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