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. |
|
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) |
Using the theoretical/conceptual and practical knowledge acquired for architectural design, design activities and research. |
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2) |
Identifying, defining and effectively discussing aesthetic, functional and structural requirements for solving design problems using critical thinking methods. |
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3) |
Being aware of the diversity of social patterns and user needs, values and behavioral norms, which are important inputs in the formation of the built environment, at local, regional, national and international scales. |
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4) |
Gaining knowledge and skills about architectural design methods that are focused on people and society, sensitive to natural and built environment in the field of architecture. |
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5) |
Gaining skills to understand the relationship between architecture and other disciplines, to be able to cooperate, to develop comprehensive projects; to take responsibility in independent studies and group work. |
|
6) |
Giving importance to the protection of natural and cultural values in the design of the built environment by being aware of the responsibilities in terms of human rights and social interests. |
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7) |
Giving importance to sustainability in the solution of design problems and the use of natural and artificial resources by considering the social, cultural and environmental issues of architecture. |
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8) |
Being able to convey and communicate all kinds of conceptual and practical thoughts related to the field of architecture by using written, verbal and visual media and information technologies. |
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9) |
Gaining the ability to understand and use technical information about building technology such as structural systems, building materials, building service systems, construction systems, life safety. |
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10) |
Being aware of legal and ethical responsibilities in design and application processes. |
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