Topics in Real Analysis (MAE615)
Undergraduate Courses Outlines - Department of Mathematics
General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
MAE615 |
| Semester |
6 |
| Course Title |
Topics in Real Analysis |
| Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
| Course Type |
Special Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students |
Yes (in English) |
| Course Website (URL) | - |
Learning Outcomes
| Learning outcomes |
The plan of the course is the achievement by the undergraduate student of the introductory background in the theory of metric spaces. |
|---|---|
| General Competences |
The objective of the course is the undergraduate student's ability achievement in analysis and synthesis of the basic background in Real Analysis. |
Syllabus
Baire spaces, the theorem of Cantor, characterization of complete metric spaces, compact metric spaces, Lebesgue's lemma, uniform continuous functions and extensions of them, completetion of a metric space and uniqueness up to isometry, oscillation of a function, continuity sets of a function which is the pointwise limit of a sequence of continuous functions, uniform convergence of a sequence of functions and related topics, Dini's theorem.
Teaching and Learning Methods - Evaluation
| Delivery |
Face-to-face | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
| ||||||||||
| Student Performance Evaluation |
Written examination at the end of the semester. |
Attached Bibliography
See Eudoxus. Additionally:
- Charalambos D. Aliprantis, Owen Burkinshaw, Principles of Real Analysis, Academic Press.