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. |
|
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) |
Be able to specify functional and non-functional attributes of software projects, processes and products. |
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2) |
Be able to design software architecture, components, interfaces and subcomponents of a system for complex engineering problems. |
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3) |
Be able to develop a complex software system with in terms of code development, verification, testing and debugging. |
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4) |
Be able to verify software by testing its program behavior through expected results for a complex engineering problem. |
|
5) |
Be able to maintain a complex software system due to working environment changes, new user demands and software errors that occur during operation. |
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6) |
Be able to monitor and control changes in the complex software system, to integrate the software with other systems, and to plan and manage new releases systematically. |
|
7) |
Be able to identify, evaluate, measure, manage and apply complex software system life cycle processes in software development by working within and interdisciplinary teams. |
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8) |
Be able to use various tools and methods to collect software requirements, design, develop, test and maintain software under realistic constraints and conditions in complex engineering problems. |
|
9) |
Be able to define basic quality metrics, apply software life cycle processes, measure software quality, identify quality model characteristics, apply standards and be able to use them to analyze, design, develop, verify and test complex software system. |
|
10) |
Be able to gain technical information about other disciplines such as sustainable development that have common boundaries with software engineering such as mathematics, science, computer engineering, industrial engineering, systems engineering, economics, management and be able to create innovative ideas in entrepreneurship activities. |
|
11) |
Be able to grasp software engineering culture and concept of ethics and have the basic information of applying them in the software engineering and learn and successfully apply necessary technical skills through professional life. |
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12) |
Be able to write active reports using foreign languages and Turkish, understand written reports, prepare design and production reports, make effective presentations, give clear and understandable instructions. |
|
13) |
Be able to have knowledge about the effects of engineering applications on health, environment and security in universal and societal dimensions and the problems of engineering in the era and the legal consequences of engineering solutions. |
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