# 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
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course116

 Academic Year 2020 – 2021 Class Period Winter Faculty Instructors Ioannis Souldatos 52hrs Instructors from Other Categories Paraskevas Alvanos 52hrs Weekly Hours 4 Class ID 600166613
SectionInstructors
2. ΤΜΗΜΑ ΒIoannis Souldatos
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
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
• 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