Syllabus Application
MATH 502
Analysis II
Faculty
Faculty of Engineering and Natural Sciences
Semester
Spring 2025-2026
Course
MATH 502 -
Analysis II
Time/Place
Time
Week Day
Place
Date
15:40-17:30
Mon
FENS-L048
Feb 16-May 22, 2026
10:40-11:30
Tue
FENS-L029
Feb 16-May 22, 2026
Level of course
Masters
Course Credits
SU Credit:3, ECTS:10
Prerequisites
-
Corequisites
-
Course Type
Lecture
Instructor(s) Information
Dimitrios Papathanasıou
Course Information
Catalog Course Description
Metric spaces and general topological spaces. Connectedness, compactness, completeness and consequences. Baire category theorem. Linear topological spaces. Open mapping, closed graph theorems. Hahn Banach theorem. Hilbert and Banach spaces.
Course Learning Outcomes:
| 1. | At the end of the course the learner should be able to define the notions of a normed space, a Banach space, a Hilbert space. |
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| 2. | At the end of the course the learner should be able to state the open mapping theorem, the closed graph theorem, the contraction fixed point theorem, the Hahn-Banach theorem, the Banach-Alaoglu theorem. |
| 3. | At the end of the course the learner should be able to compute or estimate operator norms for certain examples of operators. |
Course Objective
Studying properties of Banach and Hilbert spaces
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