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Topics in Real Analysis (MAE615): Διαφορά μεταξύ των αναθεωρήσεων

Topics in Real Analysis (MAE615): Διαφορά μεταξύ των αναθεωρήσεων

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(Νέα σελίδα με '=== General === {| class="wikitable" |- ! School | School of Science |- ! Academic Unit | Department of Mathematics |- ! Level of Studies | Undergraduate |- ! Course Code | MAE615 |- ! Semester | 6 |- ! Course Title | Topics in 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 Cours...')
 
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| See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina.
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=== Attached Bibliography ===
=== Attached Bibliography ===
* Charalambos D. Aliprantis, Owen Burkinshaw, Principles of Real Analysis, Academic Press.
 
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See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
 
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Τελευταία αναθεώρηση της 12:26, 15 Ιουνίου 2023

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAE615

Semester

6

Course Title

Topics in 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 (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 achievement by the undergraduate student of the introductory background in the theory of metric spaces.

General Competences

The objective of the course is the undergraduate student's ability achievement in analysis and synthesis of the basic background in Real Analysis.

Syllabus

Baire spaces, the theorem of Cantor, characterization of complete metric spaces, compact metric spaces, Lebesgue's lemma, uniform continuous functions and extensions of them, completetion of a metric space and uniqueness up to isometry, oscillation of a function, continuity sets of a function which is the pointwise limit of a sequence of continuous functions, uniform convergence of a sequence of functions and related topics, Dini's theorem.

Teaching and Learning Methods - Evaluation

Delivery

Face-to-face

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 39
Independent study 78
Exercises solutions 33
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.
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