MAT4052 Commutative AlgebraBahçeşehir UniversityDegree Programs ADVERTISINGGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
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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 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) To be able to apply theoretical concepts related to mass communication, consumer behavior, psychology, persuasion,sociology, marketing, and other related fields to understand how advertising and brand communication works in a free-market economy. 2
2) To be able to critically discuss and interpret theories, concepts, methods, tools and ideas in the field of advertising. 2
3) To be able to research, create, design, write, and present an advertising campaign and brand strategies of their own creation and compete for an account as they would at an advertising agency. 2
4) To be able to analyze primary and secondary research data for a variety of products and services. 2
5) To be able to develop an understanding of the history of advertising as it relates to the emergence of mass media outlets and the importance of advertising in the marketplace. 2
6) To be able to follow developments, techniques, methods, as well as research in advertising field; and to be able to communicate with international colleagues in a foreign language. (“European Language Portfolio Global Scale”, Level B1) 2
7) To be able to take responsibility in an individual capacity or as a team in generating solutions to unexpected problems that arise during implementation process in the Advertising field. 3
8) To be able to understand how advertising works in a global economy, taking into account cultural, societal, political, and economic differences that exist across countries and cultures. 2
9) To be able to approach the dynamics of the field with an integrated perspective, with creative and critical thinking, develop original and creative strategies. 2
10) To be able to to create strategic advertisements for print, broadcast, online and other media, as well as how to integrate a campaign idea across several media categories in a culturally diverse marketplace. 2
11) To be able to use computer software required by the discipline and to possess advanced-level computing and IT skills. (“European Computer Driving Licence”, Advanced Level) 2
12) To be able to identify and meet the demands of learning requirements. 2
13) To be able to develop an understanding and appreciation of the core ethical principles of the advertising profession. 2