| 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. |
|
| |
Program Outcomes |
Level of Contribution |
| 1) |
To gain both theoretical and practical knowledge about physical, cognitive, social-emotional aspects of child development. |
4 |
| 2) |
To display actions in professional practice based on ethical principles and values. |
5 |
| 3) |
To adopt the principle of lifelong learning, using efficient ways for accessing information. |
5 |
| 4) |
To know the stages of child development and to be able to use models / theories efficiently for supporting children's cognitive, affective and psycho-motor development. |
5 |
| 5) |
To plan, implement and evaluate professional projects, research and events with a sense of social responsibility, |
5 |
| 6) |
To be able to use effective communication methods in counseling and child and family-based guidance. |
3 |
| 7) |
To be sensitive to the child and family-related issues taking into account the child's stages of development, and to implement strategies for personal development of child and education methods which are vital for leading effective and productive life. |
5 |
| 8) |
To use the education and communication materials according to the child development stage, and to create proper educational environment. |
5 |
| 9) |
To take responsibilities in the field of child development and education using interdisciplinary approach, and to use information technologies, and to engage in projects and activities. |
5 |
| 10) |
To use health information technologies for research in the field of child development. |
5 |
| 11) |
To be able to monitor occupational information using at least one foreign language, to collaborate and communicate with colleagues at international level. |
5 |
| 12) |
To become a good example for colleagues and society, and represent efficiently the professional identity using advanced knowledge about child development. |
5 |