MT516 Vector Spaces II

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code MT516
Name Vector Spaces II
Term 2024-2025 Academic Year
Semester . Semester
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 Prof. Dr. GONCA AYIK


Course Goal / Objective

The aim of this course is to provide students with the ability to use mathematical reasoning and basic mathematical theories to solve various problems.

Course Content

In this course determinant functions, properties of determinants, eigenvalue and eigenvector, annihilating polynomials and invariant subspaces, triangulation and diagonalization, direct-sum decompositions, invariant direct sums and the primary decomposition theorem, cyclic subspaces and annihilators, cyclic decompositions and rational form, Jordan form, inner products, inner product spaces, orthogonal and orthogonal complement are described.

Course Precondition

None.

Resources

Linear Algebra , Kenneth Hoffman, Ray Kunze. Prentice Hall, Inc.

Notes

Lecture Notes


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Realizes determinant function and properties.
LO02 Realizes the applications of determinant function.
LO03 Realizes eigenvalues and eigenvectors.
LO04 Realizes annihilating polynomials and invariant subspaces.
LO05 Realizes triangulation and diagonalization.
LO06 Realizes direct-sum decompositions.
LO07 Realizes invariant direct sums and the primary decomposition theorem.
LO08 Realizes cyclic subspaces and annihilators.
LO09 Realizes cyclic decompositions and rational form.
LO10 Realizes Jordan form
LO11 Realizes inner products.
LO12 Realizes inner product spaces.
LO13 Realizes orthogonal and orthogonal complement.


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. 4
PLO02 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in his area of ​​expertise and other areas of mathematics. 4
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. 3
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.
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. 5
PLO09 Bilgi - Kuramsal, Olgusal Analyzes existing mathematical theories and develops new theories. 4
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. 4
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 Determinant function and properties Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
2 The applications of determinant function Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
3 Eigenvalues and eigenvectors Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
4 Annihilating polynomials and invariant subspaces Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
5 Triangulation and diagonalization Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
6 Direct-sum decompositions Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
7 Invariant direct sums Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
8 Mid-Term Exam Lecture and problem solving Ölçme Yöntemleri:
Yazılı Sınav
9 The primary decomposition theorem Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
10 Cyclic subspaces and annihilators Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
11 Jordan form Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
12 Inner product Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
13 Inner product spaces Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
14 Orthogonal Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
15 Orthogonal complement Reviewing the relevant chapters in the sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
16 Term Exams Lecture and problem solving Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Lecture 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 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

Update Time: 09.05.2024 11:37