Real Analysis (AN1)

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Graduate Courses Outlines - Department of Mathematics

General

School School of Science
Academic Unit Department of Mathematics
Level of Studies Graduate
Course Code AN1
Semester 1
Course Title Real Analysis
Independent Teaching Activities Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type General Background
Prerequisite Courses

Introduction to Topology

Language of Instruction and Examinations

Greek

Is the Course Offered to Erasmus Students Yes (in English)
Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The plan of the course is the deeper study of the theory of metric spaces. The Stone - Weirstrass theorem is presented and also there are studied theorems that involve families of equicontinuous functions. Among others there are studied the following topics: the Cantor set, totally bounded and compact metric spaces, the Hausdorff metric and the Tietze theorem. Moreover, applications of the above theorems are given.

General Competences

The objective of the course is the graduate student’s ability achievement in analysis and synthesis of deeper knowledge of Real Analysis.

Syllabus

The Ascoli - Arzela and Stone - Weirstrass theorems and applications, the Cantor set, characterization of totally bounded metric spaces via subsets of Cantor set, extensions of continuous functions and the Tietze theorem, the space S(X) of closed and bounded subsets of a metric space and the metric Hausdorff on S(X), characterization of completeness of the metric space S(X) equipped with the metric Hausdorff and applications, the selection Blashke theorem, applications of the fixed point theorem of Banach, partitions of unity.

Teaching and Learning Methods - Evaluation

Delivery

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Use of Information and Communications Technology

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Teaching Methods
Activity Semester Workload
Lectures 39
ΧΧΧ 000
ΧΧΧ 000
Course total 187.5
Student Performance Evaluation

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Attached Bibliography

Πρότυπο:MAM199-Biblio