Functional analysis

Contact Details

Manas Rachh
Arthur K Watson - 109
Email: firstname.lastname (at) yale (dot) edu
Office hours: Mon 10-11am, Thursday 4-5 pm, or by appointment

Lecture notes and reference material

  1. Fredholm Theory
  2. Hahn-Banach theorem (Section 2.3)
  3. Krein-Milman and extreme subsets
  4. Spectral theorems (Section 4.3,4.4, Chapter 5)

Problem sets (best 6 out of 7)

  1. Problem set 1, Tex file, Solution sketch (Upload date: Jan 22, Due date: Feb 5)
  2. Problem set 2, Tex file, Solution sketch (Upload date: Feb 5, Due date: Feb 19)
  3. Problem set 3, Tex file, Solution sketch (Upload date: Feb 19, Due date: Mar 5)
  4. Problem set 4, Tex File, Solution Sketch (Upload date: Mar 5, Due date: Mar 26)
  5. Problem set 5, Tex File, Solution Sketch (Upload date: Mar 26, Due date: Apr 9)
  6. Problem set 6, Tex File, Solution Sketch (Upload date: Apr 9, Due date: Apr 16)
  7. Problem set 7, Tex File, Solution Sketch (Upload date: Apr 16, Due date: Apr 25)

Practice problem sets

  1. Practice problem set 1, Tex file (Upload date: Jan 29)
  2. Practice problem set 2, Tex file (Upload date: Feb 13)
  3. Practice problem set 3, Tex file (Upload date: Feb 26)
  4. Practice problem set 4, Tex file (Upload date: Apr 2)

Midterm - in class (Mar 7)

Final (May 6, 2pm - 4pm, tentative)


The topics covered in this class will include:
  1. Hilbert spaces/Banach spaces
  2. Continuous linear functionals
  3. Weak and weak* Topologies
  4. Principles of functional analysis
  5. Some geometric aspects of function spaces
  6. Bounded linear operators and the spectral theorem
  7. Fredholm Theory and application to integral equations
I will roughly be following the text: A course in functional analysis, second edition by John B. Conway

Grading policy

6 Assignments - 30 pts
Midterm - 30 pts
Final - 40 pts

Homework policy

Late homework will not be accepted. It is okay to discuss the homework problems with other students as long as you list down your collaborators. I would highly recommend to try the problems yourself before discussing them with your peers. You must however write your own solutions!


Please feel free to give any feedback regarding the class or if you want any particular thing to be covered in class. You can provide anonymous feedback in the box below. I will be checking it on a regular basis and adapting the lectures based on that.