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Real Analysis (AN1): Διαφορά μεταξύ των αναθεωρήσεων

Real Analysis (AN1): Διαφορά μεταξύ των αναθεωρήσεων

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[[Graduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
* [[Πραγματική Ανάλυση (AN1)|Ελληνική Έκδοση]]
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=== General ===
=== General ===
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=== Syllabus ===
=== Syllabus ===


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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 ===
=== Teaching and Learning Methods - Evaluation ===
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! Delivery
! Delivery
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Teaching with talks on the blackboard.
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! Use of Information and Communications Technology
! Use of Information and Communications Technology
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! Teaching Methods
! Teaching Methods
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| Individual study
| 000
| 110
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| Exercises solving
| 000
| 38.5
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| Course total  
| Course total  
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! Student Performance Evaluation
! Student Performance Evaluation
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Final written exam or student's presentations on the blackboard. The student can choose either of the above ways of examination or both with final grade the higher one.
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Τελευταία αναθεώρηση της 16:24, 15 Ιουνίου 2023

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

Teaching with talks on the blackboard.

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 39
Individual study 110
Exercises solving 38.5
Course total 187.5
Student Performance Evaluation

Final written exam or student's presentations on the blackboard. The student can choose either of the above ways of examination or both with final grade the higher one.

Attached Bibliography

  • Charalambos D. Aliprantis, Owen Burkinshaw, Principles of Real Analysis, Academic Press.
  • Michael O Searcoid, Metric Spaces, Springer Undergraduate Mathematics Series.
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