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. |
|
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. |
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Program Outcomes |
Level of Contribution |
1) |
Have sufficient background in mathematics, science and artificial intelligence engineering. |
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2) |
Use theoretical and applied knowledge in the fields of mathematics, science and artificial intelligence engineering together for engineering solutions. |
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3) |
Identify, define, formulate and solve engineering problems, select and apply appropriate analytical methods and modeling techniques for this purpose. |
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4) |
Analyse a system, system component or process and design it under realistic constraints to meet desired requirements; apply modern design methods in this direction. |
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5) |
Select and use modern techniques and tools necessary for engineering applications. |
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6) |
Design and conduct experiments, collect data, and analyse and interpret results. |
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7) |
Work effectively both as an individual and as a multi-disciplinary team member. |
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8) |
Access information via conducting literature research, using databases and other resources |
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9) |
Follow the developments in science and technology and constantly update themself with an awareness of the necessity of lifelong learning. |
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10) |
Use information and communication technologies together with computer software with at least the European Computer License Advanced Level required by their field. |
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11) |
Communicate effectively, both verbal and written; know a foreign language at least at the European Language Portfolio B1 General Level. |
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12) |
Have an awareness of the universal and social impacts of engineering solutions and applications; know about entrepreneurship and innovation; and have an awareness of the problems of the age. |
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13) |
Have a sense of professional and ethical responsibility. |
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14) |
Have an awareness of project management, workplace practices, employee health, environment and work safety; know the legal consequences of engineering practices. |
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