MATH 414 Functional Analysis
General Presentation
- This is a (very) gentle introduction in Functional Analysis
- We do not use measure theory or/and Lebesgue integration at all
- Textbook: E. Kreyszig, Introductory
Functional Analysis, John Wiley & Sons, 1989
A few words about Functional Analysis
Functional
Analysis is a part of Analysis and hence it is concerning combined
structures (algebraic, topological, and order). The basic algebraic
structure is the vector space with no additional condition on dimension
(so most of the vector spaces are infinite dimensional) on which there
are considered some compatibile topologies. Thus, first are studied
normed vector spaces and their linear transformations, duality of these
spaces, then scalar product spaces and different kinds of convergence
(uniform, strong, weak). We present the fundamental theorems of
Functional Analysis: the Hahn-Banach Theorem, the Uniform Boundedness
Principle, the Open Mapping Theorem, and the Closed Graph Theorem.
In order to clarify the topological considerations,
we review carefully the metric spaces, Baire Category Theorem, and
compactness.
Grading
We use the following scale for calculating the
letter grades with respect to the overall calculated grade (1st Midterm
20%, 2nd Midterm 20%, Final 30%, Homework 20%, Quiz/Attendance 10):
Points
|
Letter-grade
|
85-100
|
A
|
80-84.9
|
A-
|
75-79.9
|
B+
|
70-74.9
|
B
|
65-69.9
|
B-
|
60-64.9
|
C+
|
55-59.9
|
C
|
50-54.9
|
C-
|
45-49.9
|
D+
|
40-44.9
|
D
|
0-39.9
|
F
|
Homework
It is extremely important to perform weekly the homework
(normally, five questions from the textbook). Additionally, we
recommend to all students (at least try) to solve all the other
questions in the textbook. There is no other way to understand
mathematics except doing
it.
Syllabus
Download.
Homework's Solutions
HW # 1
HW # 2
HW # 3
HW # 4
HW # 5
HW # 6
HW # 7
HW # 8
HW # 9
HW # 10
HW # 11