MT002 Introduction to Invariant Theory

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

Information

Code MT002
Name Introduction to Invariant Theory
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. ŞEHMUS FINDIK


Course Goal / Objective

Learning basic knowledge about invariant theory and observing its some applications.

Course Content

Introduction to invariant theory, Symmetric polynomials, Gröbner bases, invariant theory of finite groups, invariants of general linear group

Course Precondition

Algebra

Resources

Algorithms in Invariant Theory, B. Sturmfels

Notes

Lecture Notes


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Learns term orders on the polynomial algebra.
LO02 Learns symmetrical polynomials.
LO03 Learns elementary polynomial generators
LO04 Knows the fundamental theorem of symmetric groups and its applications
LO05 Learns the invariants of finite groups.
LO06 Learns the invariants of the general linear group.


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 5
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. 3
PLO04 Bilgi - Kuramsal, Olgusal Has basic knowledge in all areas of mathematics 5
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.
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 2
PLO08 Bilgi - Kuramsal, Olgusal It carries out original and qualified scientific studies on the subject related to its field. 4
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. 4
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. 4
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 Term orders Reading the lecture notes Öğretim Yöntemleri:
Anlatım
2 Applications of Lex, dlex, drlex orders Reading the lecture notes Öğretim Yöntemleri:
Anlatım
3 Symmetric polynomials Reading the lecture notes Öğretim Yöntemleri:
Anlatım
4 Fundamental theorem of symmetric polynomials Reading the lecture notes Öğretim Yöntemleri:
Anlatım
5 Generating elements of algebra of symmetric polynomials of degree n Reading the lecture notes Öğretim Yöntemleri:
Anlatım
6 Schur polynomials Reading the lecture notes Öğretim Yöntemleri:
Anlatım
7 Problem solving 1 Reading the lecture notes Öğretim Yöntemleri:
Anlatım
8 Mid-Term Exam Reading the lecture notes Ölçme Yöntemleri:
Yazılı Sınav
9 Gröbner bases Reading the lecture notes Öğretim Yöntemleri:
Anlatım
10 Hilbert basis theorem Reading the lecture notes Öğretim Yöntemleri:
Anlatım
11 Inariants of finite groups Reading the lecture notes Öğretim Yöntemleri:
Anlatım
12 Hilbert finiteness theorem Reading the lecture notes Öğretim Yöntemleri:
Anlatım
13 Cohen Macaulay property Reading the lecture notes Öğretim Yöntemleri:
Anlatım
14 Invariants of general linear group Reading the lecture notes Öğretim Yöntemleri:
Anlatım
15 Problem solving Reading the lecture notes Öğretim Yöntemleri:
Anlatım
16 Term Exams Reading the lecture notes Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Reading the lecture notes 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