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
		ELECTIVE

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ENGIN MERMUT

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This aim of this course (and the course MAT3046 Algebra II) is to learn the basic concepts of algebra, the classical topics: Groups, Rings and Fields. We shall concentrate on groups in this course and continue the other topics in the course MAT3046 Algebra II. We shall 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	Cyclic groups, dihedal groups, permutations groups and other basic examples of groups with their structure should be known.
2	Quotient groups (=factor groups) and Homomorphism Theorems should be known.
3	The structure of finitely generated abelian groups should be known.
4	The "measure" of symmetry of geometric figures using groups should be known.
5	Groups actions, the main role of groups everywhere, 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	Motivating questions for algebra, a historical introduction. Symmetries and groups. The classical topics of algebra: Groups, Rings and Fields.
2	Permutation groups.
3	Integers. Moduler arithmetic.
4	Polynomials over a field.
5	Elementary properties of groups. Subgroups. Cyclic groups. Dihedral groups.
6	Homomorphisms and isomorphisms of groups.
7	Cosets and Lagrange s Theorem. Quotient groups (=factor groups) and Homomorphism Theorems.
8	Midterm
9	Direct products of groups. Semidirect products of groups.
10	The structure of finitely generated abelian groups.
11	Isometries of Euclidean Space. Euler s Theorem for the regular polyhedra: the five platonic solids.
12	Symmetry groups of regular polyhedra. Finite Rotation Groups.
13	Group actions.
14	Counting orbits for a group action: Burnside's Lemma.

Recomended or Required Reading

Textbook:

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

Supplementary textbooks:

[1] John B. Fraleigh. A First Course in Abstract Algebra.
Seventh edition. Pearson, 2003.

[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 Ibrahim Karakaş. Cebir Dersleri. TÜBA Ders Kitapları Dizisi Sayı 4, 2008.

Planned Learning Activities and Teaching Methods

Assessment Methods

SORTING NUMBER	SHORT CODE	LONG CODE	FORMULA
1	MTE	MIDTERM EXAM
2	ASG	ASSIGNMENT
3	FIN	FINAL EXAM
4	FCGR	FINAL COURSE GRADE (RESIT)	MTE * 0.30 + ASG * 0.35 + FIN * 0.35
5	RST	RESIT
6	FCGR	FINAL COURSE GRADE (RESIT)	MTE * 0.30 + ASG * 0.35 + RST * 0.35

*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

e-mail: engin.mermut@deu.edu.tr
Office: (232) 3018582

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Lectures	13	4	52
Preparations before/after weekly lectures	12	4	48
Preparation for midterm exam	1	15	15
Preparation for final exam	1	20	20
Preparation for quiz etc.	12	2	24
Final	1	2	2
Midterm	1	2	2
Quiz etc.	12	1	12
TOTAL WORKLOAD (hours)			175

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