|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 Coordinator||Assoc.Prof.Dr. Nazar Şahin ÖĞÜŞLÜ|
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.
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.
|Course's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
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
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|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|
|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|
|Textbook||Linear Algebra, Author:Arif Sabuncuoğlu|
Linear Algebra, Author:Larry Smith
Linear Algebra, Author:Jim Hefferon