MATH 534 | Course Introduction and Application Information - Applied Mathematics and Statistics – With Thesis

Course Name

AI-Enhanced Scientific Computing II

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 534	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	Problem Solving Q&A Lecture / Presentation
National Occupation Classification	-
Course Coordinator	Doç. Dr. Sevin GÜMGÜM
Course Lecturer(s)	Doç. Dr. Sevin GÜMGÜM
Assistant(s)	Arş.Gör. Merve KAHRAMAN ARİMAN

Course Objectives	This course provides a focused introduction to key numerical methods and their AI-supported implementation. Students will learn to apply and analyze algorithms for linear systems, integration, differentiation, and eigenvalue problems while using AI tools for coding and verification. Emphasis is placed on practical computation and fundamental theoretical concepts.
Learning Outcomes	The students who succeeded in this course; Compute matrix and vector norms. Evaluate linear systems of equations using LU factorization. Solve linear systems of equations using iterative methods. Apply numerical differentiation techniques. Calculate integrals by numerical methods. Estimate errors in numerical integration. Find eigenvalues using numerical methods. Implement numerical algorithms using AI tools.
Course Description	This course covers key topics in scientific computing with integrated AI support. It includes matrix norms and stability, direct and iterative methods for linear systems, numerical differentiation and integration, and fundamental eigenvalue algorithms. The course emphasizes computational efficiency, error analysis, and convergence, supported by AI-based coding and verification tools.
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	Fundamental concepts and AI tool setup; academic integrity and basic matrix–vector operations.	M. Tezer, C. Bozkaya, "Numerical Analysis", (METU, 2018). Section 2.2
2	LU factorization; error analysis, stability, and AI-assisted implementation.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 2
3	PA = LU factorization; pivoting strategies, implementation, AI-assisted optimization, and numerical stability testing.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 2
4	Iterative methods: Jacobi method (AI-assisted); iteration theory, convergence analysis, AI-based implementation/optimization, and sparse matrices.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 2
5	Gauss–Seidel and SOR methods; convergence analysis, parameter selection, and AI-assisted comparison.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 2
6	Methods for SPD matrices; Cholesky and Conjugate Gradient, sparse systems, and AI-assisted performance analysis.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 2
7	Nonlinear systems of equations; Newton and quasi-Newton methods, Jacobians, and AI-assisted differentiation.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 2
8	Midterm
9	Numerical differentiation (AI-assisted); finite difference methods, error analysis, and AI-based Richardson extrapolation.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 5
10	Rounding error and extrapolation; Richardson extrapolation, error propagation, and AI-assisted error estimation.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 5
11	Newton–Cotes formulas; the trapezoidal and Simpson’s rules, AI-assisted implementation, and error estimation.	Timothy Sauer, Numerical Analysis, rnd edition, (Pearson, 2018) Chapter 5
12	Advanced integration methods; composite/open Newton–Cotes, Gauss quadrature, and AI-assisted adaptive integration.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 5
13	Eigenvalue problems: power iteration; inverse/shifted inverse iteration and AI-assisted dominant eigenvalue computation.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 2
14	QR algorithm and modern methods; QR iteration and AI-assisted QR factorization implementation.	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018) Chapter 2
15	Semester Review
16	Final Exam

Course Notes/Textbooks

Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018)

ISBN-13: 978-0-321-78367-7

Suggested Readings/Materials

M. Tezer, C. Bozkaya. "Numerical Analysis", (METU, 2018).

ISBN 13: 9789754293777

AI Tools:

ChatGPT/Claude
GitHub Copilot
Google Colab
Wolfram Alpha
Python libraries: NumPy, SciPy, Matplotlib, SymPy

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	1	10
Presentation / Jury
Project	1	10
Seminar / Workshop
Oral Exams
Midterm	1	30
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	5	70
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	1	12	12
Presentation / Jury			0
Project	1	20	20
Seminar / Workshop			0
Oral Exam			0
Midterms	1	30	30
Final Exam	1	45	45
		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.

-

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.

-

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.

-

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.

-

X

-

11

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

-

MATH 534 | Course Introduction and Application Information

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

EVALUATION SYSTEM

ECTS / WORKLOAD TABLE

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

IZMIR UNIVERSITY OF ECONOMICS GÜZELBAHÇE CAMPUS

GLOBAL CAREER

CONTRIBUTION TO SCIENCE

VALUING PEOPLE

BENEFIT TO SOCIETY