PHOTOGRAPHY AND VIDEO
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT4052	Commutative Algebra	Spring Fall	3	0	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Non-Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :
Recommended Optional Program Components:	None
Course Objectives:	To provide the necessary background (both computational and theoretical) in commutative algebra to mathematics majors.

Learning Outcomes

The students who have succeeded in this course;
A student who finishes this course successfully will have learned basic concepts of commutative algebra.

Course Content

Abelian groups, rings and fields. Vector spaces and linear transformations. Bases and matrix representations of linear transformations. Polynomial rings. Ideals, prime and maximal ideals. Quotients of polynomial rings. Modules over polynomial rings. Prime and primary ideals. Factorization of ideals in the monoid of ideals. Localizations of ideals. Zero-divisors, integral domains and rings of fractions. Unique factorization domains and Euclidean domains. Radical of an ideal. Nilradical and Jacobson radical of a ring. Operations in the lattice of ideals. Classical Euclidean division algorithm in polynomial algebras. Monomial orderings and division algorithms. Fundamental Theorem of Algebra. Finite generation of ideals in polynomial algebras. Gröbner basis and Buchberger algorithm. Examples and calculations.
Gröbner bazları ve Buchberger algoritması. Örnekler ve hesaplamalar. Gröbner basis and Buchberger algorithm. Examples and calculations. Morphisms between modules. Kernels and images of morphisms. Submodules and quotient modules. Ideals of annihilators. Internal and external sums of modules. Tensor products of modules. Submodule and ideal chains. Artinian and Noetherian rings and modules.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Abelian groups, rings and fields.
2)	Vector spaces and linear transformations. Bases and matrix representations of linear transformations.
3)	Polynomial rings. Ideals, prime and maximal ideals. Quotients of polynomial rings. Modules over polynomial rings.
4)	Prime and primary ideals. Factorization of ideals in the monoid of ideals. Localizations of ideals.
5)	Zero-divisors, integral domains and rings of fractions. Unique factorization domains and Eucledian domains.
6)	Radical of an ideal. Nilradical and Jacobson radical of a ring. Operations in the lattice of ideals.
7)	A review of covered subjects and the first exam.
8)	Classical Euclidean division algorithm in polynomial algebras. Monomial orderings and division algorithms.
9)	Fundamental Theorem of Algebra. Finite generation of ideals in polynomial algebras.
10)	Gröbner basis and Buchberger algorithm. Examples and calculations.
11)	Gröbner basis and Buchberger algorithm. Examples and calculations.
12)	A review of covered subjects and the second exam.
13)	Morphisms between modules. Kernels and images of morphisms. Submodules and quotient modules. Ideals of annihilators. Examples.
14)	Internal and external sums of modules. Tensor products of modules. Submodule and ideal chains. Artinian and Noetherian rings and modules.

Sources

Course Notes / Textbooks:	Instructor's own lecture notes. Atiyah and MacDonald, "Introduction to Commutative Algebra"
References:

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Quizzes	3	% 10
Midterms	2	% 40
Final	1	% 50
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 50
PERCENTAGE OF FINAL WORK		% 50
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	2	28
Quizzes	3	3	9
Midterms	2	10	20
Final	1	26	26
Total Workload			125

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Knowledge of photographic and video media and ability to use basic, intermediate and advanced techniques of these media.
2)	Ability to understand, analyze and evaluate theories, concepts and uses of photography and video.
3)	Ability to employ theoretical knowledge in the areas of the use of photography and video.
4)	Familiarity with and ability to review the historical literature in theoretical and practical studies in photography and video.
5)	Ability in problem solving in relation to projects in photography and video.
6)	Ability to generate innovative responses to particular and novel requirements in photography and video.
7)	Understanding and appreciation of the roles and potentials of the image across visual culture
8)	Ability to communicate distinctively by means of photographic and video images.
9)	Experience of image post-production processes and ability to develop creative outcomes through this knowledge.
10)	Knowledge of and ability to participate in the processes of production, distribution and use of photography and video in the media.
11)	Ability to understand, analyze and evaluate global, regional and local problematics in visual culture.
12)	Knowledge of and ability to make a significant contribution to the goals of public communication.
13)	Enhancing creativity via interdisciplinary methods to develop skills for realizing projects.
14)	Gaining general knowledge about the points of intersection of communication, art and technology.