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.
Analysis II (MATH 502)
2021 Spring
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10.00
Albert Erkip albert@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture
Learner centered,Discussion based learning,Task based learning
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| Programs\Type | Required | Core Elective | Area Elective |
| MA-European Studies | |||
| MA-European Studies-Non Thesis | |||
| MA-Political Science | |||
| MA-Political Science-Non Thes | |||
| MA-Visual Arts&Vis. Com Des-NT | |||
| MA-Visual Arts&Visual Com Des | |||
| MS-Bio. Sci. & Bioeng. LFI | |||
| MS-Bio. Sci. & Bioeng. LFI-ENG | |||
| MS-Biological Sci&Bioeng. | * | ||
| MS-Computer Sci.&Eng. LFI | |||
| MS-Computer Sci.&Eng. LFI-ENG | |||
| MS-Computer Science and Eng. | * | ||
| MS-Cyber Security(with thesis) | * | ||
| MS-Data Science | |||
| MS-Elec. Eng&Comp Sc.LFI-ENG | |||
| MS-Electronics Eng&Comp Sc.LFI | |||
| MS-Electronics Eng&Computer Sc | * | ||
| MS-Electronics Eng. | * | ||
| MS-Electronics Eng. LFI | |||
| MS-Electronics Eng. LFI-ENG | |||
| MS-Energy Techno.&Man. | * | ||
| MS-Industrial Eng. LFI-ENG | |||
| MS-Industrial Engineering | * | ||
| MS-Industrial Engineering LFI | |||
| MS-Manufacturing Eng-Non Thes | * | ||
| MS-Manufacturing Engineering | * | ||
| MS-Materials Sci & Engineering | * | ||
| MS-Materials Sci. & Eng. LFI | |||
| MS-Materials Sci.&Eng. LFI-ENG | |||
| MS-Mathematics | * | ||
| MS-Mechatronics | * | ||
| MS-Mechatronics LFI | |||
| MS-Mechatronics LFI-ENG | |||
| MS-Physics | |||
| MS-Physics-Non Thesis | * | ||
| MS-Psychology | |||
| MS-Psychology-Non Thesis | |||
| PHD-Biological Sci&Bioeng. | * | ||
| PHD-Comp. Sci and Eng.after UG | * | ||
| PHD-Computer Science and Eng. | * | ||
| PHD-Cyber Security | * | ||
| PHD-Electronics Eng&ComputerSc | * | ||
| PHD-Electronics Eng. | * | ||
| PHD-Electronics Eng. after UG | * | ||
| PHD-Experimental Psychology | |||
| PHD-Industrial Engineering | * | ||
| PHD-Management | |||
| PHD-Manufacturing Eng after UG | * | ||
| PHD-Manufacturing Engineering | * | ||
| PHD-Materials Sci.&Engineering | * | ||
| PHD-Mathematics | |||
| PHD-Mechatronics | * | ||
| PHD-Mechatronics after UG | * | ||
| PHD-Physics | |||
| PHD-Physics after UG | |||
| PHD-Social Psychology | |||
| PHDBIO after UG | * | ||
| PHDCYSEC after UG | * | ||
| PHDEECS after UG | * | ||
| PHDEPSY after UG | |||
| PHDIE after UG | * | ||
| PHDMAN after UG | |||
| PHDMAN after UG-Finance | |||
| PHDMAN after UG-Man. and Org. | |||
| PHDMAN after UG-Op.&Sup. Cha. | |||
| PHDMAN-Finance Area | |||
| PHDMAN-Man. and Org. Area | |||
| PHDMAN-Op. & Supp. Chain Area | |||
| PHDMAT after UG | * | ||
| PHDMATH after UG | * | ||
| PHDSPSY after UG |
CONTENT
OBJECTIVE
Studying properties of Banach and Hilbert spaces
LEARNING OUTCOME
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.
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.
At the end of the course the learner should be able to compute or estimate operator norms for certain examples of operators.
Update Date:
ASSESSMENT METHODS and CRITERIA
| Percentage (%) | |
| Midterm | 20 |
| Exam | 20 |
| Homework | 60 |
RECOMENDED or REQUIRED READINGS
| Textbook |
Erwin Kreyszig, Introductory functional analysis with applications, (1979) Wiley Classics Library, ISBN: 0-471-50731-8 |
| Optional Readings |
John B. Conway, A course in functional analysis, 2nd ed. (1990) Springer, ISBN: 0-387-97245-5 |