| Week |
Subject |
Related Preparation |
| 1) |
Abelian groups, rings and fields. |
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| 2) |
Vector spaces and linear transformations. Bases and matrix representations of linear transformations. |
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| 3) |
Polynomial rings. Ideals, prime and maximal ideals. Quotients of polynomial rings. Modules over polynomial rings. |
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| 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. |
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| 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. |
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| |
Program Outcomes |
Level of Contribution |
| 1) |
- Possess advanced level theoretical and practical knowledge supported by textbooks with updated information, practice equipments and other resources.
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|
| 2) |
Use of advanced theoretical and practical knowledge within the field.
-Interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the field. |
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| 3) |
Inform people and institutions, transfer ideas and solution proposals to problems in written and orally on issues in the field.
- Share the ideas and solution proposals to problems on issues in the field with professionals and non-professionals by the support of qualitative and quantitative data.
-Organize and implement project and activities for social environment with a sense of social responsibility.
-Monitor the developments in the field and communicate with peers by using a foreign language at least at a level of European Language Portfolio B1 General Level.
-Use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. |
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| 4) |
Evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach.
-Determine learning needs and direct the learning.
-Develop positive attitude towards lifelong learning. |
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| 5) |
Act in accordance with social, scientific, cultural and ethic values on the stages of gathering, implementation and release of the results of data related to the field.
- Possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also, environmental protection, worker's health and security. |
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| 6) |
Conduct studies at an advanced level in the field independently.
- Take responsibility both as a team member and individually in order to solve unexpected complex problems faced within the implementations in the field.
- Planning and managing activities towards the development of subordinates in the framework of a project |
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