FUNCTIONAL ANALYSIS

Informations on the recommended grades

• If you accept your recommended grade, please accept it in the Neptun system. In this case you've finished thhe course.
• If you do not accept your recommended grade, you should take an exam.
• Please note, that
  • if you accept your recommended grade, you can not correct your grade later.
  • If you decline to accept your recommended grade, you must take an exam. Your recommended grade is lost.

Exams.

• The themes of the course are listed here.
• If your recommended, but not accepted, grade is at least 3, then you will have an oral exam.
• If you have an end-term signiture only or a recommended, but not accepted, grade 2, then you will have to write first a Test as part of the exam.
• The test will be in Moodle. There will be 4-5 True-False questions about basic concepts, and 3-4 excercises. The test will be promptly evaluated.
• On the basis of the testtwo possible recommended grade will be offer for the exam:
  • The requirement for satisfactory (3) is 80%.
  • The requirement for passing (2) is 50%.
  • Under 50% the candidate is failed.
• If the student accepts the recommended grade, then the exam is over except for brief informal discussion in MS Teams.
• If the student does not accept the recommended grade based on Test, then he/she will have to sit for an oral exam.

• Oral exams
• Each student will draw 3-5 exam themes depending on complexity.
• He/she is expected to know the themes in bold face in some details. and the basic ideas of the proofs.
• There will a short time for preparation, then we will proceed interactively.

Current information. Febr 26.

• From March all HW solution must be uploaded in the Moodle system.

Lectures

• February 11 Lecture 1.
  Introduction. Abstract spaces of Functional Analysis. Convergece of sequences and continuity of functions in metric spaces.
  Read the "Preface" and "Introduction To the Student" in Saxe book.
  
• February 18 Lecture 2. (Updated.)
• February 25 Lecture 3. (Updated on p.13.)
• March 4 Lecture 4.
• March 11 Lecture 5.
• March 18 Lecture 6.
• March 25 Lecture 7.
• April 15 Lecture 8.
• April 22 Lecture 9.
• April 29 Lecture 10. Please read and understand the last slide yourself, it is HW.
• May 6 Lecture 11. Please read and understand the last slides yourself, it is HW.
• May 13 Lecture 12.

Requirements and Grading

• Every week there will a 20 minutes written test to evaluate the previous week's learning activity.
• The tests will be at the beginning of the Lecture's time slot, Thursday, starting 14:15. They are worth 10 points each.
• Every week there will be 1-2 homework assignments to be solved in writing, and a copy of the solution to be sent by email. A total of at least 8 correct solutions must be collected during the semester (possibly from fractional points). The homework assignments will posted by Friday evening.
• Send the solutions of the HW-s to functional.analysis.hw@gmail.com . The deadline is NEXT FRIDAY 8 am. (You have one week to solve the HW-s.)
• NEW From March HW solution should be uploaded to Moodle.
• Additional homework solutions in excess of the minimal requirements will be credited by 50% of its deserved score.
• NEW Every week there might be some extra homework, denoted by *. They are not-trivial. The solution worth 1 point each, that adds to the "total" one-on-one. The deadline is the second NEXT FRIDAY 8 am.
• An option: brief bibliographies of "key players" -- a possible project in 5-10 minute. It worth 5 points .
• Two of the written tests can be corrected during the first week of the exam period.
• The total score is the sum of the points of the written tests (maximum 11x10=110), plus the score collected from the excess home assignments.
• Requirement for end-term signature is 40 points.
• There will be an oral exam (or written exam) at the end of the term.
• A recommended mark is offered based on the work during the semester as follows:
  • 60-84: recommended 2
  • 85-99: recommended 3
  • 100-110: recommended 4
  • 111- : 5

Themes

• Metric spaces; Normed spaces; Inner product spaces.
• The topology of metric spaces.
• Lebesgue measure and Lebesgue integral.
• Fourier analysis in L^2 .
• Abstract linear operators.
• Generalized functions or distributions.
• An application of Hilbert space methods in Quantum Mechanics.

References