• Turkish
  • English
Course Code: 
MATH 322
Semester: 
Spring
Course Type: 
Core
P: 
3
Lab: 
0
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
6
Course Language: 
English
Course Objectives: 
To teach as much about rings and fields 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: 

Rings. Integral domains. Fermat's and Euler's theorems. Quotient field of an integral domain. Rings of polynomials. Factorization of polynomials over a field. Noncommutative rings. Ring homomorphisms and factor rings. Prime and maximal ideals. Unique factorization domains. Field extensions. Algebraic extensions. Geometric constructions. Finite fields.

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) Applies Fermat’s and Euler’s theorems

1,2

A

2) Find maximal and prime ideals in a ring

1,2

A

3) Constructs the field of quotients of an integral domain

1,2

A

4) Factorizes polynomials over rings

1,2

A

5) Finds ring homomorphisms

1,2

A

6) Determines algebraic and transcendental elements over a field

1,2

A

Course Flow

Week

Topics

Study Materials

1

Rings and fields

Textbook

2

Integral domains

Textbook

3

Fermat’s and Euler’s theorems

Textbook

4

The field of quotients of an integral domain

Textbook

5

Rings of polynomials

Textbook

6

Factorization of polynomials over a field

Textbook

7

Noncommutative examples

Textbook

8

Ordered rings and fields

Textbook

9

Homomorphisms and factor rings

Textbook

10

Prime and maximal ideals

Textbook

11

Introduction to Extension fields

Textbook

12

Algebraic extensions

Textbook

13

Geometric constructions

Textbook

14

Finite fields

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

15

30

Quizzes

-

-

-

Assignments

-

-

-

Final examination (Including self study)

1

16

16

Total Work Load

 

 

158

Total Work Load / 25 (h)

 

 

6.32

ECTS Credit of the Course

 

 

6