Groebner Bases (MAE526): Διαφορά μεταξύ των αναθεωρήσεων

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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)

https://sites.google.com/site/apostolosthomamath/teaching/

Learning Outcomes

Learning outcomes

The students will acquire with the successful completion of the course

  1. the skills to apply polynomial division
  2. the skills to compute Groebner bases
  3. 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

  • Μ. Μαλιάκας, Εισαγωγή στη Μεταθετική Άλγεβρα, 2008, "Σοφία" Ανώνυμη Εκδοτική & Εμπορική Εταιρεία, ISBN: 978-960-88637-4-3