# Introduction to Algebra

 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 Inactive Course ID 40000296

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

Registered students: 238
OrientationAttendance TypeSemesterYearECTS

 Academic Year 2018 – 2019 Class Period Spring Instructors from Other Categories Paraskevas Alvanos 39hrs Weekly Hours 3 Class ID 600121459
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
Lectures652.2
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