COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Algebra I * MT   211 3 4 4 7

Prerequisites and co-requisites
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Assoc.Prof.Dr. Nazar Şahin ÖĞÜŞLÜ
Instructors
Doç.Dr.NAZAR ŞAHİN ÖĞÜŞLÜ1. Öğretim Grup:A
Doç.Dr.NAZAR ŞAHİN ÖĞÜŞLÜ2. Öğretim Grup:A
 
Assistants
Goals
The objectives of this course are to introduce the students with the basic ideas of linear algebra including vector spaces, subspaces, basis, dimension, linear transformations, matrices, systems of linear equations, eigenvalues and eigenvectors and to teach the understanding of abstract mathematical concepts and abstract thought arising from the concepts covered in this course.
Content
Vectors in the plane and space; vector spaces, subspaces, linear dependence, bases and finite dimensional vector spaces, linear transformations, matrices, representation of linear transformations by matrices, direct sum, systems of linear equations, determinants, characteristic vectors and diagonalization.

Learning Outcomes
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
X
10
Uses effective scientific methods and appropriate technologies to solve problems
X
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
X
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
X
13
Knows programming techniques and is able to write a computer program
X
14
Is able to do mathematics both individually and in a group.
X

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Vector space, subspace Required readings
2 Linear dependence, independence and a basis of a vector space Required readings
3 Basic properties of a basis and dimension of a vector space Required readings
4 Sum of subspaces, direct sum Required readings
5 Linear transformations, their kernels and images Required readings
6 The rank of a linear transformation, isomorphism Required readings
7 Matrices Required readings
8 Mid-term exam Review of the topics discussed in the lecture notes and sources
9 Representation of linear transformations by matrices Required readings
10 The rank of a matrix, echelon matrix Required readings
11 Row equivalent matrices and systems of linear equations Required readings
12 Determinant function, properties of determinant, evaluation of determinant Required readings
13 Cramer Rule, eigen values and eigen vectors Required readings
14 Characteristic spaces and characteristic polynomial Required readings
15 Solving problems Required readings
16-17 Final exam Review of the topics discussed in the lecture notes and sources

Recommended or Required Reading
TextbookLinear Algebra, Author:Arif Sabuncuoğlu
Additional Resources
Linear Algebra, Author:Larry Smith
Linear Algebra, Author:Jim Hefferon