Mathematics (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH422

Course Name:

Galois Theory

Semester:

Spring

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Araş. Gör. GAMZE AKAR UYSAL

Course Lecturer(s):

Prof. Dr. Şükrü Yalçınkaya

Course Assistants:

Course Objective and Content

Course Objectives:	The course aims to develop all the necessary algebraic objects (groups and rings, polynomial rings, fields, field extensions) and their properties whenever needed on the way to solve that classical problem in Galois theory.
Course Content:	The content of the course consists of cubic and quartic equations, Cardano formulas, The Fundamental Theorem of Algebra, field extensions, finite, normal, separable extensions, fields of characteristic 0 and p, Galois group, Galois extension, The Fundamental Theorem of Galois theory, solvability by radicals, solvable groups, finite fields.

Learning Outcomes

The students who have succeeded in this course;
1) Will be able to formulate the precise meaning of the solvability problem of polynomial equations by radicals.
2) Will be able to distinguish normal and separable extensions of fields.
3) Will be able to use The Fundamental Theorem of Galois Theory to observe the correspondence between intermediate field extensions and subgroups of the Galois group.
4) Will be able to express the solvability of a polynomial equation by radicals using the solvability of its Galois group.
5) Will be able to apply Galois Theory to impossibility proofs of some geometric constructions.

Course Flow Plan

Week	Subject	Related Preparation
1)	Cubic and quartic equations. Cardan's Formulas.
2)	Symmetric polynomials. Discriminant.
3)	Roots of polynomials. The Fundamental Theorem of Algebra.
4)	Extension fields. Minimal polynomials. Adjoining elements.
5)	Degree of a field extension. Finite extensions. The tower theorem. Algebraic extensions. Simple extensions.
6)	Splitting fields, their uniqueness up to isomorphism.
7)	Normal extensions. Separable extensions.
8)	Midterm Exam
9)	Fields of characteristic 0 and fields of characteristic p. The Primitive Element Theorem.
10)	Galois group. Galois group of splitting fields. Permutation of the roots.
11)	Abelian equations. Galois extensions. The Fundamental Theorem of Galois Theory.
12)	Solvability by radicals. Solvable groups.
13)	Cyclotomic extensions. Regular polygons and roots of unity.
14)	Finite fields.

Sources

Course Notes / Textbooks:	Ian Stewart - Galois Theory
References:	Ders notları

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5
Program Outcomes
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4) Have the ability to think analytically and use the time effectively in the process of deduction.
5) Have the ability to search the literature, understand and interpret scientific articles.
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7) Have the ability to work efficiently in interdisciplinary teams.
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.	3
2)	Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3)	Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4)	Have the ability to think analytically and use the time effectively in the process of deduction.	3
5)	Have the ability to search the literature, understand and interpret scientific articles.	3
6)	Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7)	Have the ability to work efficiently in interdisciplinary teams.
8)	Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9)	Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10)	Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.	3
11)	Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.	2

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	3		39
Study Hours Out of Class	13	0	4		52
Midterms	1	0	15		15
Final	1	0	25		25
Total Workload					131