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Group Theory (MAE525): Διαφορά μεταξύ των αναθεωρήσεων

Group Theory (MAE525): Διαφορά μεταξύ των αναθεωρήσεων

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(Νέα σελίδα με '=== General === {| class="wikitable" |- ! School | School of Science |- ! Academic Unit | Department of Mathematics |- ! Level of Studies | Undergraduate |- ! Course Code | MAE525 |- ! Semester | 5th |- ! Course Title | Group Theory |- ! Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 6) |- ! Course Type | Special background, skills development. |- ! Prerequisite Courses | |- ! Language of Instruction and Examinations | Greek, Englis...')
 
Χωρίς σύνοψη επεξεργασίας
 
(10 ενδιάμεσες αναθεωρήσεις από τον ίδιο χρήστη δεν εμφανίζεται)
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* [[Θεωρία Ομάδων (ΜΑΕ525)|Ελληνική Έκδοση]]
{{Course-UnderGraduate-Top-EN}}
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=== General ===
=== General ===
{| class="wikitable"
{| class="wikitable"
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! Semester
! Semester
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5th
5
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! Course Title
! Course Title
Γραμμή 27: Γραμμή 31:
|-
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! Independent Teaching Activities
! Independent Teaching Activities
| Lectures (Weekly Teaching Hours: 3, Credits: 6)
| Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6)
|-
|-
! Course Type
! Course Type
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! Prerequisite Courses
! Prerequisite Courses
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| -
|-
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! Language of Instruction and Examinations
! Language of Instruction and Examinations
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|-
! Course Website (URL)
! Course Website (URL)
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| See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina.
http://users.uoi.gr/nkechag/GroupsNotesLONG3.pdf
|}
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=== Learning Outcomes ===
=== Learning Outcomes ===
{| class="wikitable"
{| class="wikitable"
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! Learning outcomes
! Learning outcomes
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* Description of the level of learning outcomes for each qualifications cycle, according to the Qualifications Framework of the European Higher Education Area
* Descriptors for Levels 6, 7 & 8 of the European Qualifications Framework for Lifelong Learning and Appendix B
* Guidelines for writing Learning Outcomes.
Familiarity with: group, abelian group, subgroup, normal subgroup, quotient group, direct product of groups, homomorphism, isomorphism, kernel of a homomorphism.  Apply group theory to describe symmetry, describe the elements of symmetry group of the regular n-gon (the dihedral group D2n). Compute with the symmetric group. Know how to show that a subset of a group is a subgroup or a normal subgroup. State and apply Lagrange's theorem. State and prove the isomorphism theorems. Sylow theorems. The classification of finite abelian groups. Normal series, central series, nilpotent groups. Applications in Geometry.
Familiarity with: group, abelian group, subgroup, normal subgroup, quotient group, direct product of groups, homomorphism, isomorphism, kernel of a homomorphism.  Apply group theory to describe symmetry, describe the elements of symmetry group of the regular n-gon (the dihedral group D2n). Compute with the symmetric group. Know how to show that a subset of a group is a subgroup or a normal subgroup. State and apply Lagrange's theorem. State and prove the isomorphism theorems. Sylow theorems. The classification of finite abelian groups. Normal series, central series, nilpotent groups. Applications in Geometry.
|-
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* Working in an interdisciplinary.
* Working in an interdisciplinary.
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=== Syllabus ===
=== Syllabus ===
* Basic properties in groups.
* Basic properties in groups.
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=== Attached Bibliography ===
=== Attached Bibliography ===
* An Introduction to the Theory of Groups (Graduate Texts in Mathematics) 4th Edition by Joseph Rotman.
 
* Θεωρία ομάδων,  Μιχάλης. Α. Γεωργιακόδης - Παναγιώτης. Ν. Γεωργιάδης
<!-- In order to edit the bibliography, visit the webpage -->
* M.A. Armstrong: "Ομάδες και Συμμετρία" (Κεφ. 1-24), Εκδόσεις "Leaderbooks".
<!-- https://wiki.math.uoi.gr/index.php/%CE%A0%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF:MAE525-Biblio -->
 
See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
 
{{MAE525-Biblio}}

Τελευταία αναθεώρηση της 12:25, 15 Ιουνίου 2023

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAE525

Semester

5

Course Title

Group Theory

Independent Teaching Activities Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6)
Course Type

Special background, skills development.

Prerequisite Courses -
Language of Instruction and Examinations

Greek, English

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

Familiarity with: group, abelian group, subgroup, normal subgroup, quotient group, direct product of groups, homomorphism, isomorphism, kernel of a homomorphism.  Apply group theory to describe symmetry, describe the elements of symmetry group of the regular n-gon (the dihedral group D2n). Compute with the symmetric group. Know how to show that a subset of a group is a subgroup or a normal subgroup. State and apply Lagrange's theorem. State and prove the isomorphism theorems. Sylow theorems. The classification of finite abelian groups. Normal series, central series, nilpotent groups. Applications in Geometry.

General Competences
  • Study particular characteristics of group theory in topology and geometry.
  • Independent and team work.
  • Working in an interdisciplinary.

Syllabus

  • Basic properties in groups.
  • Symmetries.
  • Subgroups, Direct products, Cosets.
  • Symmetric groups.
  • Normal Subgroups, Quotient groups.
  • Homomorphisms.
  • Semidirect product.
  • Classification of finite abelian groups.
  • Sylow theorems.
  • Normal series, Solvable groups. Central series, Nilpotent groups.

Teaching and Learning Methods - Evaluation

Delivery

Classroom (face-to-face)

Use of Information and Communications Technology

Communication with students

Teaching Methods
Activity Semester Workload
Lectures (13X3) 39
Working independently 78
Exercises-Homeworks 33
Course total 150
Student Performance Evaluation

Written Examination, Oral Presentation, written assignments 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:

  • An Introduction to the Theory of Groups (Graduate Texts in Mathematics) 4th Edition by Joseph Rotman.
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