| Course Description |
|
| Course Name |
: |
Algebra IV |
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| Course Code |
: |
MT 312 |
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| Course Type |
: |
Compulsory |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
3 |
|
| Course Semester |
: |
Spring (16 Weeks) |
|
| ECTS |
: |
5 |
|
| Name of Lecturer(s) |
: |
Assoc.Prof.Dr. AHMET TEMİZYÜREK
|
|
| Learning Outcomes of the Course |
: |
Defines inner product spaces and gives example.
Is able to find the orthogonal basis of a finite dimensional vector space.
Defines the orthogonal complement of a subspace and solves examples.
Demonstrates that linear transformations of a vector space defines an algebra.
Defines the concepts of eigenvalues and eigenvectors of a linear transformation and shows that the set of eigenvectors is linearly independent .
Defines the minimal polynomial of a linear transformation and shows that each eigenvalues is a root of the minimal polynomial of linear transformation
Is able to determine whether a linear transformation is diagonalizable or not.
Defines the algebraic structure of a module and simply represents the properties.
Defines the concept of field extension and can construct algebraic extension.
|
|
| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
The aim of this course is to teach the inner product spaces and some properties of the algebra of linear transformations and introduce the concepts of Module and field. |
|
| Course Contents |
: |
Real inner product spaces, Complex inner product spaces, Algebra of linear transformations, fied extensions, Modules |
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Art and Science Faculty Annex Classrooms |
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|
Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Inner product spaces and their properties |
Review of the relevant pages from sources |
Lecture and discussion |
|
2 |
Gram-Schmidt orthogonalization methods |
Review of the relevant pages from sources |
Lecture and discussion |
|
3 |
Complex inner product spaces |
Review of the relevant pages from sources |
Lecture and discussion |
|
4 |
Algebra of linear mappings |
Review of the relevant pages from sources |
Lecture and discussion |
|
5 |
Invertible and singular mappings |
Review of the relevant pages from sources |
Lecture and discussion |
|
6 |
Matrices of linear mappings |
Review of the relevant pages from sources |
Lecture and discussion |
|
7 |
Characteristic value and characteristic vectors |
Review of the relevant pages from sources |
Lecture and discussion |
|
8 |
Mid-term exam |
Review the topics discussed in the lecture notes and sources |
Written exam |
|
9 |
Diagonalizable and nondiagonalizable linear mappings |
Review of the relevant pages from sources |
Lecture and discussion |
|
10 |
Definition of a module and its properties |
Review of the relevant pages from sources |
Lecture and discussion |
|
11 |
Submodule and direct sum of modules |
Review of the relevant pages from sources |
Lecture and discussion |
|
12 |
Homomorphisms of module |
Review of the relevant pages from sources |
Lecture and discussion |
|
13 |
Field extensions |
Review of the relevant pages from sources |
Lecture and discussion |
|
14 |
Simple extension |
Review of the relevant pages from sources |
Lecture and discussion |
|
15 |
Degree of an extension |
Review of the relevant pages from sources |
Lecture and discussion |
|
16/17 |
Final exam |
Review the topics discussed in the lecture notes and sources |
written exam |
|
|
|
Required Course Resources |
| Resource Type | Resource Name |
| Recommended Course Material(s) |
 F. Başar, Lineer Cebir, ugurel printing house, 2002 ,Malatya
R. Kaya, Lieer Cebir, Anadolu Üniversity press, Eskişehir.
|
| |
| Required Course Material(s) |
P.B.Bhattachary, basic abstract algebra,Cambridge university press.
R. Kunze, Linear algebra, Prentice-Hall Inc. New Jersey.
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
1 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
4 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
4 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
5 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
0 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
2 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
4 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
2 |
|
9 |
Knows at least one computer programming language |
0 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
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 |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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