Special Topics in Algebra (MAE723)

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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE723
Semester	7
Course Title	Special Topics in Algebra
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 principal aim of the course is to introduce the students to the main tools and methods of the theory of modules and rings. At the end of the course we expect the student to have understood the definitions and basic theorems which are discussed in the course, to have understood how they are applied in discrete examples, to be able to apply the material in order to extract new elementary conclusions, and finally to perform some (no so obvious) calculations.

General Competences

The contact of the undergraduate student with the ideas and concepts of the theory of modules and rings, (a) promotes the creative, analytical and deductive thinking and the ability to work independently, (b) improves his critical thinking and his ability to apply abstract knowledge in various field.

Syllabus

• Elementary Ring Theory.
• Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains.
• Module Theory.
• Modules over polynomial rings.
• Finitely generated and free modules.
• Modules over Principal Ideal Domains.
• Decomposition Theorems.
• Applications to Linear Algebra and Abelian groups.

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:

• J.Beachy, Introductory Lectures on Rings and Modules, LMS, Cambridge University Press, (1999).
• D.Dummit, R.M.Foote, Abstract Algebra, 3 edition, Prentice Hall, (2003).
• N.Jacobson, Basic Algebra I & II, W. H. Freeman and Company, (1985 & 1989).
• S.Lang, Algebra, Graduate Texts in Mathematics, Springer (2002).
• L.Rowen, Ring Theory, Academic Press, 2 edition (1991).
• Μαλιάκας. Ταλέλλη, Πρότυπα πάνω από Περιοχές Κυρίων Ιδεωδών και Εφαρμογές, Εκδ. Σοφία (2009).
• Α. Μπεληγιάννης, Μια Εισαγωγή στη Βασική Άλγεβρα, Εκδ. Κάλλιπος (2015).