|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Advanced Linear Algebra *||MT 414||8||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||Dr. Lec. Uyesi Ela AYDIN|
Vector Spaces. Modules, direct sum of modules and free modules. Linear Operators and Eigenvalues. Invariant Subspaces, Jordan Canonical Forms. Inner product spaces and orthagonality. The course covers issues related to vector spaces, linear functions , iner product spaces, embeddings, dual spaces and double duals, annihilators, representation of linear transformations by matrices, diagonalizations and Jordan form of matrices.
Give elementary knowledge about vector spaces,The algebra of Linear Transformations, Inner product spaces, Isometries between vector spaces. Finding Dual vector spaces and double dual, Determine Annihilators of vector spaces, Relationship between functionals and linear systems, Representation of Linear Transformations by matrices. Invariant subspaces, To compute triangular, diagonal and Jordan canonical forms.
|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 spaces and find their basis||Review of the relevant pages from sources|
|2||İınner products and inner product spaces||Review of the relevant pages from sources|
|3||Orthonormal basis||Review of the relevant pages from sources|
|4||Linear Operations and embeddings||Review of the relevant pages from sources|
|5||Linear functionals and dual basis||Review of the relevant pages from sources|
|6||Double duals and annihilators||Review of the relevant pages from sources|
|7||Homogen systems and linear functionals||Review of the relevant pages from sources|
|8||Mid-term exam||Review of the topics discussed in the lecture notes and sources|
|9||Transpose of Linear functions||Review of the relevant pages from sources|
|10||Polynomial algebras||Review of the relevant pages from sources|
|11||Representation of linear transformations by matrices and diagonalizations||Review of the relevant pages from sources|
|12||Invariant subspaces||Review of the relevant pages from sources|
|13||Direct sums||Review of the relevant pages from sources|
|14||Jordan form and aplications||Review of the relevant pages from sources|
|15||Solving Problems, final exam||Review of the relevant pages from sources|
|16-17||Final Exam||Review of the topics discussed in the lecture notes and sources|
|Recommended or Required Reading|
|Textbook||Prof. Dr. H. Hilmi HACISALİHOĞLU," Lineer Cebir", Gazi Üniversitesi Yayın No: 152, 1985.|