Special Topics in Algebra (MAE723): Διαφορά μεταξύ των αναθεωρήσεων

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=== Attached Bibliography ===
=== Attached Bibliography ===
See [https://service.eudoxus.gr/public/departments#20 Eudoxus]. Additionally:
* Μ. Μαλιάκας - Ο. Ταλέλλη: «Πρότυπα πάνω σε Περιοχές Κυρίων Ιδεωδών και Εφαρμογές»,  Εκδόσεις Σοφία. 
* Μ. Μαλιάκας - Ο. Ταλέλλη: «Πρότυπα πάνω σε Περιοχές Κυρίων Ιδεωδών και Εφαρμογές»,  Εκδόσεις Σοφία. 
* Μ. Μαλιάκας: «Εισαγωγή στη Μεταθετική Άλγεβρα»,  Εκδόσεις Σοφία. 
* Μ. Μαλιάκας: «Εισαγωγή στη Μεταθετική Άλγεβρα»,  Εκδόσεις Σοφία. 
* N. Jacobson: “Basic Algebra I”, Dover Publications (1985).
* N. Jacobson: “Basic Algebra I”, Dover Publications (1985).
* S. Lang: «Άλγεβρα», Εκδόσεις Πολιτεία (2010).
* S. Lang: «Άλγεβρα», Εκδόσεις Πολιτεία (2010).

Αναθεώρηση της 12:43, 23 Ιουλίου 2022

Undergraduate Courses Outlines - Department of Mathematics

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) -

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 Eudoxus. Additionally:

  • Μ. Μαλιάκας - Ο. Ταλέλλη: «Πρότυπα πάνω σε Περιοχές Κυρίων Ιδεωδών και Εφαρμογές»,  Εκδόσεις Σοφία. 
  • Μ. Μαλιάκας: «Εισαγωγή στη Μεταθετική Άλγεβρα»,  Εκδόσεις Σοφία. 
  • N. Jacobson: “Basic Algebra I”, Dover Publications (1985).
  • S. Lang: «Άλγεβρα», Εκδόσεις Πολιτεία (2010).