Real Analysis (MAE617)
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- Undergraduate Courses Outlines
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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) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
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 the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Charalambos D. Aliprantis, Owen Burkinshaw, Principles of Real Analysis, Academic Press.
- Michael O Searcoid, Metric Spaces, Springer Undergraduate Mathematics Series.