LINEAR ALGEBRA I

Course Code:

MATH 231

Semester:

Fall

Course Type:

Core

P:

3

Lab:

2

Laboratuvar Saati:

0

Credits:

4

ECTS:

7

Course Language:

English

Course Objectives:

To provide tools for dealing with problems in many fields from a variety of disciplines and to serve as a bridge from the typical intuitive treatment of calculus to more rigorous courses such as abstract algebra and analysis.

Course Content:

Matrices and systems of linear equations. Vector spaces; subspaces, sums and direct sums of subspaces. Linear dependence, bases, dimension, quotient spaces. Linear transformations, kernel, range, isomorphism. Spaces of linear transformations. Representations of linear transformations by matrices. Determinants. Inverse of a matrix. Eigenvalues and eigenvectors. Diagonalization of a matrix.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Teaching Methods	Assessment Methods
1) Solves the systems of linear equations using matrices.	1,2	A
2) Determines spanning sets for a given vector space.	1,2	A
3) Applies Gram-Schmidt Process to an independent set of vectors to obtain an orthogonal set.	1,2	A
4) Determines if a given matrix is nonsingular.	1,2	A
5) Uses elementary matrices to compute the inverse of a matrix.	1,2	A
6) Uses determinant and adjoint to compute the inverse of a matrix.	1,2	A
7) Diagonalizes a matrix	1,2	A

Course Flow

Week	Topics	Study Materials
1	Vectors and linear equations. The idea of elimination	Textbook
2	Elimination using matrices	Textbook
3	Rules for matrix operations, inverse matrices	Textbook
4	LU-decomposition, transposes and permutations	Textbook
5	Spaces of vectors,	Textbook
6	Nullspace of A, The complete solution to Ax=b	Textbook
7	Independence, basis and dimension,	Textbook
8	Dimensions of the four subspaces	Textbook
9	Orthogonality of the four subspaces	Textbook
10	Projections, orthonormal bases and Gram-Schmidt orthonormalization process	Textbook
11	The properties of determinants, permutations and cofactors,	Textbook
12	Cramer's rule, inverses and volumes	Textbook
13	Introduction to eigenvalues,	Textbook
14	Diagonalizing a matrix	Textbook

Recommended Sources

RECOMMENDED SOURCES
Textbook	Gilbert Strang - Introduction to Linear Algebra Fifth Edition-Wellesley-Cambridge Press (2016)
Additional Resources

Material Sharing

MATERIAL SHARING
Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	100
Quizzes
Assignments
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		60
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		40
Total		100

COURSE CATEGORY

Core Courses

Course’s Contribution to Program

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)					x
2	Acquiring fundamental knowledge on fundamental research fields in mathematics					x
3	Ability form and interpret the relations between research topics in mathematics					x
4	Ability to define, formulate and solve mathematical problems				x
5	Consciousness of professional ethics and responsibilty					x
6	Ability to communicate actively			x
7	Ability of self-development in fields of interest					x
8	Ability to learn, choose and use necessary information technologies					x
9	Lifelong education					x

ECTS

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	5	70
Hours for off-the-classroom study (Pre-study, practice)	14	5	70
Mid-terms (Including self study)	1	15	15
Quizzes	-	-	-
Assignments	-	-	-
Final examination (Including self study)	1	20	20
Total Work Load			175
Total Work Load / 25 (h)			7
ECTS Credit of the Course			7

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