TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING PR. (ENGLISH) | |
| Code | YZZ105 |
| Name | Linear Algebra |
| Term | 2025-2026 Academic Year |
| Semester | 1. Semester |
| Duration (T+A) | 3-1 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3.5 National Credit |
| Teaching Language | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Label | BS Basic Science Courses C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GÜZİN YÜKSEL |
| Course Instructor |
Dr. Öğr. Üyesi Emrah KORKMAZ
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to equip students with the linear algebra concepts and methods they will need in the field of artificial intelligence, presented in a clear and comprehensible manner.
Course Content
The topics included in this course are Systems of Linear Equations and Matrices, Determinants, Euclidean Vector Spaces, and General Vector Spaces.
Course Precondition
None
Resources
Howard Anton, Chris Rorres, Elementary Linear Algebra: Applications Version, 11th Edition. Otto Bretscher, Linear Algebra with Applications, Fifth Edition.
Notes
Related digital resources
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Distinguish between matrices and matrix operations. |
| LO02 | It brings matrices into echelon form by Gaussian Elimination and Gauss-Jordan Reduction. |
| LO03 | It uses the inverse of the matrix to solve systems. |
| LO04 | Determinant calculations. |
| LO05 | Solve systems using Cramer's rule. |
| LO06 | Can draw vectors on the plane and in space and perform vector operations. |
| LO07 | Uses the basic concepts of Vector Spaces. |
| LO08 | Writes the linear spacing space. |
| LO09 | Determines linear dependence and independence of vectors. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | It provides a broad range of knowledge about fundamental Computer Science concepts, algorithms and data structures. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Learns basic computer topics such as software development, programming languages, and database management. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Understands advanced computing fields such as data science, artificial intelligence, and machine learning. | |
| PLO04 | Belirsiz | Learn about topics such as computer networks, cyber security, and database design. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develops skills in designing, implementing and analyzing algorithms. | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Gains the ability to use different programming languages effectively | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Learns data analysis, database management and big data processing skills. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Gains practical experience by working on software development projects. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Strengthens collaboration and communication skills within the team. | |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | It provides a mindset open to technological innovations. | 3 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Encourages continuous learning and self-improvement competence. | 4 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Develops the ability to solve complex problems. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to Systems of Linear Equations and Gaussian Elimination Method | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 2 | Matrices and Matrix Operations, Inverses; Algebraic Properties of Matrices | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 3 | Elementary Matrices and Method for Finding A −1 | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 4 | More on Linear Systems and Invertible Matrices, Diagonal, Triangular, and Symmetric Matrices | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Determinants by Cofactor Expansion | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 6 | Evaluating Determinants by Row Reduction | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Properties of Determinants and Cramer’s Rule | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Repetition of the topics covered from lecture notes and resources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Vectors in 2-Space, 3-Space, and n-Space | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 10 | Norm, Dot Product, and Distance in Rⁿ | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 11 | Real Vector Spaces and Subspaces | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 12 | Linear Independence | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 13 | Coordinates and Basis | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | Row space, Column space and Null space | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 15 | Rank, Nullity, and Fundamental Matrix Spaces | Reading relevant sections of course materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 16 | Term Exams | Repetition of the topics covered from lecture notes and resources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Repetition of the topics covered from lecture notes and resources | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 128 | ||
| Total Workload / 25 (h) | 5,12 | ||
| ECTS | 5 ECTS | ||