|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Algebra IV *||MT 312||6||3||3||5|
|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. Dilek KAHYALAR|
The aim of this course is to teach the matrix groups with algebraic viewpoints and to teach linear transformations which is determined by matrix groups in an inner space.
Matrix groups, Linear transformations which is determined by by matrix groups in an inner spaces
|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||Field, Skew field and Quaternions||Required readings|
|2||Matrices and Linear transformations||Required readings|
|3||The general Linear groups||Required readings|
|4||All matrix groups are real linear groups||Required readings|
|5||Hermitian transformations and Hermitian matices||Required readings|
|6||Symmetric transformations and Symmetric matices||Required readings|
|7||Inner spaces with finite dimension over a field or skew field||Required readings|
|9||Uniter group and transformations||Required readings|
|10||Orthogonal group and transformations||Required readings|
|11||Invariant subspaces and orthogonal groups||Required readings|
|12||Orthogonal matrices and isometries||Required readings|
|13||Self-adjoint transformations and orthogonal groups||Required readings|
|14||Orthogonal transformations on dual spces||Required readings|
|15||Orthogonal transformations on dual spces||Required readings|
|Recommended or Required Reading|