Real Analysis (MAE617)
Undergraduate Courses Outlines - Department of Mathematics
General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code | MAE511 |
| Semester |
5 |
| Course Title |
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 |
| Course Website (URL) |
http://www.math.uoi.gr/GR/studies/undergraduate/courses/perigr/MAE_511.pdf |
Learning Outcomes
| Learning outcomes |
The course aims in presenting topics concerning real valued functions defined on a metric space. Pointwise and uniform convergence of a sequence of functions are discussed as so as topics like Ascoli-Arzela theorem and Stone-Weirstrass theorem. Applications of the above are also given. |
|---|---|
| General Competences |
|
Syllabus
Function spaces on a metric space (X,d), pointwise and uniform convergence of sequence of functions, the space B(X) of real bounded functions on X-, the space C(X) of continuous functions on X – equicontinuous subsets of C(X), Ascoli-Arzela theorem and applications, Dini's theorem, Stone-Weierstrass theorem and applications, separable metric spaces, Lindelof's theorem on Euclidean spaces, the Cantor set, the Cantor function-applications.
Teaching and Learning Methods - Evaluation
| Delivery |
Face-to-face | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology |
Use of ICT for the presentation and communication for submission of the exercises | ||||||||||
| 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.
- Michael O Searcoid, Metric Spaces, Springer Undergraduate Mathematics Series.