COURSE INFORMATON
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 Type
Course Coordinator Assoc.Prof.Dr. Dilek KAHYALAR
Instructors
Dr. Öğr. ÜyesiLEYLA BUGAY1. Öğretim Grup:A
Dr. Öğr. ÜyesiLEYLA BUGAY2. Öğretim Grup:A
 
Assistants
Goals
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.
Content
Matrix groups, Linear transformations which is determined by by matrix groups in an inner spaces

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 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
8 Mid-term exam Summary
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
16-17 Final exam

Recommended or Required Reading
Textbook
Additional Resources