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 3055	ALGEBRA I	COMPULSORY	4	0	0	7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR MÜNEVVER PINAR EROĞLU

Offered to

Mathematics (English)
Mathematics (Evening)

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	Dihedal groups, permutations groups and other basic examples of groups with their structure should be known.
2	The structure of cyclic groups should be known.
3	Quotient groups (=factor groups) and Homomorphism Theorems should be known.
4	The structure of finitely generated abelian groups should be known.
5	Groups actions, the main role of groups everywhere, should be known.
6	Sylow Theorems should be knownn.

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. The classical topics of algebra: Groups, Rings and Fields.
2	Symmetries.
3	Elementary properties of groups. Subgroups.
4	The structure of cyclic groups.
5	Group of Permutations. Dihedral groups.
6	Product of groups. Semidirect products.
7	The structure of finitely generated abelian groups.
8	Prpblem solving.
9	Quotient groups (=factor groups) and Homomorphisms.
10	Isomorphisms Theorems
11	Group action on a set.
12	Applications of G-sets to counting. Burnside's Formula.
13	Sylow Theorems
14	Free Abelian Groups. The proof of the Fundamental Theorem of finitely generated abelian groups.

Recomended or Required Reading

Textbook: John B. Fraleigh and Neal Brand. A First Course in Abstract Algebra, 8th edition. Pearson, 2020.

Supplementary textbooks:

[1] Frederick M. Goodman. Algebra, Abstract and Concrete, 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 Ibrahim Karakaş. Cebir Dersleri. TÜBA 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	MTE	MIDTERM EXAM
2	FIN	FINAL EXAM
3	FCG	FINAL COURSE GRADE	MTE * 0.50 + FIN * 0.50
4	RST	RESIT
5	FCGR	FINAL COURSE GRADE (RESIT)	MTE * 0.50 + RST * 0.50

Further Notes About Assessment Methods

None

Assessment Criteria

50% (Midterm exam) + 50% (Final exam)

Language of Instruction

English

Course Policies and Rules

Active participation in the course, preparing in advance by studying the weekly topics through the recommended textbooks and lecture notes, solving the assigned problems prior to class, reviewing the topics covered in each session, and clarifying any unclear concepts through discussion will significantly contribute to your success in this course.

Contact Details for the Lecturer(s)

Münevver Pınar Eroğlu
e-mail : mpinar.eroglu@deu.edu.tr
Office: (232) 301 85 93

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.4	PO.5	PO.6	PO.7	PO.8	PO.9	PO.10	PO.11	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
LO.6	4	4	4	4	4	4	4	4	4	4	4	4	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