Groebner Bases (MAE526)

Undergraduate Courses Outlines - Department of Mathematics

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 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

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