Groebner Bases (MAE526): Διαφορά μεταξύ των αναθεωρήσεων
(Νέα σελίδα με '=== General === {| class="wikitable" |- ! 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 |- !...') |
|||
Γραμμή 36: | Γραμμή 36: | ||
|- | |- | ||
! Prerequisite Courses | ! Prerequisite Courses | ||
| | | - | ||
|- | |- | ||
! Language of Instruction and Examinations | ! Language of Instruction and Examinations | ||
Γραμμή 50: | Γραμμή 50: | ||
https://sites.google.com/site/apostolosthomamath/teaching/ | https://sites.google.com/site/apostolosthomamath/teaching/ | ||
|} | |} | ||
=== Learning Outcomes === | === Learning Outcomes === | ||
{| class="wikitable" | {| class="wikitable" |
Αναθεώρηση της 13:00, 28 Ιουνίου 2022
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