FOREIGN TRADE (TURKISH) | |||||
Associate | TR-NQF-HE: Level 5 | QF-EHEA: Short Cycle | EQF-LLL: Level 5 |
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. |
Language of instruction: | English |
Type of course: | Non-Departmental Elective |
Course Level: | Associate (Short 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. |
The students who have succeeded in this course; A student who finishes this course successfully will have learned basic concepts of commutative algebra. |
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. |
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. |
Course Notes / Textbooks: | Instructor's own lecture notes. Atiyah and MacDonald, "Introduction to Commutative Algebra" |
References: |
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 |
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 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | He/she comprehends the main theories and terminology of International Trade. | |
2) | He/she comprehends the custom operations. | |
3) | He/she applies international finance and accounting knowledge to business life. | |
4) | He/she has skills of using computer and software. | |
5) | He/she analyses Turkey and EU foreign trade structure. | |
6) | He/she brings in the basic reason of international marketing. | |
7) | He/she consults basic law rules and legislation which built the legal frame of foreign trade. | |
8) | He/she evaluates and analyses risks which foreign trade companies may meet. | |
9) | He/she comprehends the international logistics and transportation. | |
10) | He/she has the qualification and eligibility to work on international platform. | |
11) | He/she uses efficient oral and written communication skills. | |
12) | He/she follows and applies the national and international actual and the economic developments about foreign trade. | |
13) | He/she has vocational ethical value that market needs in qualified staff, can use Turkish effectively in writing and speaking communication; have proficiency in foreign language knowledge to making international correspond. |