TÜRKÇE
ENGLISH
Information
| Code | MT211 |
| Name | Algebra I |
| Semester | 3. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 7 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ |
Course Goal
The objectives of this course are to introduce the students with the basic ideas of linear algebra including vector spaces, subspaces, basis, dimension, linear transformations, matrices, systems of linear equations, eigenvalues and eigenvectors and to teach the understanding of abstract mathematical concepts and abstract thought arising from the concepts covered in this course.
Course Content
Vectors in the plane and space; vector spaces, subspaces, linear dependence, bases and finite dimensional vector spaces, linear transformations, matrices, representation of linear transformations by matrices, direct sum, systems of linear equations, determinants, characteristic vectors and diagonalization.
Course Precondition
No
Resources
Linear Algebra, Author:Larry Smith, Linear Algebra, Author:Jim Hefferon
Notes
Linear Algebra, Author:Arif Sabuncuoğlu
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Explain basic definition in linear algebra. |
| LO02 | Learn the concept of vector spaces, sub spaces, basis and dimension. |
| LO03 | Learns the concept of basis. |
| LO04 | Evaluate linear transformations. |
| LO05 | Compute matrix representations of a linear transformation. |
| LO06 | Solves systems of linear equations. |
| LO07 | Computes determinants. |
| LO08 | Find eigen values and the corresponding eigen vectors of a linear transformation. |
| LO09 | Develops knowledge and skills in linear algebra. |
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. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 5 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 5 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to express the basic theories of mathematics both correctly. | 5 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 4 |
| 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. | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 5 |
| 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. | 4 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| 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. | 3 |
| 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. | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Vector space, subspace | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Linear dependence, independence and a basis of a vector space | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Basic properties of a basis and dimension of a vector space | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Sum of subspaces, direct sum | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Linear transformations, their kernels and images | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | The rank of a linear transformation, isomorphism | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Matrices | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Representation of linear transformations by matrices | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | The rank of a matrix, echelon matrix | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Row equivalent matrices and systems of linear equations | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Determinant function, properties of determinant, evaluation of determinant | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Cramer Rule, eigen values and eigen vectors | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Characteristic spaces and characteristic polynomial | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Solving problems | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 6 | 84 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 164 | ||
| Total Workload / 25 (h) | 6,56 | ||
| ECTS | 7 ECTS | ||