# Introduction to Real Analysis

 Title ΕΙΣΑΓΩΓΗ ΣΤΗΝ ΠΡΑΓΜΑΤΙΚΗ ΑΝΑΛΥΣΗ / Introduction to Real Analysis Code 0207 Faculty Sciences School Mathematics Cycle / Level 1st / Undergraduate Teaching Period Winter Common Yes Status Active Course ID 40000495

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

Registered students: 480
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course535.5

 Academic Year 2019 – 2020 Class Period Winter Faculty Instructors Dimitrios Betsakos 26hrs Romanos diogenis Malikiosis 39hrs Michail Marias 13hrs Weekly Hours 3 Class ID 600147624
SectionInstructors
1. ΤΜΗΜΑ ΑDimitrios Betsakos, Michail Marias
2. ΤΜΗΜΑ ΒRomanos diogenis Malikiosis
Mode of Delivery
• Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Course Content (Syllabus)
Real numbers - Countable and uncountable sets - Sequences and series - permutations of series - representations of real numbers - The Cantor set and Cantor’s function - Special classes of functions (monotone, bounded variation, absolutely continuous, convex) - Sequences and series of functions - uniform convergence and applications - nowhere differentiable continuous functions - space filling curves - equicartinuity - Azzela’s-Ascoli’s theorem - Weierstrass approximation theorem - Lebesque’s measure.
Keywords
real numbers, countable sets, uncountable sets, Cantor set, sequences and series functions, .
Course Organization
Lectures391.3
Exams30.1
Total1655.5
Student Assessment
Student Assessment methods
• Written Exam with Short Answer Questions (Summative)
• Written Exam with Extended Answer Questions (Summative)
• Written Exam with Problem Solving (Summative)
Bibliography
Course Bibliography (Eudoxus)
1. Δ. Μπετσάκος, Εισαγωγή στην Πραγματική Ανάλυση, Εκδόσεις Αφοι Κυριακίδη, 2016 2. W. Rudin, Αρχές Μαθηματικής Ανάλυσης, Leader Books, 2014 3. Π. Ξενικάκης, Πραγματική Ανάλυση, Εκδόσεις Ζήτη, 1995
Last Update
15-03-2020