COURSE INFORMATON
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 Type
Course Coordinator Dr. Lec. Uyesi Ela AYDIN
Instructors
Dr. Öğr. ÜyesiELA AYDIN1. Öğretim Grup:A
Dr. Öğr. ÜyesiELA AYDIN2. Öğretim Grup:A
 
Assistants
Goals
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.
Content
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.

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
10
Uses effective scientific methods and appropriate technologies to solve problems
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
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
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
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
TextbookProf. Dr. H. Hilmi HACISALİHOĞLU," Lineer Cebir", Gazi Üniversitesi Yayın No: 152, 1985.
Additional Resources