Algebraic Structures II
| Title | ΑΛΓΕΒΡΙΚΕΣ ΔΟΜΕΣ ΙΙ / Algebraic Structures II |
| Code | Ν0107Α |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate, 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Common | Yes |
| Status | Active |
| Course ID | 600019633 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 309
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Compulsory Course | Winter/Spring | - | 6 |
| Academic Year | 2023 – 2024 |
| Class Period | Spring |
| Faculty Instructors |
|
| Instructors from Other Categories |
|
| Weekly Hours | 4 |
| Class ID | 600230551
|
| Section | Instructors |
|---|---|
| 1. ΤΜΗΜΑ Α2 | Chrysostomos Psaroudakis, Charilaos Vavatsoulas |
| 2. ΤΜΗΜΑ Β | Angelos Koutsianas, Charilaos Vavatsoulas |
| 3. ΑΣΚΗΣΕΙΣ | Charilaos Vavatsoulas |
| 4. ΤΜΗΜΑ Α1 | Hara-Myrto-Agapi Charalambous, Charilaos Vavatsoulas |
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600230551
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=6522
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Examination)
Prerequisites
Required Courses
- 0110 ELEMENTS OF LINEAR ALGEBRA
Learning Outcomes
Upon successful completion of the course the students
i) will recognize the algebraic structures of rings and fields
ii) will be able to handle general rings and especially polynomila rings
iii) will be able to do computations with ideals
iv) will be able to apply the isomorphism theorems
v) will be able to study factorization problems in integral domains
vi) will be able to do simple computationw with rings and field extesnsions
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Make decisions
- Work autonomously
- Work in teams
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Rings with identity, Subrings, zero divisors, Product of rings, Characteristic of a ring, the rings R[a], Integral Domain, the group of invertible elements, Gauss integers, Fields, Subfields, Ideals, Sum and Product of Ideals, Quotient ring, Commutative rings, Prime and Maximals Ideals, Ring Homomorphisms, 1st Ring Homomorphisms Theorem, Fraction Field, Division in integral domain, Irreducible elements, Polynomial Ring K[x], Polynomials Division, Division Algorithm, GCD, Irreducible polynomials, Irreducibility Criteria, Principal Ideal Domain, Unique Factorization Domain, the Polynomial Ring K[X1, ..., Xn]
Educational Material Types
- Notes
- Video lectures
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
- Use of ICT in Student Assessment
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | |||
| Reading Assigment | 125 | 4.2 | |||
| Tutorial | 13 | 0.4 | |||
| Exams | 3 | 0.1 | |||
| Total | 180 | 6 |
Student Assessment
Description
Writen Final Exam
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
- Αλγεβρικές Δομές II του Ε. Ψωμόπουλου.
- Εισαγωγή στην Άλγεβρα του J. Fraleigh.
- Μία εισαγωγή στην άλγεβρα, Βάρσος Δ, Δερζιώτης Δ, Εμμανουήλ Γ., Μαλιάκας Μ., Ταλέλλη Ο.
- Εισαγωγή στην Άλγεβρα, Ανδρεαδάκης, Αθανασόπουλος
- Άλγεβρα, Πουλάκης Δημήτριος Μ.
- Επανάληψη στην Άλγεβρα, Michael Holz
- Μία Εισαγωγή στη Βασική Αλγεβρα [electronic resource], Α. Μπεληγιάννης, kallipos.gr
- Ασκήσεις Βασικής Αλγεβρας, Α. Μπεληγιάννης. Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, 2016
Last Update
17-01-2024
