WS 20/21: Functional Analysis (tutorials)

This course has come to the end. See student evaluation reports (in Polish).

Lecutre: prof. Piotr Rybka (Thursdays, 10:15 - 11:45)
Tutorial: Kuba Skrzeczkowski (Thursdays, 12:15 - 13:45)
USOS: link

This is a basic course for 3rd year students introducting fundamental concepts of normed spaces, Banach spaces and Hilbert spaces, providing general framework to study infinite dimensional spaces as well as operators acting on them that one meets in modern theory of Probability, PDEs, Numerical Analysis or Optimization.

Grading: at most 30 points collected from any of these:

Admission to the final exam after collecting either

Textbook: There is an excellent textbook by Haim Brezis that contains the relevant theory, intuitive explanations and problems to solve (both easy and hard). Some people recommend the book by Rudin but I find it too extensive, too difficult to understand and too general for the first course in Functional Analysis (especially if you are more applications-oriented).

Last year tutorial : Here is a link to the last year tutorial. There are some materials (problems, solutions) that may be helpful. Problems discussed this year will be similar but not exactly the same (so far, I skipped Phillips Lemma and invertibility conditions).

COVID related info : We gonna meet on Zoom each Thursday. You are expected to turn on your camera and audio (in case you don't have appropriate equipment contact me before 15/10). I will upload content of the iPad blackboard and videos from the class below. Each week I will offer online office hours on Zoom. To compensate for the social distancing, you are expected to submit homeworks in groups of 2. You should discuss content of the lecture and the tutorial with your friend.

Problem Sets :

My notes (maybe helpful?) :

Homeworks are listed here

Solutions to homeworks :

Zoom blackboards and YouTube links: :

Group office hours: :

Class results (homework, activities) are updated here.

Special Problems are here. Some solutions will be posted below.

Others :

Class journal :