| 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) |
Build up a body of knowledge in mathematics, science and Energy Systems Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. |
|
| 2) |
Ability to identify, formulate, and solve complex Energy Systems Engineering problems; select and apply proper modeling and analysis methods for this purpose.
|
|
| 3) |
Ability to design complex Energy systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. |
|
| 4) |
Ability to devise, select, and use modern techniques and tools needed for solving complex problems in Energy Systems Engineering practice; employ information technologies effectively. |
|
| 5) |
Ability to design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Energy Systems Engineering. |
|
| 6) |
Ability to cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Energy Systems-related problems |
|
| 7) |
Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions. |
|
| 8) |
Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself. |
|
| 9) |
Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Energy Systems Engineering applications. |
|
| 10) |
Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development. |
|
| 11) |
Acquire knowledge about the effects of practices of Energys Systems Engineering on health, environment, security in universal and social scope, and the contemporary problems of Energys Systems engineering; is aware of the legal consequences of Energys Systems engineering solutions. |
|
BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
