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. |
|
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Program Outcomes |
Level of Contribution |
1) |
Develop close interest in human mind and behavior, and attain critical thinking skills (in particular the ability to evaluate psychological theories using empirical evidence), as well as appreciating psychology as an evidence based science. |
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2) |
Gain a biopsychosocial understanding of human behavior, namely, the biological, psychological, social determinants of behavior. |
|
3) |
Acquire theoretical and applied knowledge and learn about basic psychological concepts and perspectives |
|
4) |
Familiarize with methodology and data evaluation techniques by being aware of scientific research methods (i.e. correlational, experimental, longitudinal, case study). |
|
5) |
Employ ethical sensitivity while doing assessment, research or working with groups. |
|
6) |
Familiarize with the essential perspectives of psychology (cognitive, developmental, clinical, social, behavioral, and biological). |
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7) |
Get the opportunity and skills to evaluate qualitative and quantitative data, write reports, and present them. |
|
8) |
Attain preliminary knowledge for psychological measurement and evaluation. |
|
9) |
To have a basic knowledge of other disciplines (e.g. sociology, history, political science, communication studies, philosophy, anthropology, literature, law, art, etc) that can contribute to psychology and to be able to make use of this knowledge in understanding and interpreting of psychological process. |
3 |