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Information
| Code | MT401 |
| Name | Introduction to Matrix Theory |
| Term | 2024-2025 Academic Year |
| Semester | 7. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. DİLEK KAHYALAR |
| Course Instructor |
Doç. Dr. DİLEK KAHYALAR
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
To teach the matrix theory which is used in various areas of mathematics and to demostrate the ways in which it is used.
Course Content
Matrix operations. Determinants and properties of determinants. Rank of a matrix, Equivalent matrices. Similar matrices. Elementary row (column) operations. Elementary matrices. Adjoint of a matrix. Inverse of a matrix. Solution of the system of linear equations. Canonical forms. Quadratic form. Bilinear form.
Course Precondition
none
Resources
Matrix Operations Schamus's Series
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | It bases the mathematical knowledge taught in Secondary Education on theoretical foundations. |
| LO02 | Knows the importance of basic notions in Algebra, Analysis and Topology |
| LO03 | Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
| LO04 | Is able to express basic theories of mathematics properly and correctly both written and verbally |
| LO05 | Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
| LO06 | Expresses clearly the relationship between objects while constructing a model |
| LO07 | Knows the mathematical models such as formulas and graphs. |
| LO08 | Knows the mathematics models such as table and diagram. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | 4 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 3 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | 3 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 3 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 3 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 4 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 3 |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 3 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 2 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Basic matrix operations | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 2 | Determinants of matrices | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 3 | Minors and cofactors | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 4 | Equivalence of matrices | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 5 | Adjoint and its properties | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 6 | Equivalent Matrices | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 7 | Inverse of a Matrix | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Solution of Linear Equations Systems using matrices | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 10 | LU Decomposition | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 11 | Biliner forms | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 12 | Canonical forms | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 13 | Matrix functions | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | Generalized inverses | Reading the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Solving problems | Review and problem solving | Öğretim Yöntemleri: Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 16 | Term Exams | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review 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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||