Introduction to Algebra
| Title | ΕΙΣΑΓΩΓΗ ΣΤΗΝ ΑΛΓΕΒΡΑ ΚΑΙ ΣΤΗ ΘΕΩΡΙΑ ΑΡΙΘΜΩΝ / Introduction to Algebra |
| Code | 0102Α |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Common | Yes |
| Status | Active |
| Course ID | 600019625 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 603
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Compulsory Course | 1 | 1 | 6 |
| Academic Year | 2020 – 2021 |
| Class Period | Winter |
| Faculty Instructors |
|
| Instructors from Other Categories |
|
| Weekly Hours | 4 |
| Class ID | 600166613
|
| Section | Instructors |
|---|---|
| 1. ΤΜΗΜΑ Α | Paraskevas Alvanos |
| 2. ΤΜΗΜΑ Β | Ioannis Souldatos |
| 3. ΦΡΟΝΤΙΣΤΗΡΙΟ | Ioannis Souldatos, Paraskevas Alvanos |
Course Type 2016-2020
- Background
- General Knowledge
- Scientific Area
- Skills Development
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/1/600166613
- At the Website of the School: www.math.auth.gr
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Learning Outcomes
Upon successful completion of the course, students should have
- Understand the basic concepts of Mathematical Structures
- Understand the basic concepts of Number Theory
- solves Algebra's computational and theoretical problems
- solves computational and theoretical problems of Number Theory
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
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Sets, Functions. Equivalence relations and order relations. Operations in a set.
The set of natural numbers. Mathematical Induction. Principle of good order.
Countable sets. Newton's identities.
Groups, Ring Bodies: Definitions and Examples. The ring of integers.
Divisibility. Prime numbers. The Euclidean Algorithm. GCD, LCM. Fundamental
theorem of number theory. The ring of modn congruences. The
Zp field. Linear congruences. Multiplicative functions.
Keywords
Sets, functions, relations, natural numbers, mathematical induction, divisibility, linear congruences, multiplicative functions.
Educational Material Types
- Notes
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Communication with Students
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | ✓ | ||
| Reading Assigment | 97 | 3.2 | ✓ | ||
| Tutorial | 26 | 0.9 | ✓ | ||
| Exams | 3 | 0.1 | ✓ | ||
| Total | 165 | 5.5 |
Student Assessment
Description
Written final examination
Bibliography
Course Bibliography (Eudoxus)
Ε. Ψωμόπουλου, Εισαγωγλη στην Άλγεβρα, Εκδ. Ζήτη
Δ. Πουλάκης, Άλγεβρα, Εκδ. Ζήτη
Κ. Κάλφα, Εισαγωγή στην Άλγεβρα, Εκδόσεις Ζήτη
Last Update
22-07-2020
