Teaching Assistant: Introduction to Functional Analysis (2024)

In the first semester of 2024 (February-June) I acted as the Teaching Assistant for professor Vinícius Morelli in the course “Introduction to Functional Analysis” (MAT0334/MAT5721) for both undergraduates and post-graduates.

Teaching Assistant responsabilities

In Brazil we use the term “monitor” for this position, and as the expectations for what a “teaching assistant” would do may vary from country to country I list bellow exactly what I did:

• I graded the problem sheets of the students (only the portion of the problem sheets that actually).
• I held two weekly 1-hour sessions to help the students learn the subject and solve problems.
• I did not grade tests.
• I did not give any lectures.

Topics explored in MAT0334

What and introductory course in Functional Analysis tackles might also change depending on the university and lecturer, so I list bellow some of the main topics discussed throughout the semester (these are only a small sample of topics taken from the problem sheets and don’t represent the depth to which these topics were explored):

• Normed and Banach spaces.
• Equivalent norms and bounded linear operators.
• $\ell_p$ spaces.
• The Hahn-Banach theorem, adjoint operators and reflexivity.
• The Uniform Boundedness Principle, the Open Mapping Theorem and the Closed Graph Theorem.
• Hilbert spaces.

Bibliography

• G. Botelho, D. Pellegrino, E. Teixeira, Fundamentos de Análise Funcional (2015).
• C. Hönig, Análise Funcional e Aplicações (1990).
• E. Kreyszig, Introductory Functional Analysis with Applications (1989).
• R. Megginson, An Introduction to Banach Space Theory (1998).
• W. Rudin, Functional Analysis (1991).