Groebner Bases (MAE526)
General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
MAE526 |
| Semester |
5 |
| Course Title |
Groebner Bases |
| Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
| Course Type |
Special Background |
| Prerequisite Courses | |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students |
YES |
| Course Website (URL) |
Learning Outcomes
| Learning outcomes |
The students will acquire with the successful completion of the course
|
|---|---|
| General Competences |
The course aim is for the student to acquire the ability in analysis and synthesis of knowledge in Computational Algebra and produces free, creative and inductive thinking. |
Syllabus
Polynomial rings. Hilbert;s basis Theorem. Noetherian rings. Monomial οrders. Division Alghorithm. Groebner bases. S-polynomials and Buchberger;s alghorithm. Irreducible and universal Groebner bases. Nullstellensatz Theorem. Applications of Groebner: bases in elimination, Algebraic Geometry, field extensions, Graph Theory and Integer Programming.
Teaching and Learning Methods - Evaluation
| Delivery |
Classroom (face-to-face) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | |||||||||||
| Teaching Methods |
| ||||||||||
| Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
- Μ. Μαλιάκας, Εισαγωγή στη Μεταθετική Άλγεβρα, 2008, "Σοφία" Ανώνυμη Εκδοτική & Εμπορική Εταιρεία, ISBN: 978-960-88637-4-3