MT517 Vector Spaces

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

Information

Code MT517
Name Vector Spaces
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 Dr. Öğr. Üyesi ELA AYDIN


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

Update Time: 09.05.2024 11:37