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Information
| Code | MAT112 |
| Name | Linear Algebra - II |
| Term | 2023-2024 Academic Year |
| Semester | 2. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Dr. Öğr. Üyesi ELA AYDIN |
| Course Instructor |
Dr. Öğr. Üyesi ELA AYDIN
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
To give insight and skill about the concrete aspects of the abstract linear algebra,
Course Content
The contents of this course A base of vector space and its dimension, inner products spaces , understand the relation between matrices and linear transformation, determine eigenvalue and eigenvector and find similar matrices.
Course Precondition
None.
Resources
Arif Sabuncuoğlu, Lineer Cebir, Nobel yayın dağıtım,2000.
Notes
Bernard Kolman, David R. Hill, Lineer Cebir, ((Translation) Palme Yayıncılık Press,2000.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Find a base and dimension of vector space. |
| LO02 | Understands linear transformation and their properties. |
| LO03 | Write a matrix form for a linear transformation. |
| LO04 | Calculate the length and angle using inner product the orthogonal complement of a space. |
| LO05 | Determine eigenvalue and related eigenvector. |
| LO06 | Write similar matrices and diagonal matrices. |
| LO07 | Do different applications of determinants. |
| LO08 | Calculate the rank of a matrix. |
| LO09 | Calculate with complex numbers in linear algebra and solve the systems. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the essence fundamentals and concepts in the field of Probability, Statistics and Mathematics | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Emphasize the importance of Statistics in life | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Define basic principles and concepts in the field of Law and Economics | 2 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Produce numeric and statistical solutions in order to overcome the problems | 1 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use proper methods and techniques to gather and/or to arrange the data | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Utilize computer systems and softwares | 1 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Construct the model, solve and interpret the results by using mathematical and statistical tehniques for the problems that include random events | 1 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Apply the statistical analyze methods | 1 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Make statistical inference(estimation, hypothesis tests etc.) | 1 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Generate solutions for the problems in other disciplines by using statistical techniques | 1 |
| PLO11 | Bilgi - Kuramsal, Olgusal | Discover the visual, database and web programming techniques and posses the ability of writing programme | 1 |
| PLO12 | Bilgi - Kuramsal, Olgusal | Construct a model and analyze it by using statistical packages | 3 |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Distinguish the difference between the statistical methods | 1 |
| PLO14 | Beceriler - Bilişsel, Uygulamalı | Be aware of the interaction between the disciplines related to statistics | 2 |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Make oral and visual presentation for the results of statistical methods | 4 |
| PLO16 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have capability on effective and productive work in a group and individually | 3 |
| PLO17 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs | 3 |
| PLO18 | Yetkinlikler - Öğrenme Yetkinliği | Develop scientific and ethical values in the fields of statistics-and scientific data collection |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Linear functions, one to one and onto functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 2 | Kernel and images of linear functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 3 | Matrices of linear transformations | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 4 | equvalences of matrices | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 5 | Sthandard inner product in space and plane | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 6 | Inner products and orthogonality | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 7 | Gramm-Schmidt orthogonalization | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Eigenvalues and eigenvectors | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 10 | Diagonalization and triangularization of matrices | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 11 | Diagonalization of symetric matrices | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 12 | Determinant function applications | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 13 | Rank of matrices | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 14 | Complex numbers in Linear algebra | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 15 | Solving problems, final exam | Review of the relevant pages from sources | Öğretim Yöntemleri: Problem Çözme |
| 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 | 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 | 7 | 7 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 109 | ||
| Total Workload / 25 (h) | 4,36 | ||
| ECTS | 4 ECTS | ||