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. |
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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. |
|
12) |
A review of covered subjects and the second exam. |
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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) |
Adequate knowledge in mathematics, science and civil engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems. |
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2) |
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. |
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3) |
Ability to design a complex system, process, structural and/or structural members to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. |
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4) |
Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in civil engineering applications; ability to use civil engineering technologies effectively. |
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5) |
Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or civil engineering research topics. |
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6) |
Ability to work effectively within and multi-disciplinary teams; individual study skills. |
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7) |
Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. |
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8) |
Awareness of the necessity of lifelong learning; ability to access information to follow developments in civil engineering technology. |
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9) |
To act in accordance with ethical principles, professional and ethical responsibility; having awareness of the importance of employee workplace health and safety. |
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10) |
Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development. |
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11) |
Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of civil engineering solutions. |
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