Group Theory (MAE525)
General
School |
School of Science |
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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, 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. |
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General Competences |
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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) | ||||||||||
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Use of Information and Communications Technology |
Communication with students | ||||||||||
Teaching Methods |
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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
- An Introduction to the Theory of Groups (Graduate Texts in Mathematics) 4th Edition by Joseph Rotman.
- Θεωρία ομάδων, Μιχάλης. Α. Γεωργιακόδης - Παναγιώτης. Ν. Γεωργιάδης
- M.A. Armstrong: "Ομάδες και Συμμετρία" (Κεφ. 1-24), Εκδόσεις "Leaderbooks".