INTERNATIONAL TRADE AND BUSINESS | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
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: | 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. |
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) | Has theoretical and practical knowledge on management, business, trade, economy, entrepreneurship, innovation, sustainable development related to International Trade and Business and can use this information | |
2) | Can collect data from different sources in the global business world and successfully apply research techniques, use information and communication technologies. | |
3) | Can analyze opportunities and threats with strategic thinking skills by using different resources and channels in the ever-changing global business world. | |
4) | Can communicate orally and in writing with a good knowledge of English grammar. | |
5) | He / she can transfer the knowledge and skills he / she has acquired in the field to the relevant people in written and oral form and evaluate them critically. | |
6) | Adopts the principles of business ethics with the awareness of professional responsibility and can apply these principles within the framework of legal rules in the field of global trade and business. | |
7) | He / she can collaborate in and out of the field, take responsibility, respect cultural differences and have ethical values. | |
8) | Has sufficient awareness of social rights, justice, cultural values, environmental awareness, occupational health and safety. | |
9) | With the lifelong learning skill acquired, she/he can identify learning needs and improve herself/himself |