| Week |
Subject |
Related Preparation |
| 1) |
Polynomial algebras over fields, their ideals and quaotients. Euclidean division algorithm. |
|
| 2) |
Free monoids. Lexicographical ordering. Other monomial orderings. |
|
| 3) |
Buchberger algorithm and Groebner bases. |
|
| 4) |
Buchberger algorithm and Groebner bases. |
|
| 5) |
Irreducible polynomials and field extensions. |
|
| 6) |
Symmetry groups of field extensions and Galois extensions. |
|
| 7) |
Examples from Galois extensions and calculations. |
|
| 8) |
The Fundamental Theorem of Algebra. Algebraic closure. Seperable closure. |
|
| 9) |
Transcendental extensions and transcendence degree. Krull dimension of an algebra. |
|
| 10) |
Noetherian algebras and finite generation. Nilpotent elements, nilpotent and nil ideals. Radicals. |
|
| 11) |
Nullstellensatz. |
|
| 12) |
Affine varieties. Examples. |
|
| 13) |
Zariski topology. Irreducible subvarieties. |
|
| 14) |
Selected tpoics from affine algebraic geometry. |
|
| |
Program Outcomes |
Level of Contribution |
| 1) |
Ability to assimilate mathematic related concepts and associate these concepts with each other.
|
5 |
| 2) |
Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
|
5 |
| 3) |
Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. |
|
| 4) |
Ability to make individual and team work on issues related to working and social life. |
|
| 5) |
Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. |
5 |
| 6) |
Ability to use mathematical knowledge in technology. |
|
| 7) |
To apply mathematical principles to real world problems. |
|
| 8) |
Ability to use the approaches and knowledge of other disciplines in Mathematics. |
|
| 9) |
Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. |
4 |
| 10) |
To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. |
|
| 11) |
To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. |
4 |
| 12) |
To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. |
3 |
BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
