MATH 538 | Course Introduction and Application Information - Applied Mathematics and Statistics – With Thesis

Course Name

Mathematical and Statistical Modeling

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 538	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	Discussion Lecture / Presentation
National Occupation Classification	-
Course Coordinator	Doç. Dr. Sevin GÜMGÜM
Course Lecturer(s)	Doç. Dr. Sevin GÜMGÜM Dr.Öğretim Üyesi Demet ERSOY ÖZDEK Dr.Öğretim Üyesi NECLA KOÇHAN Prof. Dr. GÖZDE YAZGI TÜTÜNCÜ AŞÇI Prof. Dr. İSMİHAN BAYRAMOĞLU
Assistant(s)	Arş.Gör. Merve KAHRAMAN ARİMAN

Course Objectives	The aim of this course is to equip students with skills in constructing, analyzing, and solving mathematical and statistical models for real-world problems.
Learning Outcomes	The students who succeeded in this course; Explain key concepts of mathematical and statistical modeling. Select appropriate model structures from alternatives for real-world problems. Apply basic differential equations, probability calculations, linear system of equations for modelling real-world problems. Produce computational solutions using Python/R/Matlab. Prepare scientific reports and presentations of model results.
Course Description	This course provides a comprehensive introduction to constructing, analyzing, and interpreting mathematical and statistical models for real-world phenomena. Students learn to formulate deterministic and stochastic models using differential equations, optimization structures, probability, and statistical tools. Emphasis is placed on selecting appropriate modeling frameworks and translating theoretical structures into computational implementations. The course integrates hands-on practice with proposed software packages to produce and evaluate model-based solutions. By the end of the course, students will be able to design and communicate robust models through scientific reports and presentations.
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	Fundamentals of scientific modeling; deterministic and stochastic models.	Simon Serovajsky, Mathematical Modelling, 2024. Section 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 5.1
2	Deterministic Models 1: Differential equation–based modeling.	Simon Serovajsky, Mathematical Modelling, 2024. Section 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 5.1
3	Deterministic Models 1: Differential equation–based modeling.	Simon Serovajsky, Mathematical Modelling, 2024.Section 2.1, 2.2, 2.3, 2.4, 3.1–3.6, 4.1–4.4, 10.1–10.3
4	Deterministic Models 1: Differential equation–based modeling.	Simon Serovajsky, Mathematical Modelling, 2024.Section 2.1, 2.2, 2.3, 2.4, 3.1–3.6, 4.1–4.4, 10.1–10.3
5	Deterministic Models 2: Optimization-based modeling.	Simon Serovajsky, Mathematical Modelling, 2024. Section 16.1, 16.2, 16.3, 16.4, 16.5, 20.1, 20.2, 20.3, 20.4, 20.5
6	Deterministic Models 2: Optimization-based modeling.	Simon Serovajsky, Mathematical Modelling, 2024. Section 16.1, 16.2, 16.3, 16.4, 16.5, 20.1, 20.2, 20.3, 20.4, 20.5
7	Stochastic Models 1: Probability-based modeling; Markov processes.	Sheldon M. Ross, Introduction to Probability Models, 10th edition. Chapter 4
8	Stochastic Models 1: Probability-based modeling; Markov processes.	Sheldon M. Ross, Introduction to Probability Models, 10th edition. Chapter 6
9	Midterm Exam
10	Stochastic Models 2: Statistical modeling: regression, GLM, time series.	Simon Serovajsky, Mathematical Modelling, 2024. Section 18.2, 21.1, 21.2, 21.3, 21.4
11	Stochastic Models 2: Statistical modeling: regression, GLM, time series.	Simon Serovajsky, Mathematical Modelling, 2024. Section 18.2, 21.1, 21.2, 21.3, 21.4
12	Producing computational solutions using Python/R/Matlab.	Simon Serovajsky, Mathematical Modelling, 2024. Section 2.1–2.4,10.1–10.3, 12.1–12.4
13	Producing computational solutions using Python/R/Matlab.	Simon Serovajsky, Mathematical Modelling, 2024. Section 2.1–2.4,10.1–10.3,12.1–12.4
14	Ethical and moral dimensions of scientific modeling.	Winsberg, E. (2010). Science in the Age of Computer Simulation. University of Chicago Press.
15	Applied project and scientific presentation.
16	Final Exam

Course Notes/Textbooks

Simon Serovajsky, Mathematical Modelling.
Chapman & Hall/CRC (Taylor & Francis Group),
ISBN: 9781032147871, January 29, 2024.
Ross, Sheldon M. Introduction to Probability Models. 10th ed., Academic Press, 2010.

ISBN-13: 978-0123756862

Winsberg, E. (2010). Science in the Age of Computer Simulation. University of Chicago Press.

ISBN-13: 978-0-226-90202-9

Suggested Readings/Materials

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	1	20
Presentation / Jury	1	10
Project	1	20
Seminar / Workshop
Oral Exams
Midterm	1	20
Final Exam
Total

Weighting of Semester Activities on the Final Grade	4	70
Weighting of End-of-Semester Activities on the Final Grade	1	30
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	3	42
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	4	5	20
Presentation / Jury	1	15	15
Project	1	30	30
Seminar / Workshop			0
Oral Exam			0
Midterms	1	30	30
Final Exam		40	0
		Total	185

#

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.

-

X

-

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.

-

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.

-

X

-

6

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

-

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.

-

X

8

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

-

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.

-

11

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

-

MATH 538 | Course Introduction and Application Information

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

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