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Information
| Code | MT555 |
| Name | Computational Group Theory I |
| Term | 2024-2025 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 |
1 |
Course Goal / Objective
Study Proportions of some elamantary groups and some free grop constructions
Course Content
Basic Definitions, Group Actions, Group presentations, Abelian Group presentations,Represantation Theory,Moduls,Field Theory
Course Precondition
Yok
Resources
Computation with Finitely Presented Groups Charles C. SIMS
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Notions basic definitions |
| LO02 | Learns information representation of groups |
| LO03 | Makes calculate on finitely permutation groups |
| LO04 | Makes Coset Enumerations |
| LO05 | Knows Group presentations |
| LO06 | Learns Represantation Theory, Cohomology and characters |
| LO07 | Makes calculate by Polycyclic Groups |
| LO08 | Knows how calculate finitely presented groups |
| LO09 | Make advances calculate on finitely groups |
| LO10 | Learns Rewriting System |
| LO11 | Learns Automoto and automatic groups |
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. | 4 |
| 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 | 3 |
| 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 | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | 4 |
| 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. | |
| 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. | 5 |
| 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 | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Basic definitions, Group Effects, Group Presentations, Semitic Presentations, Abelyen Group Presentations | Lecture Discussion | |
| 2 | Represantation Theory | Lecture Discussion | |
| 3 | Computer Representation of Groups, Use of Random Methods in Computable Groups, Calculations with Homomorphisms | Lecture Discussion | |
| 4 | Calculation of orbits and stabilizers, Schreier vectors, Block system generation, base and generator sets | Lecture Discussion | |
| 5 | Simple methods, Koset calculation strategies, Subgroup presentations, Group presentations | Lecture Discussion | |
| 6 | To find presentation of a group, Todd-Coxeter-Schreier-Sims Algorithm | Lecture Discussion | |
| 7 | Calculations in finite fields, Cohomology, Character Table Calculation | Lecture Discussion | |
| 8 | Mid-Term Exam | Lecture Discussion | |
| 9 | Polycyclic presentation | Lecture Discussion | |
| 10 | Finitely automorphism Groups | Lecture Discussion | |
| 11 | Some useful subgroups, Calculation compositions and Chief Series, Soluble radical method applications | Lecture Discussion | |
| 12 | Monoid presentations, Rewriting Systems | Lecture Discussion | |
| 13 | Rewriting Systems on Monoid and Groups | Lecture Discussion | |
| 14 | Finitely automoto, Finitely automoto operations | Lecture Discussion | |
| 15 | Automatic Groups | 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 | ||