Group Theory (MAE525)

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)	http://users.uoi.gr/nkechag/GroupsNotesLONG3.pdf

Learning Outcomes

Learning outcomes

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.

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

• 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".