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. |
|
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. |
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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) |
Build up a body of knowledge in mathematics, science and industrial engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. |
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2) |
Identify, formulate, and solve complex engineering problems; select and apply proper analysis and modeling methods for this purpose. |
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3) |
Design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. The ability to apply modern design methods to meet this objective. |
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4) |
Devise, select, and use modern techniques and tools needed for solving complex problems in industrial engineering practice; employ information technologies effectively. |
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5) |
Design and conduct experiments, collect data, analyze and interpret results for investigating the complex problems specific to industrial engineering. |
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6) |
Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working independently. |
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7) |
Demonstrate effective communication skills in both oral and written English and Turkish. Writing and understanding reports, preparing design and production reports, making effective presentations, giving and receiving clear and understandable instructions. |
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8) |
Recognize the need for lifelong learning; show ability to access information, to follow developments in science and technology, and to continuously educate him/herself. |
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9) |
Develop an awareness of professional and ethical responsibility, and behaving accordingly. Information about the standards used in engineering applications. |
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10) |
Know business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development. |
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11) |
Know contemporary issues and the global and societal effects of modern age engineering practices on health, environment, and safety; recognize the legal consequences of engineering solutions. |
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12) |
Develop effective and efficient managerial skills. |
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