Real Analysis (MAE617)

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School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code MAE617


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


Is the Course Offered to Erasmus Students


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
  • Working independently
  • Team work
  • Working in an international environment
  • Working in an interdisciplinary environment
  • Production of new research ideas.


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



Use of Information and Communications Technology

Use of ICT for the presentation and communication for submission of the exercises

Teaching Methods
Activity Semester Workload
Lectures 39
Home exercises 30
Independent study 81
Course total 150
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.