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Information
| Code | MT517 |
| Name | Vector Spaces |
| Term | 2024-2025 Academic Year |
| Term | Fall |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek 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
The aim of this course is introduce the basic concepts of algebra, understant the properties of algebra develop the ability to prove propositions.
Course Content
Learn some concepts about vectors and matrices, write a basis of a vector spaces and find the coordinates of the vectors, find dual and double dual spaces of a vector spaces, construct tha polynomial algebra and elemantary theorems about polynomials.
Course Precondition
None.
Resources
Linear Algebra , Kenneth Hoffman, Ray Kunze. Prentice Hall, Inc.
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learn basic concepts and the correspondence between vectors and matrices. |
| LO02 | Write a basis of a vector spaces and find the coordinates of the vectors, |
| LO03 | Find the dual and double dual spaces of vector spaces, find annihilator spaces. |
| LO04 | Construct polynomial algebra and say theorems about polynomials. |
| LO05 | Knowsthe determinant function and permutations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 1 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 1 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 3 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | 1 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 5 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Linear equations, matrices and the correspondence between systems and matrices. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 2 | Solving homogen and linear equations by using row-elementary. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 3 | Product matrices, non-singular matrices and Cramer System. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 4 | Vector spaces and subalgebras. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 5 | Basis, dimension and coordinates. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 6 | Linear functions and teh algbebra of linear functions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 7 | Isomorphisms and the representations of matrices. | 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 | Linear functionals, dual spacesi annihilators. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 10 | Double dual and the transpoze of linear functions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 11 | Construct of polynomial algebra, Lagrange Interpolation. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 12 | Ideals of polynomial algebras prime decomposition of the polynoms. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 13 | Commutative rings and determinant function. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 14 | Applications of determinants. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 15 | Permutations. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Lecture and problem solving | Yöntem Seçilmemiş |
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 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||