Analysis II (MATH 502)

2021 Spring
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10.00
Albert Erkip albert@sabanciuniv.edu,
Click here to view.
English
Doctoral, Master
--
Formal lecture
Learner centered,Discussion based learning,Task based learning
Click here to view.

CONTENT

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.

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.

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
R. E. Megginson Introduction to Banach Space Theory
A. Taylor and D. Lay Introduction to Functional Analysis
P. R. Halmos Introduction to Hilbert Space
P. R. Halmos Hilbert Space Problem Book
W. Rudin Real and Complex Analysis
W. Rudin Functional Analysis
L. W. Baggett Functional Analysis: A Primer
S. K. Berberian Lectures in Functional Analysis
C. W. Groetsch Elements of Applicable Functional Analysis
Dunford and Schwartz Linear Operators (3 Volumes)
Riesz and Sz. Nagy Functional Analysis
K. Yosida Functional Analysis