Group Theory (MAE525)
Undergraduate Courses Outlines - Department of Mathematics
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) |
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 Eudoxus. Additionally:
- An Introduction to the Theory of Groups (Graduate Texts in Mathematics) 4th Edition by Joseph Rotman.