# Algebraic Structures I

 Title ΑΛΓΕΒΡΙΚΕΣ ΔΟΜΕΣ Ι / Algebraic Structures I Code 0106Α Faculty Sciences School Mathematics Cycle / Level 1st / Undergraduate Teaching Period Winter Common Yes Status Active Course ID 600019629

### Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 18
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course326

 Academic Year 2020 – 2021 Class Period Spring Faculty Instructors Instructors from Other Categories Class ID 600185442
SectionInstructors
1. ΤΜΗΜΑ ΑAthanasios Papistas
2. ΤΜΗΜΑ ΒChrysostomos Psaroudakis
Course Type 2016-2020
• Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
• Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
• Greek (Instruction, Examination)
General Competences
• Apply knowledge in practice
• Retrieve, analyse and synthesise data and information, with the use of necessary technologies
• Work autonomously
• Be critical and self-critical
• Advance free, creative and causative thinking
Course Content (Syllabus)
Groups, Subgroups, Group generated by a set, Homomorphisms of groups, Permutation groups, Lagrange Theorem, Order of a group and order of an element, Euler's Theorem, Fermat's Theorem, Wilson's Theorem and their applications in arithmetics, Normal subgroups, Quotient group, Isomorphism theorems, Cyclic groups, classification of cyclic groups and their applications (Primitive roots (mod n)), product of subgroups, Direct product of groups.
Keywords
Groups, Quotient group, Isomorphism theorems, Cyclic groups, Classification
Educational Material Types
• Notes
• Book
Course Organization
Lectures391.3
Tutorial260.9
Exams30.1
Total1806
Student Assessment
Description
Examinations
Student Assessment methods
• Written Exam with Extended Answer Questions (Summative)
• Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
1. Αλγεβρικές Δομές Ι, Ε. Ψωμόπουλος, ΖΗΤΗ, 2010 2. Μία Εισαγωγή στην Άλγεβρα, Δ. Βάρσος, Δ. Δεριζιώτης, Γ. Εμμανουήλ, Μ. Μαλιάκας, Α. Μελάς, Ο. Ταλλέλη, ISBN: 978-960-6706-37-0, ΣΟΦΙΑ, 2012 3. Εισαγωγή στην Άλγεβρα, Ανδρεαδάκης, ISBN: 978-960-266-056-0, ΑΘΑΝΑΣΟΠΟΥΛΟΣ, 1993 4. Εισαγωγή στην Άλγεβρα, J. Fraleigh, ISBN: 978-960-7309-71-6, Πανεπιστημιακές Εκδόσεις Κρήτης 5. Μαθήματα Θεωρίας Ομάδων, Α. Πάπιστας, ISBN: 978-960-603-110-6, [ηλεκτρ. βιβλ.] Αθήνα:Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, ID Ευδόξου: 320082 6. Άλγεβρα, Δ.Μ. Πουλάκης, ISBN: 978-960-456-388-3, Εκδόσεις ΖΗΤΗ, Θεσσαλονίκη, 2015 7. Μία Εισαγωγή στη Βασική Άλγεβρα, Α. Μπεληγιάννης, ISBN: 978-960-603-262-2, [ηλεκτρ. βιβλ.] Αθήνα:Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, ID Ευδόξου: 320362 8. Επανάληψη στην Άλγεβρα: Σύντομη Θεωρία και Ασκήσεις, M.Holz, ISBN: 978-960-266-399-8, Εκδόσεις Συμμετρία
Last Update
22-07-2020