Topics in Real Analysis (MAE615): Διαφορά μεταξύ των αναθεωρήσεων
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=== General === | === General === | ||
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! Course Website (URL) | ! Course Website (URL) | ||
| | | See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina. | ||
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=== Learning Outcomes === | === Learning Outcomes === | ||
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=== Attached Bibliography === | === Attached Bibliography === | ||
See [https://service.eudoxus.gr/public/departments#20 Eudoxus]. | <!-- In order to edit the bibliography, visit the webpage --> | ||
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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: | |||
{{MAE615-Biblio}} |
Τελευταία αναθεώρηση της 12:26, 15 Ιουνίου 2023
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General
School |
School of Science |
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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. |
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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 | ||||||||||
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Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
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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.