• Turkish
  • English
Course Code: 
MATH 321
Semester: 
Fall
Course Type: 
Core
P: 
3
Lab: 
0
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
7
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

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

Activities

Quantity

Duration
(Hour)

Total
Workload
(Hour)

Course Duration (14x Total course hours)

14

3

42

Hours for off-the-classroom study (Pre-study, practice)

14

5

70

Mid-terms (Including self study)

2

16

32

Quizzes

-

-

-

Assignments

-

-

-

Final examination (Including self study)

1

20

20

Total Work Load

 

 

164

Total Work Load / 25 (h)

 

 

6.56

ECTS Credit of the Course

 

 

7