ABSTRACT ALGEBRA

Course Code:

MATH 322

Semester:

Spring

Course Type:

Core

P:

2

Lab:

2

Laboratuvar Saati:

0

Credits:

3

ECTS:

6

Prerequisite Courses:

LINEAR ALGEBRA I

BASIC ALGEBRAIC STRUCTURES

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	Program Learning Outcomes	Teaching Methods	Assessment Methods
1) Applies Fermat’s and Euler’s theorems	1,2,4	1,2	A
2) Find maximal and prime ideals in a ring	1,2,4,7	1,2	A
3) Constructs the field of quotients of an integral domain	1,2,4,7	1,2	A
4) Factorizes polynomials over rings	1,2,3,4,7,9	1,2	A
5) Finds ring homomorphisms	1,2,4,7	1,2	A
6) Determines algebraic and transcendental elements over a field	1,2,4,7,9	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
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)	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

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