Group Theory (MAE525)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
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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 |
|
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 |
| ||||||||||
| 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.