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: 497
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Compulsory Course | 5 | 3 | 5.5 |
| Academic Year | 2023 – 2024 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600230490
|
| Section | Instructors |
|---|---|
| 1. ΤΜΗΜΑ Α | Andreas Koutsogiannis |
| 2. ΤΜΗΜΑ Β | Dimitrios Betsakos |
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600230490
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
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | |||
| Reading Assigment | 123 | 4.1 | |||
| Exams | 3 | 0.1 | |||
| Total | 165 | 5.5 |
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
03-11-2022
