Introduction to Algebra and Number Theory

Course Information
TitleΕΙΣΑΓΩΓΗ ΣΤΗΝ ΑΛΓΕΒΡΑ ΚΑΙ ΣΤΗ ΘΕΩΡΙΑ ΑΡΙΘΜΩΝ / Introduction to Algebra and Number Theory
Code0102Α
FacultySciences
SchoolMathematics
Cycle / Level1st / Undergraduate
Teaching PeriodWinter
CommonYes
StatusActive
Course ID600019625

Programme of Study: Merikīs Foítīsīs (2014-sīmera)

Registered students: 4
OrientationAttendance TypeSemesterYearECTS
KORMOSCompulsory Course116

Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 215
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course116
Class Information
Academic Year2025 – 2026
Class PeriodWinter
Faculty Instructors
Instructors from Other Categories
Weekly Hours4
Total Hours52
Class ID
600276107
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)
  • English (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)
Operations. Sets. De Morgan's laws. Propositional calculus. Peano axioms. Equivalence relations and order relations. Monoids and semigroups. The ring of integers. Mathematical Induction. Divisibility. Prime numbers. The Euclidean Algorithm. GCD and LCM. Fundamental theorem of Arithmetic. The ring of congruences modulo n. Linear congruences.
Keywords
Sets, functions, relations, natural numbers, mathematical induction, divisibility, linear congruences.
Educational Material Types
  • Notes
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Communication with Students
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures39✓
Reading Assigment97✓
Tutorial26✓
Exams3✓
Total165
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 Α. Τσολομύτης, Σύνολα και Αριθμοί
Last Update
17-01-2024