Dokuz Eylül University Information Package / Courses Catalog

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type Of Course	D	U	L	ECTS
MAT 3046	ALGEBRA II	ELECTIVE	4	0	0	7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR SALAHATTIN ÖZDEMIR

Offered to

Mathematics (Evening)
Mathematics (English)

Course Objective

The aim of this course (and the course MAT3055 Algebra I) is to learn the basic concepts of algebra, the classical topics: Groups, Rings and Fields. In the course MAT3055 Algebra I, we have concentrated on groups. Now we shall study rings and fields in this course MAT3046 Algebra II. The main aim of this course is to study Galois Theory of Fields. We shall start with the classical algebra problem: finding a formula for the roots of polynomial equations. This question leads to Galois theory. We shall follow this historical motivation to understand how algebra evolved as it is today. We shall continue to study some more topics about groups, rings and fields that are covered in the course Basic Algebraic Structures .

Learning Outcomes of the Course Unit

1	Rings, Integral domains and fields with the basic examples should be known.
2	Ideals, homomorphisms and quotient rings should be known.
3	Euclidean domains, principal ideal domains, unique factorization domains should be known.
4	Field extensions should be known.
5	Splitting fields and automorphisms of fields should be known.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week	Subject	Description
1	Rings, integral domains and fields.
2	The field of quotients of an integral domain.
3	Rings of polynomials. Factorization of polynomials over a field.
4	Ideals. Homomorphisms and Quotient Rings.
5	Prime and maximal ideals.
6	Principal Ideal Domains. Euclidean Domains. Unique Factorization Domains.
7	Problem solving.
8	Field Extensions.
9	Algebraic Extensions.
10	Finite Fields.
11	Automorphism of Fields.
12	Splitting Fields.
13	Separable Extensions.
14	Introduction to Galois Theory.

Recomended or Required Reading

Textbook:

John B. Fraleigh and Neal Brand. A First Course in Abstract Algebra.
Eighth edition. Pearson, 2021.

Supplementary textbooks:

[1] Frederick M. Goodman. Algebra, Abstract and Concrete, Stressing Symmetry. Pearson, 2003. Online edition 2.6: http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm

[2] William J. Gilbert and W. Keith Nicholson. Modern Algebra with Applications. Second edition. John Wiley & Sons, 2004.

[3] Joseph A. Gallian. Contemporary Abstract Algebra. Ninth edition. Cengage Learning, 2017.

[4] Michael Artin. Algebra. Second edition, Pearson, 2010.

[5] Joseph J. Rotman. A First Course in Abstract Algebra with Applications. Third edition, Pearson, 2006.

[6] David S. Dummit and Richard M. Foote. Abstract Algebra. Third edition. John Wiley & Sons, 2004.

[7] M. A. Armstrong. Groups and Symmetry. Springer, 1988.

[8] Nathan C. Carter. Visual Group Theory Mathematical Association of America, 2009.

[9] David W. Farmer. Groups and Symmetry, A Guide to Discovering Mathematics. AMS, 1996.

[10] Elbert A. Walker. Introduction to Abstract Algebra. Random House/Birkhauser, 1987. Online available:
http://emmy.nmsu.edu/~elbert/

[11] John Stillwell. Elements of Algebra. Springer, 1994.

[12] Robert H. Redfield. Abstract Algebra, A Concrete Introduction. Pearson, 2001.

[13] Israel Kleiner. A History of Abstract Algebra. Birkha user, 2007.

[14] Halil I brahim Karakas . Cebir Dersleri. TU BA Ders Kitapları Dizisi Sayı 4, 2008.

Planned Learning Activities and Teaching Methods

Lecture notes, presentations, problem solving, discussions and exams

Assessment Methods

SORTING NUMBER	SHORT CODE	LONG CODE	FORMULA
1	VZ	Vize
2	FN	Final
3	BNS	BNS	VZ * 0.40 + FN * 0.60
4	BUT	Bütünleme Notu
5	BBN	Bütünleme Sonu Başarı Notu	VZ * 0.40 + BUT * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

The passing grade will be evaluated as 40% midterm exam and 60% final exam. Class participation is important.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

e-mail: salahattin.ozdemir@deu.edu.tr
Phone: (232) 301 8608
Office: B 351/1

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Lectures	14	4	56
Preparations before/after weekly lectures	14	4	56
Preparation for midterm exam	1	20	20
Preparation for final exam	1	40	40
Final	1	2	2
Midterm	1	2	2
TOTAL WORKLOAD (hours)			176

Contribution of Learning Outcomes to Programme Outcomes

PO/LO	PO.1	PO.2	PO.3	PO.8	PO.9	PO.12	PO.13
LO.1	3	4	5	3	4	3	4
LO.2	5	5	4	3	4	3	4
LO.3	4	5	4	3	4	3	4
LO.4	4	5	4	3	4	3	4
LO.5	4	5	4	3	4	3	4

COURSE UNIT TITLE

DEGREE PROGRAMMES

Description of Individual Course Units

Offered By

Level of Course Unit

Course Coordinator

Offered to

Course Objective

Learning Outcomes of the Course Unit

Mode of Delivery

Prerequisites and Co-requisites

Recomended Optional Programme Components

Course Contents

Recomended or Required Reading

Planned Learning Activities and Teaching Methods

Assessment Methods

Further Notes About Assessment Methods

Assessment Criteria

Language of Instruction

Course Policies and Rules

Contact Details for the Lecturer(s)

Office Hours

Work Placement(s)

Workload Calculation

Contribution of Learning Outcomes to Programme Outcomes

CONTACT INFORMATION