Introduction to Algebra

Course Information
TitleΕΙΣΑΓΩΓΗ ΣΤΗΝ ΑΛΓΕΒΡΑ ΚΑΙ ΣΤΗ ΘΕΩΡΙΑ ΑΡΙΘΜΩΝ / Introduction to Algebra
Code0102
FacultySciences
SchoolMathematics
Cycle / Level1st / Undergraduate
Teaching PeriodWinter/Spring
CommonNo
StatusInactive
Course ID40000296

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

Registered students: 460
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course115.5

Class Information
Academic Year2018 – 2019
Class PeriodWinter
Faculty Instructors
Instructors from Other Categories
Weekly Hours3
Class ID
600120789
SectionInstructors
1. ΤΜΗΜΑ ΑDimitrios Poulakis, Paraskevas Alvanos
2. ΤΜΗΜΑ ΒParaskevas 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
Language of Instruction
  • Greek (Instruction, Examination)
Learning Outcomes
Successful completion of the course offers the student knowledge of the basic concepts and structures of Algebra and Number Theory, and the basic ability to transfer this knoweledge.
General Competences
  • Apply knowledge in practice
  • Retrieve, analyse and synthesise data and information, with the use of necessary technologies
  • Work autonomously
  • Appreciate diversity and multiculturality
  • 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)
The course is part of the module of courses that aim to offer dexterities for teaching mathematics in Secondary Education. Sets, Functions. Cartesian product. Equivalence relations. Ordering. Operations on a set. Semigroups., Monoids. Natural numbers. Mathematical induction. Well ordering principle. Complex Numbers. Countable sets. Elements of combinatorial theory. The ring of integers. Divisibility. Euclidean algorithm. GCD, LCM. Bezout's identity. Solutions of the linear equation ax+by= c. Rationals in base n. Prime numbers. Wilson's theorem. Fundamental theorem of arithmetic. Rings modulo n. Fields modulo p. Linear equivalences and systems. Chinese Remainder Theorem, Euler's function, Fermat's Small Theorem, Groups, Euler's Theorem, Groups, ISomorphism of Groups, Classification of groups of small order.
Educational Material Types
  • Notes
  • Video lectures
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Communication with Students
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures652.2
Reading Assigment581.9
Tutorial391.3
Exams30.1
Total1655.5
Student Assessment
Description
Written final examination
Student Assessment methods
  • Written Exam with Multiple Choice Questions (Formative, Summative)
  • Written Exam with Short Answer Questions (Formative, Summative)
  • Written Exam with Extended Answer Questions (Formative)
  • Written Exam with Problem Solving (Formative, Summative)
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
24-04-2019