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Information
| Code | IEM718 |
| Name | Numerical Linear Algebra |
| Term | 2022-2023 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 | Doç. Dr. ERSİN KIRAL |
Course Goal / Objective
To give insight and skill about the concrete aspects of linear algebra,To provide basic concepts of matrices and the systems of homogeny and linear equations,To solve the systems using matrices,To teach vector spaces and abstract mathematical concepts,To teach abstract thought
Course Content
Review of the basic concepts of the group theory from undergraduate-level , categories, free products, free objects, free abelian groups, finitely generated Abelian groups, classification of finite groups , Normal series, Nilpotent and solvable groups.
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Defines the concepts Semigroup, Monoid and group . |
| LO02 | Defines the group homomorphism and , knows subgroup,some special groups and their properties |
| LO03 | Knows in detail the structure of normal subgroups cosets and quotient groups |
| LO04 | Express and proves the isomorphism theorems for groups Knows the concepts of freee groups, free abelian groups, finitely generated abelian groups |
| LO05 | Knows the action of a group on a set and classification of finite groups of low order |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explains contemporary concepts about Econometrics, Statistics, and Operation Research | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Explains relationships between acquired knowledge about Econometrics, Statistics, and Operation Research | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Explains how to apply acquired knowledge in the field to Economics, Business, and other social sciences | |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Performs conceptual analysis to develop solutions to problems | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Models problems with Mathematics, Statistics, and Econometrics | |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Interprets the results obtained from the most appropriate method to predict the model | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Synthesizes the information obtained by using different sources within the framework of academic rules in a field that does not research | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution | |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Searches for new approaches and methods to solve problems being faced | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Presents analysis results conveniently | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Collects/analyzes data in a purposeful way | |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Converts its findings into a master's thesis or a professional report in Turkish or a foreign language | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Develops solutions for organizations using Econometrics, Statistics, and Operation Research | |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Performs an individual work to solve a problem with Econometrics, Statistics, and Operation Research | |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads by taking responsibility individually and/or within the team | |
| PLO16 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning, it constantly renews itself by following the current developments in the field of study | |
| PLO17 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a package program of Econometrics, Statistics, and Operation Research or writes a new code | |
| PLO18 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Interprets the feelings, thoughts and behaviors of the related persons correctly/expresses himself/herself correctly in written and verbal form | |
| PLO19 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on economic and social events by following current issues | |
| PLO20 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to basic concepts that will be needed in the group theory | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 2 | Semigroup, monoid, group and homomorphisms of groups | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 3 | Cyclic groups, cosets and counting | Reviewing the relevant chaptes in the Sources | |
| 4 | Normal subgroups and quotient groups | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 5 | Symmetric, Alternating and dihedral groups | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 6 | Categories | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 7 | Free objects in the category of groups, generators and relations | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Reviewing the relevant chaptes in the Sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Free abelian groups | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 10 | Finitely generated abelian groups | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 11 | Action of a group on a set | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 12 | Sylow Theorems | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 13 | Classification of finite groups of low order. | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 14 | Normal series | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 15 | Nilpotent and solvable grops | Reviewing the relevant chaptes in the Sources | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Reviewing the relevant chaptes in the Sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Reviewing the relevant chaptes in the Sources | Ölçme Yöntemleri: Yazılı Sınav |