Number Theory
| Title | ΘΕΩΡΙΑ ΑΡΙΘΜΩΝ / Number Theory |
| Code | 0136 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | No |
| Status | Active |
| Course ID | 40002474 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 1
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2016 – 2017 |
| Class Period | Spring |
| Instructors from Other Categories | |
| Class ID | 600038316
|
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/1/600038316
- At the Website of the School:
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
Prerequisites
Required Courses
- 0102 Introduction to Algebra
- 0106 Algebraic Structures I
Learning Outcomes
With the successful fullfilled of the course the students get self-activation and increase their ability to solve comlpicate unknown problems.
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Adapt to new situations
- Make decisions
- Work autonomously
- Generate new research ideas
- Respect natural environment
- Demonstrate social, professional and ethical commitment and sensitivity to gender issues
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Linear congruents modulo n. Systems of linear congruents . Euler function. Arithmetic multiplicative functions. Polynomial congruents, Diophantic equations. Pythagorean Triples. Fermat’s Theorem for n=4. Quadratic residues. Quadratic reciprocity low. Quadratic number fields. Unsolved problems.
Keywords
modn, congruents, arithmetic functions, quadtatic residues, quadratic reciprocity lows, Diophantic equations, quadratic number fields.
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | ✓ | ||||
| Tutorial | |||||
| Total |
Student Assessment
Description
Written examinations οf progress and final written examinations.
Information is given during the first lecture.
Student Assessment methods
- Written Exam with Multiple Choice Questions (Formative)
- Written Exam with Short Answer Questions (Formative)
- Written Assignment (Formative, Summative)
- Written Exam with Problem Solving (Formative)
Bibliography
Course Bibliography (Eudoxus)
1. Θεωρία αριθμών, Δ.Μ. Πουλάκης, ISBN: 960-431-429-7, ΖΗΤΗ, 1997
2. Μία Εισαγωγή στη Θεωρία Αριθμών, Δ. Δεριζιώτης, ISBN: 978-960-6706-44-8, ΣΟΦΙΑ, 2012
3. Θεωρία αριθμών, Π. Τσαγκάρης, ISBN: 978-960-266-143-7, ΑΘΑΝΑΣΟΠΟΥΛΟΣ, 2010
4. Θεωρία Αριθμών και Εφαρμογές, Ι.Αντωνιάδης, Α. Κοντογεώργης, ISBN: 978-618-82124-5-9, [ηλεκτρ. βιβλ.] Αθήνα:Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, ID Ευδόξου: 320067
5. Υπολογιστική Θεωρία Αριθμών, Δ. Πουλάκης, ISBN: 978-960-603-127-4, [ηλεκτρ. βιβλ.] Αθήνα:Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, ID Ευδόξου: 320067¬¬¬
Additional bibliography for study
J. Fraleigh, Eισαγωγή στην Άλγεβρα, Πανεπιστημιακές Εκδόσεις Κρήτης
Last Update
26-05-2016
