Topics in Real Analysis (MAE615)

Undergraduate Courses Outlines - Department of Mathematics

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)	-

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. Additionally:

• Charalambos D. Aliprantis, Owen Burkinshaw, Principles of Real Analysis, Academic Press.