learning Outcomes	The students who succeeded in this course; solve counting problems using relations and functions. apply finite state machines to model and analyze the computational process. apply the principle of inclusion and exclusion. solve counting problems using generating functions solve recurrence relations
Course Description	This course covers fundamental and advanced topics in discrete mathematics, including Cartesian products, relations and functions, the pigeonhole principle, integer partitions, and exponential generating functions. Emphasis is also placed on solving first- and second-order linear recurrence relations, as well as analyzing nonhomogeneous and nonlinear recurrence relations.
Related Sustainable Development Goals

Course Category	Core Courses
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation
1	Introduction	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003. 1.1-1.4 (3-35)
2	Relations and Functions: Cartesian products and relations, functions	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003.5.1, 5.2 (247-259)
3	Relations and Functions: Stirling numbers of the second kind, the pigeonhole principle	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003. 5.3-5.5 (260-277)
4	Relations and Functions: Computational complexity, analysis of algorithms	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003.5.7, 5.8 (289-301)
5	Finite State Machines: Language, finite state machines	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003. 6.1-6.3 (309-331)
6	Relations Revisited: Properties of relations, partial orders, equivalence relations	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003.7.1, 7.3, 7.4 (337-370)
7	The Principle of Inclusion and Exclusion: The basic principle, generalizations of the principle, applications	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003. 8.1, 8.2 (385-401)
8	Midterm Exam
9	Generating Functions: Definition and basic properties, partition of integers	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003. 9.1-9.3 (415-435)
10	Generating Functions: The exponential generating function, applications	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003. 9.4 (436-439)
11	Recurrence Relations: First order linear recurrence relations	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003.10.1 (447-455)
12	Recurrence Relations: Second order linear recurrence relations	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003.10.2 (456-469)
13	Recurrence Relations: Non-homogeneous recurrence relations	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003. 10.3 (470-481)
14	Recurrence Relations: The method of generating functions, nonlinear recurrence relations	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003. 10.4, 10.5 (482-495)
15	Semester Review
16	Final Exam

Course Notes/Textbooks	"Discrete and Combinatorial Mathematics: An Applied Introduction" by R.P. Grimaldi, Pearson, 5th Edition, 2003. ISBN-13: 978-0201726343
Suggested Readings/Materials

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques	2	10
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	40
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	3	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	4	56
Field Work			0
Quizzes / Studio Critiques	2	17	34
Portfolio			0
Homework / Assignments			0
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	37	37
Final Exam	1	50	50
		Total	225

#

Program Competencies/Outcomes

* Contribution Level

1

2

3

4

5

1

To be able to demonstrate independent and critical thinking in Applied Mathematics and Statistics.

-

X

-

2

To be able to define problems in Applied Mathematics/Statistics and verify whether they are mathematically/statistically consistent.

-

3

To be able to analyse and solve real life problems using applied methods and interdisciplinary approach of Mathematics/Statistics.

-

X

-

4

To be able to independently conduct, conclude, and report on specialized research in Applied Mathematics and Statistics.

-

X

-

5

To be able to efficiently use national and international resources, for staying updated in the field, communicating with colleagues, and following the related literature.

-

6

To be able to develop proficiency in using computer software widely utilized in the fields of Applied Mathematics and Statistics.

-

X

-

7

To be able to evaluate solution processes efficiently using mathematical reasoning and modeling in order to contribute to the solutions of social and scientific problems.

-

8

To be able to synthesize theoretical frameworks with practical applications through mathematical and statistical methods.

-

X

9

To be able to develop strategies, policies and plans for problems and research areas in Applied Mathematics/Statistics in order to interpret the results and translate them into practice.

-

10

To be able to translate key topics, events, and phenomena in Applied Mathematics and Statistics into the context of other scientific disciplines.

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11

To be able to engage in lifelong learning by continuously updating and improving knowledge and skills in Applied Mathematics and Statistics.

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MATH 524 | Course Introduction and Application Information

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