| Week |
Subject |
Related Preparation |
| 1) |
Abelian groups, rings and fields. |
|
| 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) |
Adequate knowledge in mathematics, science and electric-electronic engineering subjects; ability to use theoretical and applied information in these areas to model and solve engineering problems. |
|
| 2) |
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. |
|
| 3) |
Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues, according to the nature of the design.) |
|
| 4) |
Ability to devise, select, and use modern techniques and tools needed for electrical-electronic engineering practice; ability to employ information technologies effectively. |
|
| 5) |
Ability to design and conduct experiments, gather data, analyze and interpret results for investigating engineering problems. |
|
| 6) |
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. |
|
| 7) |
Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. |
|
| 8) |
Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. |
|
| 9) |
Awareness of professional and ethical responsibility. |
|
| 10) |
Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development. |
|
| 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 engineering solutions. |
|
BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
