TÜRKÇE
ENGLISH
Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (MASTER) (WITH THESIS) | |
| Code | MT575 |
| Name | Free Algebras and PI Algebras II |
| Term | 2026-2027 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 | Belirsiz |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ŞEHMUS FINDIK |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
The aim of this course is to teach Grassmann algebras and their polynomial identities, algebras of upper triangular matrices and their polynomial identities, polynomial algebras and their automorphisms, free associative algebras and their automorphisms, and free Lie algebras and their automorphisms.
Course Content
The primary focus of this course includes Grassmann algebras and their polynomial identities, algebras of upper triangular matrices and their polynomial identities, polynomial algebras and their automorphisms, free associative algebras and their automorphisms, and free Lie algebras and their automorphisms.
Course Precondition
None
Resources
Free algebras and PI-algebras: graduate course in algebra, 2000, V. Drensky
Notes
PI-algebras, 2006, N. Jacobson
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learns the polynomial identities of Grassmann algebras. |
| LO02 | Learns the polynomial identities of upper triangular matrix algebras. |
| LO03 | Learns automorphisms of polynomial algebras. |
| LO04 | Learns automorphisms of free associative algebras. |
| LO05 | Learns automorphisms of free Lie algebras. |
| LO06 | Learns automorphisms of free metabelian Lie algebras. |
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. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his 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. | |
| 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. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 5 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 5 |
| 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. | 4 |
| 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. | |
| 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. | 5 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Grassmann algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 2 | Polynomial identities of Grassmann algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 3 | Upper triangular matrix algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 4 | Polynomial identities of upper triangular matrix algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 5 | Polynomial algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 6 | Automorphisms of polynomial algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 7 | Problem solving | Reading the lecture notes | Öğretim Yöntemleri: Soru-Cevap |
| 8 | Mid-Term Exam | Reading the lecture notes | Öğretim Yöntemleri: Soru-Cevap |
| 9 | Free associative algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 10 | Automorphisms of free associative algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 11 | Free Lie algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 12 | Automorphisms of free Lie algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 13 | Free metabelian Lie algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 14 | Automorphisms of free metabelian Lie algebras | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 15 | Repetition of topics | Reading the lecture notes | Öğretim Yöntemleri: Soru-Cevap |
| 16 | Term Exams | Reading the lecture notes | Öğretim Yöntemleri: Soru-Cevap |
| 17 | Term Exams | Reading the lecture notes | Öğretim Yöntemleri: Soru-Cevap |
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 | ||