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. |
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5) |
Zero-divisors, integral domains and rings of fractions. Unique factorization domains and Eucledian domains. |
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6) |
Radical of an ideal. Nilradical and Jacobson radical of a ring. Operations in the lattice of ideals. |
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7) |
A review of covered subjects and the first exam. |
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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) |
To learn and compare major sociology perspectives, both classical and contemporary, and apply all of them to analysis of social conditions. |
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2) |
To be able to identify the basic methodological approaches in building sociological and anthropological knowledge at local and global levels |
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3) |
To be able to use theoretical and applied knowledge acquired in the fields of statistics in social sciences. |
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4) |
To have a basic knowledge of other disciplines (including psychology, history, political science, communication studies and literature) that can contribute to sociology and to be able to make use of this knowledge in analyzing sociological processes |
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5) |
To have a knowledge and practice of scientific and ethical principles in collecting, interpreting and publishing sociological data also develop ability how to share this data with experts and lay people, using effective communication skills |
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6) |
To develop competence in analyzing and publishing sociological knowledge by using computer software for quantitative and qualitative analysis; and develop an attitute for learning new techniques in these fields. |
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7) |
To identify and to have a knowledge of the theories related to urban and rural sociology and demography, and political sociology, sociology of gender, sociology of body, visual sociology, sociology of work, sociology of religion, sociology of knowledge and sociology of crime. |
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8) |
To have knowledge of how sociology is positioned as a scientific discipline from a philosophical and historical perspective |
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9) |
To have the awareness of social issues in Turkish society, to develop critical perspective in analysing these issues and to have a knowledge of the works of Turkish sociologists and to be able to transfer this knowledge |
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10) |
To have the awareness of social issues and global societal processes and to apply sociological analysis to development and social responsibility projects |
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11) |
To have the ability to define a research question, design a research project and complete a written report for various fields of sociology, either as an individual or as a team member. |
|
12) |
To be able to transfer the knowledge gained in the areas of sociology to the level of secondary school. |
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