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Information
| Code | MT006 |
| Name | special topics in lie algebras |
| Term | 2024-2025 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. ZEYNEP ÖZKURT |
| Course Instructor |
1 |
Course Goal / Objective
The aim of this course is to develop students' ability to make various calculations on varieties by allowing them to recognize varieties.
Course Content
Variational theory, finite base problem, algebras over commutative and unitary rings, finite Lie rings
Course Precondition
no
Resources
Jacobson, Lie Algebras
Notes
Karin Erdman, Mark Wildon Introduction to Lie Algebras
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understand and use the theory of variation. |
| LO02 | As an important tool can form the product of varieties. |
| LO03 | Can prove the finite base problem by using important techniques related to partial ordered sets. |
| LO04 | Learns the existence of various varieties |
| LO05 | Knows the structure of algebras on the unit elements and commutative rings. |
| LO06 | Learn to use different techniques to prove finite base properties. |
| LO07 | Learn how to use different techniques to solve finite base problem of finite Lie rings. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows the results of previous research in a special field of mathematics | 2 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 2 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 3 |
| 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. | 2 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | It carries out original and qualified scientific studies on the subject related to its field. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | |
| 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. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have foreign language knowledge at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 3 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | It presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Homogeneous structures in free Lie algebras, representations of symmetric group | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 2 | Alphabetic order, frobenius algebras and modules | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 3 | Structure of the Ln (V) module | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 4 | Identity relations and variants | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 5 | Free algebra of multiple homogeneous varieties, independent identities system | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 6 | Product of varieties, Basic definitions | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 7 | Embedded theorems, free algebras of varieties | Study pages related to the subject in source books. | Ölçme Yöntemleri: Yazılı Sınav |
| 8 | Mid-Term Exam | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 9 | Subalgebras of variants, metabelian varieties | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 10 | Young diagrams | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 11 | Semivarieties | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 12 | Finite base problem, definition of problem | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 13 | A generalization of Hilbert's base theorem, examples of non-finite varieties | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 14 | Special Lie algebras | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 15 | Special Lie algebras1 | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 16 | Exercises | Study pages related to the subject in source books. | Öğretim Yöntemleri: Anlatım |
| 17 | Term Exams | Study pages related to the subject in source books. | 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 | ||