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Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (PhD) | |
| Code | MT569 |
| Name | Topics in Lie Algebras |
| Term | 2018-2019 Academic Year |
| Term | Fall |
| 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 | Prof. Dr. ZERRİN GÜL ESMERLİGİL |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
The aim of this course is to enable students to learn Lie algebras and their applications that provide identity relations.
Course Content
Rings, Modules, Algebras, Semi-Product Multiplication, Direct Total, Ideals Series, Lie algebra on modules, semisimple series, Nilpotent Lie algebras, Soluble Lie algebras, Free algebra, Free Lie algebra
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learn to explain the theory of Lie algebras in a modern way. |
| LO02 | Learns the existence of Lie algebras which have a relation of identity. |
| LO03 | Perform the Lie algebras which have a relation of identity. |
| LO04 | Knows the structure of algebras on the unit elements and commutative rings. |
| LO05 | Learn the proof techniques of some important results by using series of ideals in Lie algebras. |
| LO06 | Understands the concept of freedom, basics of free Lie algebras. |
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 | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics | |
| 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. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | |
| PLO08 | Bilgi - Kuramsal, Olgusal | It carries out original and qualified scientific studies on the subject related to its field. | |
| 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. | 3 |
| 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. | |
| 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. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Rings, Moduls, Fields | Lecture Discussion | |
| 2 | Semidirect multiplies, Direct sums, ideal series | Lecture Discussion | |
| 3 | Moduls, Modul on Lie algebras,semibasic series | Lecture Discussion | |
| 4 | Nilpotent Lie algebras, Frattini subalgebras, endomorfizm of Nilpotent Lie algebras | Lecture Discussion | |
| 5 | Solvable Lie algebras, Engel Lie algebras | Lecture Discussion | |
| 6 | Frattini Teory for Lie algebras, Graded algebras | Lecture Discussion | |
| 7 | Homogen subalgebras, Restricted Lie algebras | Lecture Discussion | |
| 8 | Mid-Term Exam | Lecture Discussion | |
| 9 | Free groupoid | Lecture Discussion | |
| 10 | Free algebras,Free Lie algebras | Lecture Discussion | |
| 11 | Free asosociative algebras, | Lecture Discussion | |
| 12 | Basis of Free Lie algebras | Lecture Discussion | |
| 13 | Subalgebras of Free Lie algebras | Lecture Discussion | |
| 14 | Free generators, Universal enveloping algebras and Poincare- Birkhof- Witt Theorems | Lecture Discussion | |
| 15 | Free Decomposition | Lecture Discussion | |
| 16 | Term Exams | Lecture Discussion | |
| 17 | Term Exams | Lecture Discussion |
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 | ||