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. |
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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. |
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11) |
Gröbner basis and Buchberger algorithm. Examples and calculations. |
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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. |
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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) |
Setting up various spaces in national and international contexts, carrying out designs, planning and applications that could satisfy various user groups and respond various requirements in the field of Interior Architecture, |
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2) |
Analyzing the information gathered from the framework of actual physical, social and economical constraints and user requirements, and synthesizing these with diverse knowledge and considerations in order to create innovative spatial solutions, |
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3) |
Generating creative, innovative, aesthetic and unique spatial solutions by using tangible and abstract concepts, |
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4) |
Using at least one of the illustration and presentation technologies competently, that the field of interior architecture requires, |
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5) |
Reporting, presenting and transferring the design, practice and research studies to the specialists or laymen by using visual, textual or oral communication methods, efficiently and accurately, |
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6) |
Embracing and prioritizing man-environment relationships, user health, safety and security, and universal design principles in the field of interior architecture, |
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7) |
Design understanding and decision making that respects social and cultural rights of the society, cultural heritage and nature, |
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8) |
Being aware of national and international values, following developments and being equipped about ethical and aesthetical subjects in the fields of interior architecture, design and art, |
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9) |
Having absolute conscious about legal regulations, standards and principles; and realizing professional ethics, duties and responsibilities in the field of Interior Architecture, |
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