MT540 Field Theory

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

Information

Code MT540
Name Field 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. HAYRULLAH AYIK


Course Goal / Objective

The aim of this course is to teach some basic properties of Field and Galois Theories to the students.

Course Content

In this course extension of fields, seperable extensions, automorphisms of fields, basic properties of Galois Theory, Lagrance theorem and Wedderburn theorem are described.

Course Precondition

None

Resources

Lecture Notes- Fields and Galois Theory Andrew Hubery

Notes

Introduction to finite fields and their applications, RUDOLF LIDL, HARALD NIEDERREITER, 1994


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Knows the field extensions.
LO02 Knows the simple and algebraic extensions.
LO03 Knows the seperable extensions.
LO04 Knows the field automorphisms.
LO05 Knows the normal extensions.
LO06 Knows the basic properties of Galois Theory.
LO07 Knows the primitive element theorem.
LO08 Knows the Lagrance theorem an cyclic extensions.
LO09 Knows the Wedderburn theorem.


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. 3
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 1
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 3
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. 3
PLO09 Bilgi - Kuramsal, Olgusal Analyzes existing mathematical theories and develops new theories. 2
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.
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.
PLO13 Yetkinlikler - Öğrenme Yetkinliği Adheres to the ethical rules required by its scientific title


Week Plan

Week Topic Preparation Methods
1 Field extensions Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
2 Simple and algebraic extensions Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
3 Certain applications of simple extensions Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
4 Certain applications of algebraic extensions Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
5 Seperable extensions Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
6 Automorphisms of fields Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
7 Normal extensions Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Problem Çözme, Soru-Cevap
8 Mid-Term Exam Review and problem solving Ölçme Yöntemleri:
Yazılı Sınav
9 Basic properties of Galois theory Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Tartışma
10 Certain results and applications of Galois theory Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
11 Primitive element theoem Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
12 Lagrange theorem Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap
13 Cyclic extension Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Tartışma
14 Wedderburn theoremi Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Problem Çözme
15 Finding solutions with rooths Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Problem Çözme
16 Term Exams Review and problem solving Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Review and problem solving 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: 17.06.2024 12:25