MT555 Computational Group Theory I

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code MT555
Name Computational Group Theory I
Term 2024-2025 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 Doktora Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. ZERRİN GÜL ESMERLİGİL


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 Öğretim Yöntemleri:
Anlatım, Tartışma
2 Represantation Theory Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
3 Computer Representation of Groups, Use of Random Methods in Computable Groups, Calculations with Homomorphisms Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
4 Calculation of orbits and stabilizers, Schreier vectors, Block system generation, base and generator sets Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
5 Simple methods, Koset calculation strategies, Subgroup presentations, Group presentations Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
6 To find presentation of a group, Todd-Coxeter-Schreier-Sims Algorithm Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
7 Calculations in finite fields, Cohomology, Character Table Calculation Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
8 Mid-Term Exam Lecture Discussion Ölçme Yöntemleri:
Yazılı Sınav
9 Polycyclic presentation Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
10 Finitely automorphism Groups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
11 Some useful subgroups, Calculation compositions and Chief Series, Soluble radical method applications Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
12 Monoid presentations, Rewriting Systems Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
13 Rewriting Systems on Monoid and Groups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
14 Finitely automoto, Finitely automoto operations Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
15 Automatic Groups Lecture Discussion Öğretim Yöntemleri:
Anlatım, Tartışma
16 Term Exams Lecture Discussion Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Lecture Discussion 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

Update Time: 09.05.2024 11:39