COURSE SYLLABUS

LINEAR ALGEBRA

1	Course Title:	LINEAR ALGEBRA
2	Course Code:	MAT1078
3	Type of Course:	Compulsory
4	Level of Course:	First Cycle
5	Year of Study:	1
6	Semester:	2
7	ECTS Credits Allocated:	6
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. BASRİ ÇELİK
16	Course Lecturers:	Doç.Dr. Atilla AKPINAR Prof.Dr. Esen İYİGÜN
17	Contactinformation of the Course Coordinator:	Prof.Dr.Basri ÇELİK basri@uludag.edu.tr 0224.2941762
18	Website:
19	Objective of the Course:	To provide a fundamental understanding of linear algebra, especially linear equation systems, matrices, determinant and their usage, solutions of linear equations system.
20	Contribution of the Course to Professional Development	To understand the role of vector, vector spaces, systems of linear equations, matrices in their profession.

Learning Outcomes:

1	Acquires an understanding of some fundamental ideas of linear algebra, including vectors, vector spaces, linear independence, bases, dimension and linear transformations, especially in the case of Rn.;
2	Enhances your capability for studying abstraction and producing formal mathematical arguments (proofs).;
3	Learns some important applications of linear algebra in other mathematical disciplines.;
4	Understands the relationship between geometry and linear algebra, including the roles of inner products and orthogonality.;
5	Writes solutions to problems involving linear algebra in a clear, mathematically-correct,and grammatically-correct fashion.;
6	Uses elementary row operations, elementary matrices and matrix algebra to solve systems of equations.;
7	Develops your ability to solve problems involving linear equations, matrices, determinants and vectors.;

22	Course Content:

Week	Theoretical	Practical
1	Contens and description of this course, vectors, vector directions, length of vector, zero vector.
2	Components of vector, location vector, parallel vectors, point-vector relations, vector sum, vector product, multiplication of vectors by scalars, scalar (dot) product, vector space, lines and planes in space and their applications, subvector spaces.
3	Inner product spaces, norm of a vector, angle between two vector, projection vector, Schwarz inequality, orthogonal and orthonormal vectors, unit vector, Pythagoras theorem, Bessel inequality.
4	Linear depence and indepence of vectors, bases and dimension of a vector, Gramm-Schmidt orthogonalization method.
5	Matrices, row and column of matrices, dimension of matrix, square matrix, zero matrix, addition matrix, multiplication of matrix by scalar, transpose matrix, row matrix, sütun matrix, symmetric and antisymmetric matrix, diagonal matrix.
6	Multiplication of matrices, unit matrix, scalar matrix, submatrix, inverse matrix, (upper and lower) triangular matrix.
7	Determinant of order 2, determinant of order 3 and Sarrus Rule, Determinants of order n: Laplace expansion by a row and by a column, properties of determinants.
8	Feedback
9	Special determinants, minor and cofactor, adjoint matrix, calculation of inverse matrix.
10	Information about general linear equations system, matrix form of linear equations system, solutions of some linear systems by inverse matrix method.
11	Homogen linear equations system and their solutions.
12	Cramer systems (n=m ), linear equations system with n>m and n<m.
13	Elementary operations, echelon matrices.
14	Solutions of linear equations system by elementary operations.

23	Textbooks, References and/or Other Materials:	1) Linear Algebra Lecture Notes (in Turkish), Basri ÇELİK. 2) Lineer Cebir, Prof. Dr. Süleyman ÇİFTÇİ, Dora Yayınevi, 2015, Bursa. 3)Prof. Dr.H.Hilmi Hacısalihoğlu, 1985, Lineer Cebir, 3.Baskı, Gazi Üniversitesi, Ankara, 765s. 4) Prof. Dr. H.Hilmi Hacısalihoğlu, Doç.Dr. Mustafa Balcı, Yrd.Doç.Dr.Fikri Gökdal, 1986, Temel ve Genel Matematik 2, 3.Baskı, Ankara, 316 s. 5) Erdoğan Esin, H.Hilmi Hacısalihoğlu, Ertuğrul Özdamar, 1987, Çözümlü Lineer Cedir Problemleri, 1.Baskı, Ankara, 1069s.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course	Homeworks and online exams
Information

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	7	98
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	9	9
Others	14	1	14
Final Exams	1	13	13
Total WorkLoad			176
Total workload/ 30 hr			5,87
ECTS Credit of the Course			6

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

	PQ1	PQ2	PQ6
LO1	5	5	4
LO2	5	4	4
LO3	5	4	4
LO4	5	4	4
LO5	5	4	4
LO6	5	4	4
LO7	5	4	4

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High