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Information
| Code | MATZ212 |
| Name | Linear Algebra II |
| Term | 2024-2025 Academic Year |
| Semester | 4. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Belirsiz |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. AYTEN PINAR BAL |
| Course Instructor |
1 |
Course Goal / Objective
To build the foundations of geometry courses by enabling the student to learn basic topics such as vector spaces, linear independence and inner product spaces.
Course Content
This course covers basic linear algebra concepts such as vector spaces and subspaces, linear independence and linear combinations. The structure and properties of vector spaces will be analyzed by detailing stretching, basis and dimension. Linear transformations, kernel and image of these transformations, the concept of isomorphism, eigenvalues and eigenvectors will be introduced. Characteristic polynomials, diagonalization of matrices, inner product spaces, orthogonality of vectors and orthonormal vector sets will also be covered.
Course Precondition
no prerequisites.
Resources
Bernard Kolman and David R. Hill. Applied Linear Algebra. Palme publishing
Notes
related digital resources
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Creates different examples of vector spaces. |
| LO02 | Explains vector space and its relations with the concepts of subspace, linear dependence-independence, stretching, base. |
| LO03 | Explain inner product space and write non-routine examples. |
| LO04 | Write different sets of orthogonal and orthonormal vectors in the inner product space. |
| LO05 | Defines linear transformations on different vector spaces |
| LO06 | Finds the matrix corresponding to a given linear transformation. |
| LO07 | Diagonalizes a given matrix. |
| LO08 | Determine kernel-image spaces on different vector spaces. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has enough knowledge about mathematics. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Has pedagogical knowledge about teaching profession and field. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Implements classroom management approaches to be used in educational environments effectively. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Prepares the learning environments in which appropriate teaching methods are used for effective mathematics education in accordance with development and age levels. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Knows the relationship between Mathematics-Society-Environment-History and uses it in professional and daily life. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Uses Turkish properly and effectively according to the rules. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Selects and designs appropriate materials, in mathematics teaching. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Monitors students' progress using different assessment and evaluation methods and techniques. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Takes responsibility as an individual and as a team member to solve problems related to the field. | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Has life-long learning awareness. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Shares his/her knowledge and skills, problems and solutions that he/she identified by means of oral and written communication with the expert and non-expert people. | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Uses information and communication technologies and other related materials for an effective mathematics teaching. | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Has enough foreign language knowledge to follow foreign resources related to the field. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Has the knowledge of the purpose, structure and functioning of the Turkish education system. | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Becomes a teacher who adheres to Atatürk's principles and revolutions. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Vector spaces | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 2 | The concepts of basis and dimension of vector space | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Tartışma, Gösterip Yaptırma |
| 3 | Sub-vector spaces | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 4 | Linear functions | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 5 | Matrix representations of linear transformations | Examination of related resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 6 | Kernel and image of a linear transformation | Examination of related resources | Öğretim Yöntemleri: Alıştırma ve Uygulama, Gösterip Yaptırma, Anlatım |
| 7 | Rank-zero theorem and its applications | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 8 | Mid-Term Exam | exam preparation | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Inner product spaces | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 10 | Inner product spaces 2 | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 11 | Orthogonality of vectors, orthonormal vector sets | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 12 | Eigenvalues and Eigenvectors | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 13 | Diagonalization | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 14 | Diagonalization 2 | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 15 | General review | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 16 | Term Exams | exam preparation | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | exam preparation | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 2 | 28 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 2 | 28 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 1 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 88 | ||
| Total Workload / 25 (h) | 3,52 | ||
| ECTS | 4 ECTS | ||