Specialized Topics in Algebra (ΑΛ6)

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• Graduate Courses Outlines
• Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	ΑΛ6
Semester	2
Course Title	Specialized Topics in Algebra
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes	The aim of the course is for the postgraduate student to reach a good level of theoretical background on topics related to the theory of commutative rings.
General Competences	The aim of the course is to empower the postgraduate student to analyse and compose basic notions of Commutative Algebra.

Syllabus

Topics of Commutative and Combinatorial Algebra: Hilbert's Basis theorem, Primary Decomposition, Localization, Dimension, Hilbert Series, Groebner Bases, Simplicial complexes and homology, Stanley-Reisner ideals, Hilbert's Nullstellensatz theorem.

Teaching and Learning Methods - Evaluation

Delivery	Face to face
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures 39 Study of theory 78 Solving of Exercises 70.5 Course total 187.5
Student Performance Evaluation	Written exam at the end of semester (obligatory), problem solving or/and intermediate exams (optional)

Attached Bibliography

• Μαλιάκας Μιχάλης, Εισαγωγή στην Μεταθετική Άλεβρα, Εκδόσεις Σοφία, 2008
• Atiyah, M. F.; Macdonald, I. G., Introduction to commutative algebra. Addison-Wesley Publishing Co., 1969 ix+128 pp.