MATH 532 | Course Introduction and Application Information - Applied Mathematics and Statistics – With Thesis

Course Name

AI-Enhanced Scientific Computing I

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 532	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)	Dr.Öğretim Üyesi Demet ERSOY ÖZDEK
Assistant(s)	Arş.Gör. Merve KAHRAMAN ARİMAN

Course Objectives	This course aims to teach core numerical methods and their AI-supported implementation. Students will learn to solve nonlinear equations, apply interpolation and least-squares techniques, and analyze differential equations while using AI tools effectively for algorithm development and verification.
Learning Outcomes	The students who succeeded in this course; Apply root-finding techniques to compute the roots of nonlinear functions using numerical methods. Construct interpolation polynomials with Lagrange and Newton methods. Apply least-squares methods to solve linear and nonlinear systems. Model real-world problems using least-squares techniques. Solve initial value problems for ordinary differential equations using finite difference methods. Evaluate correctness of AI-generated numerical codes. Compare classical numerical analysis and modern AI approaches together to build computational intuition. Evaluate responsible and ethical AI usage by explaining proper attribution, verification steps, and limitations of AI-generated solutions.
Course Description	This course covers the theory and applications of numerical analysis methods and focuses on the computer-based solution of mathematical problems. The course includes numerical computation, modeling, and programming, as well as the use of artificial intelligence tools in solving numerical problems.
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 and AI Introduction	Timothy Sauer, Numerical Analysis, 3nd edition, (Pearson, 2018), chap. 0
2	Nonlinear Equations I, Bisection Method, Fixed-Point Iteration with AI Activities	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018), chap. 1.1-1.2
3	Nonlinear Equations II (AI-Enhanced), Newton Method, Secant Method with AI Activities	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018), chap. 1.3-1.4
4	Root-Finding Methods, Rate of Convergence, AI-assisted parameter exploration	Timothy Sauer, Numerical Analysis, 3rd edition, (Pearson, 2018), chap. 1.5-1.6
5	Interpolation I, AI-Assisted Lagrange Polynomials, Newton Divided Differences with AI Activity	Timothy Sauer, Numerical Analysis, 3nd edition, (Pearson, 2018), chap. 3.1-3.2
6	Interpolation II, Finite Differences, Newton Forward/Backward formulas	Timothy Sauer, Numerical Analysis, 3nd edition, (Pearson, 2018), chap 3.3-3.4
7	Interpolation Error Analysis, Error bounds, Runge phenomenon and Visualization with AI Activity	Timothy Sauer, Numerical Analysis, 3nd edition, (Pearson, 2018), chap3.5
8	Midterm Exam
9	Advanced Interpolation, Hermite Interpolation, Chebyshev Polynomials, AI-Assisted Implementation and Stability Analysis	Timothy Sauer, Numerical Analysis, 3nd edition, (Pearson, 2018), chap. 3.6-3.7
10	Least Squares I, Discrete Least Squares, Normal Equations, QR factorization with AI Activity	Timothy Sauer, Numerical Analysis, 3nd edition, (Pearson, 2018), chap. 4.1-4.2
11	Least Squares II, Public health/engineering models, Overdetermined systems	Timothy Sauer, Numerical Analysis, 3nd edition, (Pearson, 2018), chap 4.3-4.4
12	QR Factorization, Gram-Schmidt orthogonalization, Applications with AI	Timothy Sauer, Numerical Analysis, 3nd edition, (Pearson, 2018), chap. 4.5
13	ODEs & Introduction to PINNs, Initial Value Problems, Euler Method, Classical vs AI Methods	Timothy Sauer, Numerical Analysis, 3nd edition, (Pearson, 2018), chap. 6.1-6.2
14	VP Analysis & Modern Methods, Truncation error analysis, Trapezoid Method, Stability analysis, AI vs Classical method comparison	Timothy Sauer, Numerical Analysis, 3nd edition, (Pearson, 2018), chap. 6.3-6.4
15	Semester Review
16	Final Exam

Course Notes/Textbooks

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

ISBN 13: 978-0-13-469645-4

Suggested Readings/Materials

Chenney, W., & Kincaid, D. Numerical Mathematics and Computing. Cengage Learning.

ISBN-13 for 7th Ed: 978-0534389021

ChatGPT (Free/Plus) or Claude (Free/Pro)

GitHub Copilot (Free for students)
Google Colab (Free)
Wolfram Alpha (Free)
MATLAB/Python Documentation

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	4	56
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	1	20	20
Presentation / Jury			0
Project	1	21	21
Seminar / Workshop			0
Oral Exam			0
Midterms	1	30	30
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.

-

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 532 | 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