Algebraic Number Theory
| Title | ΑΛΓΕΒΡΙΚΗ ΘΕΩΡΙΑ ΑΡΙΘΜΩΝ / Algebraic Number Theory |
| Code | 0165 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Common | No |
| Status | Active |
| Course ID | 40000308 |
Programme of Study: Merikīs Foítīsīs (2014-sīmera)
Registered students: 1
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| KORMOS | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 37
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | 7 | 4 | 5.5 |
| Academic Year | 2023 – 2024 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600230553
|
Course Type 2011-2015
Knowledge Deepening / Consolidation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600230553
- eLearning:
Erasmus
The course is also offered to exchange programme students.
Prerequisites
Required Courses
- 0106Α Algebraic Structures I
- Ν0107Α Algebraic Structures II
General Competences
- Apply knowledge in practice
- Make decisions
- Work autonomously
- Work in teams
- Advance free, creative and causative thinking
Course Content (Syllabus)
Fields Extensions, Symmetric Polynomials, Modules and Free Abelian Groups, Algebraic Number, Conjugates and Discriminant, Algebraic Integers, Number Fields, Integral Basis, Norm and Trace, Ring of Algebraic Integers, Quadratic Fields, Cyclotomic Fields, Noetherian Rings, Fractional Ideals, Factorization of Ideals in a product of Primes Ideals, Ideals Norm, Geometric Representation of Algebraic Numbers, Minkowski's Theorem, Class Group and Class Number, Computational Methods, Fields with Class Number 1, Application in the Resolution of Diophantine Equations.
Keywords
Algebraic number, Number fields, Quadratic fields, Cyclotomic fields, Unique factorization of ideals, Class group, Class number, Diophatine equations
Educational Material Types
- Notes
- 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 | ✓ | |||
| Reading Assigment | 123 | ✓ | ✓ | ||
| Exams | 3 | ✓ | |||
| Total | 165 |
Student Assessment
Student Assessment methods
- Written Exam with Multiple Choice Questions (Formative, Summative)
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Exam with Problem Solving (Formative)
Bibliography
Course Bibliography (Eudoxus)
1 - Αντωνιάδης Ι., Κοντογεώργης Α., Αλγεβρική Θεωρία Αριθμών.
Additional bibliography for study
1. Algebraic Number Theory του Frazer Jarvis, 2014, Springer, διαθέσιμο ηλεκτρονικά
https://search.heal-link.gr/Record/978-3-319-07545-7
2. Κ. Λάκκης, Θεωρία Αριθμών
3. Algebraic Number Theory and Fermat's Last Theorem, Ian Stewart και David Tall, CRS press, τρίτη έκδοση 2016
Last Update
17-01-2024
