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School of Science
Department of Mathematics
|Level of Studies||
|Independent Teaching Activities||Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6)|
Special background, skills development.
|Language of Instruction and Examinations||
|Is the Course Offered to Erasmus Students||
|Course Website (URL)||See eCourse, the Learning Management System maintained by the University of Ioannina.|
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.
- Basic properties in groups.
- Subgroups, Direct products, Cosets.
- Symmetric groups.
- Normal Subgroups, Quotient groups.
- Semidirect product.
- Classification of finite abelian groups.
- Sylow theorems.
- Normal series, Solvable groups. Central series, Nilpotent groups.
Teaching and Learning Methods - Evaluation
|Use of Information and Communications Technology||
Communication with students
|Student Performance Evaluation||
Written Examination, Oral Presentation, written assignments in Greek (in case of Erasmus students in English) which includes resolving application problems.
- An Introduction to the Theory of Groups (Graduate Texts in Mathematics) 4th Edition by Joseph Rotman.