MATZ212 Linear Algebra II

4 ECTS - 3-0 Duration (T+A)- 4. Semester- 3 National Credit

Information

Code MATZ212
Name Linear Algebra II
Term 2024-2025 Academic Year
Semester 4. Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 4 ECTS
National Credit 3 National Credit
Teaching Language Türkçe
Level Belirsiz
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. AYTEN PINAR BAL
Course Instructor
1


Course Goal / Objective

To build the foundations of geometry courses by enabling the student to learn basic topics such as vector spaces, linear independence and inner product spaces.

Course Content

Vector spaces, subspaces, linear independence, linear combinations; stretching, basis and dimension; linear transformations, kernel and image of a linear transformation; isomorphisms, eigenvalues and eigenvectors; characteristic polynomials; diagonalization, inner product spaces, orthogonality of vectors, orthonormal vector sets

Course Precondition

no prerequisites.

Resources

Bernard Kolman and David R. Hill. Applied Linear Algebra. Palme publishing

Notes

related digital resources


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Creates different examples of vector spaces.
LO02 Explains vector space and its relations with the concepts of subspace, linear dependence-independence, stretching, base.
LO03 Explain inner product space and write non-routine examples.
LO04 Write different sets of orthogonal and orthonormal vectors in the inner product space.
LO05 Define linear transformations on different vector spaces and identify kernel-image spaces.
LO06 Finds the matrix corresponding to a given linear transformation.
LO07 Diagonalizes a given matrix.


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Has enough knowledge about mathematics. 5
PLO02 Bilgi - Kuramsal, Olgusal Has pedagogical knowledge about teaching profession and field.
PLO03 Bilgi - Kuramsal, Olgusal Implements classroom management approaches to be used in educational environments effectively.
PLO04 Bilgi - Kuramsal, Olgusal Prepares the learning environments in which appropriate teaching methods are used for effective mathematics education in accordance with development and age levels.
PLO05 Bilgi - Kuramsal, Olgusal Knows the relationship between Mathematics-Society-Environment-History and uses it in professional and daily life.
PLO06 Bilgi - Kuramsal, Olgusal Uses Turkish properly and effectively according to the rules.
PLO07 Bilgi - Kuramsal, Olgusal Selects and designs appropriate materials, in mathematics teaching.
PLO08 Bilgi - Kuramsal, Olgusal Monitors students' progress using different assessment and evaluation methods and techniques.
PLO09 Bilgi - Kuramsal, Olgusal Takes responsibility as an individual and as a team member to solve problems related to the field.
PLO10 Beceriler - Bilişsel, Uygulamalı Has life-long learning awareness.
PLO11 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Shares his/her knowledge and skills, problems and solutions that he/she identified by means of oral and written communication with the expert and non-expert people.
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Uses information and communication technologies and other related materials for an effective mathematics teaching.
PLO13 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Has enough foreign language knowledge to follow foreign resources related to the field.
PLO14 Yetkinlikler - Öğrenme Yetkinliği Has the knowledge of the purpose, structure and functioning of the Turkish education system.
PLO15 Yetkinlikler - Öğrenme Yetkinliği Becomes a teacher who adheres to Atatürk's principles and revolutions.


Week Plan

Week Topic Preparation Methods
1 Vector spaces Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
2 The concepts of basis and dimension of vector space Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Tartışma, Gösterip Yaptırma
3 Sub-vector spaces Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
4 Linear functions Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
5 Matrix representations of linear transformations Examination of related resources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma
6 Kernel and image of a linear transformation Examination of related resources Öğretim Yöntemleri:
Alıştırma ve Uygulama, Gösterip Yaptırma, Anlatım
7 Rank-zero theorem and its applications Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
8 Mid-Term Exam exam preparation Ölçme Yöntemleri:
Yazılı Sınav
9 Inner product spaces Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
10 Inner product spaces 2 Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
11 Orthogonality of vectors, orthonormal vector sets Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
12 Eigenvalues and Eigenvectors Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
13 Diagonalization Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
14 Diagonalization 2 Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
15 General review Examination of related resources Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma
16 Term Exams exam preparation Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams exam preparation Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 2 28
Out of Class Study (Preliminary Work, Practice) 14 2 28
Assesment Related Works
Homeworks, Projects, Others 1 0 0
Mid-term Exams (Written, Oral, etc.) 1 8 8
Final Exam 1 24 24
Total Workload (Hour) 88
Total Workload / 25 (h) 3,52
ECTS 4 ECTS

Update Time: 14.05.2024 02:05