Title  ΕΙΣΑΓΩΓΗ ΣΤΗΝ ΑΛΓΕΒΡΑ ΚΑΙ ΣΤΗ ΘΕΩΡΙΑ ΑΡΙΘΜΩΝ / Introduction to Algebra 
Code  0102 
Faculty  Sciences 
School  Mathematics 
Cycle / Level  1st / Undergraduate 
Teaching Period  Winter/Spring 
Common  No 
Status  Active 
Course ID  40000296 
Programme of Study: UPS of School of Mathematics (2014today)
Registered students: 259
Orientation  Attendance Type  Semester  Year  ECTS 

Core  Compulsory Course  1  1  5.5 
Academic Year  2019 – 2020 
Class Period  Spring 
Instructors from Other Categories 

Weekly Hours  3 
Class ID  600147662

Type of the Course
 Background
 General Knowledge
 Scientific Area
 Skills Development
Course Category
Specific Foundation / Core
Mode of Delivery
 Face to face
Digital Course Content
 eStudy Guide https://qa.auth.gr/en/class/1/600147662
 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 selfcritical
 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
15032020