DIGITAL GAME DESIGN
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT1041	Linear Algebra	Spring	3	0	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Non-Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :	Instructor MAHMOUD JAFARI SHAH BELAGHI
Course Lecturer(s):	Prof. Dr. SÜREYYA AKYÜZ Assoc. Prof. HALE GONCE KÖÇKEN Assist. Prof. DİLRÜBA ÖZMEN ERTEKİN Prof. Dr. NAFİZ ARICA
Recommended Optional Program Components:	None
Course Objectives:	To define matrix operations such as addition, multiplication, inversion and to prove some of related properties; To teach to solve a system of linear equations by using matrices; To give the definitions of a vector space, subspace, base and dimension and to prove some of related theorems; To introduce the notion of a linear map and the types of linear maps (such as injective, surjective and bijective); To teach the matrix representation of linear mappings and proving some of related properties; To construct the space of linear mappings and to give its structural properties; To define the transpose of a linear functional and to prove related properties.

Learning Outcomes

The students who have succeeded in this course;
1. Solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion.
2. Carry out matrix operations, including inverses and determinants.
3. Demonstrate understanding of the concepts of vector space and subspace.
4. Demonstrate understanding of linear independence, span, and basis.
5. Determine eigenvalues and eigenvectors and solve eigenvalue problems.
6. Apply principles of matrix algebra to linear transformations.

Course Content

Systems of linear equations, matrices; Vector spaces, subspaces, base and dimension, coordinate; Linear mappings, kernel and image subspaces; Matrix representations of linear mappings; Linear functional, transpose of a linear mapping. Eigenvalues and eigenvectors, diagonalization of matrices.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	- Introduction to Systems of Linear Equations - Gaussian Elimination and Gauss-Jordan Elimination
2)	- Operations with Matrices - Properties of Matrix Operations
3)	- The Inverse of a Matrix
4)	- The Determinant of a Matrix - Evaluation of a Determinant Using Elementary Operations
5)	- Properties of Determinants
6)	- Vectors in R^n - Vector Spaces \ review.
7)	- Subspaces of Vector Spaces - Spanning Sets and Linear Independence
8)	- Basis and Dimension
9)	- Rank of a Matrix and Systems of Linear Equations
10)	- Introduction to Linear Transformations
11)	- The Kernel and Range of a Linear Transformation
12)	- Matrices for Linear Transformations - Transition Matrices and Similarity \ review.
13)	- Eigenvalues and Eigenvectors - Diagonalization
14)	- Symmetric Matrices and Orthogonal Diagonalization

Sources

Course Notes / Textbooks:	Elementary Linear Algebra, Howard Anton, Wiley Publishing Co. (2000)
References:	1.Lang, S., "Linear Algebra", Addison-Wesley Publishing Company, (1968). 2.Hoffman, K. M., Kunze R. A., "Linear Algebra", Printice Hall, 2. edition, (1971). 3.Koç, C., "Basic Linear Algebra", Matematik Vakfı, (1995). 4. Lipschutz, S., "Linear Algebra, Schaum’s Outline Series", McGraw-Hill, Inc., (1974). 5.Kolman, B., Hill, D. R., "Introductory Algebra with Applications", Prentice Hall

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Midterms	2	% 60
Final	1	% 40
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 60
PERCENTAGE OF FINAL WORK		% 40
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	7	98
Midterms	2	2	4
Final	1	2	2
Total Workload			146

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Comprehend the conceptual importance of the game in the field of communication, ability to implement the player centered application to provide design.
2)	Analyze, synthesize, and evaluate information and ideas from various perspectives.
3)	Analyze the key elements that make up specific game genres, forms of interactions, mode of narratives and understand how they are employed effectively to create a successful game.
4)	Understand game design theories and methods as well as implement them during game development; to make enjoyable, attractive, instructional and immersive according to the target audience.
5)	Understand the technology and computational principles involved in developing games and master the use of game engines.
6)	Understand the process of creation and use of 2D and 3D assets and animation for video games.
7)	Understand and master the theories and methodologies of understanding and measuring player experience and utilize them during game development process.
8)	Comprehend and master how ideas, concepts and topics are conveyed via games followed by the utilization of these aspects during the development process.
9)	Manage the game design and development process employing complete documentation; following the full game production pipeline via documentation.
10)	Understand and employ the structure and work modes of game development teams; comprehend the responsibilities of team members and collaborations between them while utilizing this knowledge in practice.
11)	Understand the process of game publishing within industry standards besides development and utilize this knowledge practice.
12)	Pitching a video game to developers, publishers, and players; mastering the art of effectively communicating and marketing the features and commercial potential of new ideas, concepts or games.