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Information
| Unit | FACULTY OF EDUCATION |
| ELEMENTARY MATHEMATICS EDUCATION PR. | |
| 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 |
| Label | FE Field Education Courses C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. AYTEN PINAR BAL |
| Course Instructor |
Dr. Öğr. Üyesi Emrah KORKMAZ
(Bahar)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The purpose of this course is to ensure that students learn the basic concepts and theorems of the topics in the course content that form the foundations of linear algebra. By applying their theoretical knowledge to practical problems, students will discover the importance of linear algebra in various scientific fields.
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, orthonormal vector sets Gram-Schmidt process will also be covered.
Course Precondition
no prerequisites.
Resources
1-) Anton, H., & Rorres, C. (2010). Elementary Linear Algebra: Applications Version. John Wiley & Sons. 2-) Lang, S. (1987). Linear Algebra. Springer. 3-) Hoffman, K. M., & Kunze, R. A. (1971). Linear Algebra. Prentice Hall. SUPPLEMENTARY BOOKS: 1-) Kolman, B., & Hill, D. R. (1996). Introductory Linear Algebra with Applications. Prentice Hall. 2-) Koç, C. (1995). Basic Linear Algebra. Matematik Vakfı.
Notes
related digital resources
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understands the fundamental properties of vector spaces and subspaces. |
| LO02 | Understands and applies the concepts of linear independence, linear combination, and span. |
| LO03 | Can determine the basis and dimension of a vector space. |
| LO04 | Understands linear transformations and can determine the kernel and image spaces of a linear transformation. |
| LO05 | Learns the concept of isomorphism and evaluates the structural similarities between vector spaces. |
| LO06 | Calculates eigenvalues and eigenvectors, and performs diagonalization of matrices using the characteristic polynomial. |
| LO07 | Examines the orthogonality of vectors in inner product spaces and can construct orthonormal bases. |
| LO08 | Can orthonormalize a set of vectors using the Gram-Schmidt process. |
| LO09 | Applies the theoretical foundations of linear algebra to practical problems. |
| LO10 | Discovers the importance of linear algebra in other scientific fields with the knowledge gained. |
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. | 3 |
| 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. | 3 |
| 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. | 2 |
| 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 space definition and properties. | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 2 | Subvector spaces. | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Tartışma, Gösterip Yaptırma |
| 3 | Linear independence and span. | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 4 | Basis and dimension. | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 5 | Coordinates, change of basis, and direct sums. | 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, Nullity, and Fundamental Matrix Subspaces. | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 8 | Mid-Term Exam | exam preparation | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Linear transformations and their properties. | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 10 | Image and kernel spaces, isomorphisms. | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 11 | Matrices for linear transformations. | 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 | Inner Product Spaces. | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 15 | Norm, Orthogonality, and the Gram-Schmidt Process. | 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 |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 50 | 20 |
| 1. Short Exam | 25 | 10 |
| 2. Short Exam | 25 | 10 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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.) | 3 | 8 | 24 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 104 | ||
| Total Workload / 25 (h) | 4,16 | ||
| ECTS | 4 ECTS | ||