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Information
| Code | MT516 |
| Name | Vector Spaces II |
| Term | 2024-2025 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GONCA AYIK |
| Course Instructor |
1 |
Course Goal / Objective
The aim of this course is to provide students with the ability to use mathematical reasoning and basic mathematical theories to solve various problems.
Course Content
In this course determinant functions, properties of determinants, eigenvalue and eigenvector, annihilating polynomials and invariant subspaces, triangulation and diagonalization, direct-sum decompositions, invariant direct sums and the primary decomposition theorem, cyclic subspaces and annihilators, cyclic decompositions and rational form, Jordan form, inner products, inner product spaces, orthogonal and orthogonal complement are described.
Course Precondition
None.
Resources
Linear Algebra , Kenneth Hoffman, Ray Kunze. Prentice Hall, Inc.
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Realizes determinant function and properties. |
| LO02 | Realizes the applications of determinant function. |
| LO03 | Realizes eigenvalues and eigenvectors. |
| LO04 | Realizes annihilating polynomials and invariant subspaces. |
| LO05 | Realizes triangulation and diagonalization. |
| LO06 | Realizes direct-sum decompositions. |
| LO07 | Realizes invariant direct sums and the primary decomposition theorem. |
| LO08 | Realizes cyclic subspaces and annihilators. |
| LO09 | Realizes cyclic decompositions and rational form. |
| LO10 | Realizes Jordan form |
| LO11 | Realizes inner products. |
| LO12 | Realizes inner product spaces. |
| LO13 | Realizes orthogonal and orthogonal complement. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 1 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 5 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 4 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | 1 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 4 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Determinant function and properties | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | The applications of determinant function | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Eigenvalues and eigenvectors | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Annihilating polynomials and invariant subspaces | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Triangulation and diagonalization | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Direct-sum decompositions | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Invariant direct sums | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Lecture and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The primary decomposition theorem | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Cyclic subspaces and annihilators | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Jordan form | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Inner product | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Inner product spaces | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Orthogonal | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Orthogonal complement | Reviewing the relevant chapters in the sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Term Exams | Lecture and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Lecture and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||