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Information
| Code | MT001 |
| Name | Introduction to Gröbner Bases |
| Term | 2024-2025 Academic Year |
| Term | Fall |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ŞEHMUS FINDIK |
| Course Instructor |
1 |
Course Goal / Objective
Learning basic knowledge about Gröbner Bases and observing their some applications.
Course Content
Introduction to Gröbner Bases, Term orders, Division algorithm, Gröbner Bases, S-polynomials and Buchberger algorithm, Reduced Gröbner Bases, Applications of Gröbner Bases
Course Precondition
Algebra
Resources
An Introduction to Gröbner Bases, W. W. Adams, P. Loustaunau
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learns term orders on the polynomial algebra. |
| LO02 | Learns the division algorithm on the polynomial algebra. |
| LO03 | Knows Noetherian rings |
| LO04 | Knows Hilbert basis theorem with its proof. |
| LO05 | Learns the reduced word. |
| LO06 | Knows Gröbner bases and basic applications of Gröbner bases. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows the results of previous research in a special field of mathematics | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | 5 |
| PLO08 | Bilgi - Kuramsal, Olgusal | It carries out original and qualified scientific studies on the subject related to its field. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 5 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have foreign language knowledge at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 4 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | It presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Polynomial algebra and affine n-space | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 2 | Varieties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 3 | The relationship between the ideals of polynomial algebra and varieties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 4 | Term orders | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 5 | Applications of Lex, dlex, drlex orders | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 6 | Reduced words | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 7 | Problem solving 1 | 7. Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | 8. Reading the lecture notes | Öğretim Yöntemleri: Soru-Cevap |
| 9 | Division algorithm | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 10 | Noetherian rings. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 11 | Hilbert basis theorem. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 12 | Gröbner bases | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 13 | Applications of Gröbner bases 1 | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 14 | Applications of Gröbner bases | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım |
| 15 | Repetition of topics. | 15. Reading the lecture notes | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams 1 | 16. Reading the lecture notes | Öğretim Yöntemleri: Soru-Cevap |
| 17 | Term Exams | 17. Reading the lecture notes | Öğretim Yöntemleri: Soru-Cevap |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||