Specialized Topics in Algebra (ΑΛ6): Διαφορά μεταξύ των αναθεωρήσεων

Τελευταία αναθεώρηση της 17:28, 15 Ιουνίου 2023

Ελληνική Έκδοση
Graduate 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	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.

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+{{Course-Graduate-Top-EN}}
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 === General ===
@@ Γραμμή 27: / Γραμμή 29: @@
 |-
 ! Course Type
-| General Background
+| Special Background
 |-
 ! Prerequisite Courses
@@ Γραμμή 49: / Γραμμή 51: @@
 ! Learning outcomes
 |
-ΧΧΧ
+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
 |
-ΧΧΧ
+The aim of the course is to empower the postgraduate student to analyse and compose basic notions of Commutative Algebra.
 |}
 === Syllabus ===
-ΧΧΧ
+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 ===
@@ Γραμμή 66: / Γραμμή 68: @@
 ! Delivery
 |
-ΧΧΧ
+Face to face
 |-
 ! Use of Information and Communications Technology
-|
+| -
-ΧΧΧ
 |-
 ! Teaching Methods
@@ Γραμμή 81: / Γραμμή 82: @@
 | 39
 |-
-| ΧΧΧ
+| Study of theory
-| 000
+| 78
 |-
-| ΧΧΧ
+| Solving of Exercises
-| 000
+| 70.5
 |-
 | Course total
@@ Γραμμή 93: / Γραμμή 94: @@
 ! Student Performance Evaluation
 |
-ΧΧΧ
+Written exam at the end of semester (obligatory), problem solving or/and intermediate exams (optional)
 |}
@@ Γραμμή 99: / Γραμμή 100: @@
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