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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.

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

Course Flow

Week

Topics

Study Materials

1

Systems of linear equations

Textbook

2

Solutions of Homogeneous systems, null space of a matrix

Textbook

3

Vector space properties, linear combinations

Textbook

4

Spanning sets

Textbook

5

Linear independence and nonsingular matrices

Textbook

6

Linear dependence and spans

Textbook

7

Orthogonality, inner products

Textbook

8

Orthogonal vectors, Gram-Schmidt Process

Textbook

9

Matrix operations, transposes and symmetric matrices

Textbook

10

Adjoint of a matrix

Textbook

11

Hermitian matrices

Textbook

12

Elementary matrices, inverse of a matrix

Textbook

13

Column space, row space, null space of a matrix

Textbook

14

Determinants

Textbook

Recommended Sources

Textbook

A First Course in Linear Algebra, Robert A Breezer. Linear Algebra with Applications, Steven Leon.

Additional Resources

Abstract Linear Algebra, Curtis Morton.

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

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

20

20

Quizzes

-

-

-

Assignments

-

-

-

Final examination (Including self study)

1

16

16

Total Work Load

 

 

176

Total Work Load / 25 (h)

 

 

7.04

ECTS Credit of the Course

 

 

7