Groebner Bases (MAE526): Διαφορά μεταξύ των αναθεωρήσεων

Τελευταία αναθεώρηση της 12:25, 15 Ιουνίου 2023

Ελληνική Έκδοση
Undergraduate Courses Outlines
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Department of Mathematics
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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)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes	The students will acquire with the successful completion of the course the skills to apply polynomial division the skills to compute Groebner bases the skills to apply Groebner bases techniques to problems coming from elimination theory, Algebraic Geometry, filed extensions, Graph Theory and Integer programming.
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

Activity	Semester Workload
Lectures (13X3)	39
Working independently	78
Exercises-Homeworks	33
Course total	150

Student Performance Evaluation

Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems.

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

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+| See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina.
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 Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems.
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 === Attached Bibliography ===
-* Μ. Μαλιάκας, Εισαγωγή στη Μεταθετική Άλγεβρα, 2008, "Σοφία" Ανώνυμη Εκδοτική & Εμπορική Εταιρεία, ISBN: 978-960-88637-4-3
+<!-- In order to edit the bibliography, visit the webpage -->
+<!-- https://wiki.math.uoi.gr/index.php/%CE%A0%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF:MAE526-Biblio -->
+See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
+{{MAE526-Biblio}}