INTRODUCTION TO GROUP THEORY

Course Code:

MATH 321

Semester:

Fall

Course Type:

Core

P:

3

Lab:

0

Laboratuvar Saati:

0

Credits:

3

ECTS:

7

Prerequisite Courses:

BASIC ALGEBRAIC STRUCTURES

Course Language:

English

Course Objectives:

To teach as much about groups as one can in a first course to constitute a firm foundation for more specialized work and to provide valuable experience for any further axiomatic study of mathematics.

Course Content:

Binary operations, groups, subgroups, cyclic groups and generators. Permutation groups. Orbits, cycles and alternating groups. Cosets and Lagrange theorem. Direct products. Finitely generated Abelian groups. Isomorphism theorems. Cayley's theorem. Factor groups, simple groups, series of groups, group action. Sylow theorems and applications. Free groups. Group representations.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Teaching Methods	Assessment Methods
1) Classifies finite abelian groups	1,2	A
2) Finds the Sylow subgroups of a group	1,2	A
3) Compute factor groups	1,2	A
4) Finds group homomorphisms	1,2	A
5) Determines if groups are isomorphic or not	1,2	A
6) Determines if a group is simple	1,2	A

Course Flow

Week	Topics	Study Materials
1	Groups, subgroups, cyclic groups	Textbook
2	Permutation groups, orbits, cycles, alternating groups	Textbook
3	Cosets and the theorem of Lagrange	Textbook
4	Direct product and finitely generarted abelian groups	Textbook
5	Homomorphisms, factor groups	Textbook
6	Simple groups	Textbook
7	Group action on a set	Textbook
8	Isomorphism theorems	Textbook
9	Series of groups	Textbook
10	Sylow theorems	Textbook
11	Applications of the Sylow theory	Textbook
12	Free abelian groups	Textbook
13	Free groups	Textbook
14	Groups presentations	Textbook

Recommended Sources

Textbook	A First Course in Abstract Algebra, J. Fraleigh.
Additional Resources

Material Sharing

Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	2	100
Quizzes
Assignments
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

COURSE CATEGORY

Expertise/Field Courses

Course’s Contribution to Program

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)			x
2	Acquiring fundamental knowledge on fundamental research fields in mathematics					x
3	Ability form and interpret the relations between research topics in mathematics					x
4	Ability to define, formulate and solve mathematical problems					X
5	Consciousness of professional ethics and responsibilty					x
6	Ability to communicate actively		x
7	Ability of self-development in fields of interest					x
8	Ability to learn, choose and use necessary information technologies			x
9	Lifelong education					x

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	4	56
Hours for off-the-classroom study (Pre-study, practice)	14	4	56
Mid-terms (Including self study)	1	15	15
Quizzes	-	-	-
Assignments	-	-	-
Final examination (Including self study)	1	20	20
Total Work Load			147
Total Work Load / 25 (h)			5.88
ECTS Credit of the Course			6

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