Information Of Programmes

INSTITUTE OF SCIENCE / MAT603 - MATHEMATICS (DOCTORATE DEGREE)

Code: MAT603

Course Title: THEORY OF FIELD

Theoretical+Practice: 3+0

ECTS: 6

Year/Semester of Study

1 / Fall Semester

Level of Course

3rd Cycle Degree Programme

Type of Course

Optional

Department

MATHEMATICS (DOCTORATE DEGREE)

Pre-requisities and Co-requisites

None

Mode of Delivery

Face to Face

Teaching Period

14 Weeks

Name of Lecturer

SEZER SORGUN (ssorgun@nevsehir.edu.tr)

Name of Lecturer(s)

Language of Instruction

Turkish

Work Placement(s)

None

Objectives of the Course

The aim of this lesson is to assist the student in learning ideas about theory of fields.

Learning Outcomes		PO	MME
The students who succeeded in this course:
LO-1	know basic concepts of field teory and field extensions	PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues.	Examination Performance Project
LO-2	know basic concepts of ring theory.	PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues.	Examination
LO-3	Know splitting field and normal extension.	PO-3 Students will be dominated by current issues in mathematics.	Examination
LO-4	Know simple finite and algebraic extensions.	PO-3 Students will be dominated by current issues in mathematics.	Examination
PO: Programme Outcomes MME:Method of measurement & Evaluation

Course Contents
Polinamials over a ring, Primitive polinomials and irreducibility, Splitting Fields, The minimial polinomial and testing of irreducibility, Lattice of subfields of a field, Types of extension field, Finitely generated extrensions, Simle, finite and algebraic extensions, Simle, finite and algebraic extensions, Algebraic extensions and algebraic closure, Splittig fields and normal extensions, Embeddings and separability, Embeddings and separability, Algebraic independence
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Polinamials over a ring	Lecture and discussion of mutual
2	Primitive polinomials and irreducibility	Lecture and discussion of mutual
3	Splitting Fields	no
4	The minimial polinomial and testing of irreducibility	Lecture and discussion of mutual
5	Lattice of subfields of a field	Lecture and discussion of mutual
6	Types of extension field	Lecture and discussion of mutual
7	Finitely generated extrensions	Lecture and discussion of mutual
8	mid-term exam
9	Simle, finite and algebraic extensions	Lecture and discussion of mutual
10	Simle, finite and algebraic extensions	Lecture and discussion of mutual
11	Algebraic extensions and algebraic closure	Lecture and discussion of mutual
12	Splittig fields and normal extensions	Lecture and discussion of mutual
13	Embeddings and separability	Lecture and discussion of mutual
14	Embeddings and separability	Lecture and discussion of mutual
15	Algebraic independence	Lecture and discussion of mutual
16	final exam
Recommend Course Book / Supplementary Book/Reading
1	Thomas W. Hungerford, Graduate text in mathmatics, springer, 1974
2	steven Roman, Field Theory, Springer
Required Course instruments and materials
Books of field teory

Assessment Methods
Type of Assessment	Week	Hours	Weight(%)
mid-term exam	8	2	30
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project	7	2	10
8.Term Paper	14	2	10
9.Project
final exam	16	2	50

Student Work Load
Type of Work	Weekly Hours	Number of Weeks	Work Load
Weekly Course Hours (Theoretical+Practice)	3	14	42
Outside Class
a) Reading	2	14	28
b) Search in internet/Library	2	14	28
c) Performance Project	3	7	21
d) Prepare a workshop/Presentation/Report			0
e) Term paper/Project	3	7	21
Oral Examination			0
Quiz			0
Laboratory exam			0
Own study for mid-term exam	3	8	24
mid-term exam	2	1	2
Own study for final exam	3	8	24
final exam	2	1	2
			0
			0
Total work load;			192