| 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 computer engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.
|
|
| 2) |
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose.
|
2 |
| 3) |
Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
|
3 |
| 4) |
Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in computer engineering applications; ability to use information technologies effectively.
|
|
| 5) |
Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or computer engineering research topics.
|
3 |
| 6) |
Ability to work effectively within and multi-disciplinary teams; individual study skills.
|
2 |
| 7) |
Ability to communicate effectively in verbal and written Turkish; knowledge of at least one foreign language; ability to write active reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
|
|
| 8) |
Awareness of the necessity of lifelong learning; ability to access information, to follow developments in science and technology and to renew continuously.
|
|
| 9) |
To act in accordance with ethical principles, professional and ethical responsibility; information on the standards used in engineering applications.
|
|
| 10) |
Information on business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; information about sustainable development.
|
|
| 11) |
Knowledge of the effects of engineering practices on health, environment and safety in the universal and social scale and the problems of the era reflected in engineering; awareness of the legal consequences of engineering solutions.
|
|
BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
